Metrics for 2tan (problem 3.3.2)

analyze114.0ms (0.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50.6%	49.4%	0%	0%	0%	0
0%	0%	50.6%	49.4%	0%	0%	0%	1
0%	0%	50.6%	49.4%	0%	0%	0%	2
0%	0%	25.3%	74.7%	0%	0%	0%	3
0%	0%	25.3%	74.7%	0%	0%	0%	4
0%	0%	19%	81%	0%	0%	0%	5
0%	0%	15.8%	84.2%	0%	0%	0%	6
0%	0%	11.1%	88.9%	0%	0%	0%	7
0%	0%	8.7%	91.3%	0%	0%	0%	8
0%	0%	5.9%	94.1%	0%	0%	0%	9
0%	0%	4.5%	95.5%	0%	0%	0%	10
0%	0%	3.1%	96.9%	0%	0%	0%	11
0%	0%	2.7%	97.3%	0%	0%	0%	12

Compiler

Compiled 28 to 18 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

...c/correct-round.rkt:119:19: 38.0ms (47.3% of total)

ival-<: 20.0ms (24.9% of total)

ival-tan: 8.0ms (10% of total)

ival-mult: 3.0ms (3.7% of total)

ival-add: 2.0ms (2.5% of total)

ival-fabs: 2.0ms (2.5% of total)

ival-sub: 2.0ms (2.5% of total)

ival-and: 2.0ms (2.5% of total)

ival-<=: 2.0ms (2.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample7.3s (39.5%)

Results

3.9s	25981×	0	precondition
1.2s	4460×	1	valid
460.0ms	3796×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 4.0s

ival-tan: 916.0ms (22.6% of total)

...c/correct-round.rkt:119:19: 878.0ms (21.7% of total)

ival-sub: 357.0ms (8.8% of total)

ival-<: 335.0ms (8.3% of total)

ival-mult: 319.0ms (7.9% of total)

ival-<=: 299.0ms (7.4% of total)

ival-fabs: 295.0ms (7.3% of total)

ival-add: 288.0ms (7.1% of total)

ival-and: 184.0ms (4.5% of total)

backward-pass: 128.0ms (3.2% of total)

const: 50.0ms (1.2% of total)

Bogosity

preprocess68.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

376×	`fnmadd-define`
344×	`fnmsub-define`
344×	`fmsub-define`
320×	`sum3-define`
308×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	43	42
2	94	42
3	198	42
4	507	42
5	917	42
6	1285	42
7	1548	42
8	1684	42
9	1711	42
0	6	7
1	9	7
2	14	7
3	21	7
4	31	7
5	63	7
6	122	7
7	210	7
8	295	7
9	401	7
10	479	7
11	485	7
0	485	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (tan (+ x eps)) (tan x))

Outputs
(- (tan (+ x eps)) (tan x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Call 2

Inputs
(- (tan (+ x eps)) (tan x))
(- (tan (+ (neg x) eps)) (tan (neg x)))
(- (tan (+ x (neg eps))) (tan x))
(neg (- (tan (+ (neg x) eps)) (tan (neg x))))
(neg (- (tan (+ x (neg eps))) (tan x)))
(- (tan (+ eps x)) (tan eps))

Outputs
(- (tan (+ x eps)) (tan x))
(- (tan (+ (neg x) eps)) (tan (neg x)))
(+ (tan x) (tan (- eps x)))
(- (tan (+ x (neg eps))) (tan x))
(- (tan (- x eps)) (tan x))
(neg (- (tan (+ (neg x) eps)) (tan (neg x))))
(- (tan (- x eps)) (tan x))
(neg (- (tan (+ x (neg eps))) (tan x)))
(+ (tan x) (tan (- eps x)))
(- (tan (+ eps x)) (tan eps))
(- (tan (+ x eps)) (tan eps))

explain138.0ms (0.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
220	2	(-1.8679596455730118e-165 5.741547154853979e-168)	3	(-9.852733431089526e-252 1.2698469975690234e-253)	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`
3	0	-	0	-	`(tan.f64 (+.f64 x eps))`
0	0	-	0	-	`x`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(tan.f64 x)`
0	0	-	0	-	`eps`

Results

85.0ms	286×	1	valid
22.0ms	226×	0	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-tan: 15.0ms (48.1% of total)

backward-pass: 7.0ms (22.4% of total)

ival-add: 5.0ms (16% of total)

ival-sub: 4.0ms (12.8% of total)

const: 1.0ms (3.2% of total)

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(tan.f64 x)
✓	cost-diff	(+.f64 x eps)
✓	cost-diff	(tan.f64 (+.f64 x eps))
✓	cost-diff	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Rules

124×	`fnmadd-define`
122×	`sum3-define`
80×	`fma-lowering-fma.f32`
80×	`fnmsub-define`
80×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(+ x eps)
x
eps
(tan x)

Outputs
(- (tan (+ x eps)) (tan x))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(tan (+ x eps))
(tan.f64 (+.f64 x eps))
(+ x eps)
(+.f64 x eps)
x
eps
(tan x)
(tan.f64 x)

localize62.0ms (0.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(tan.f64 x)
✓	accuracy	99.8%	(tan.f64 (+.f64 x eps))
✓	accuracy	61.9%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

29.0ms	143×	1	valid
25.0ms	113×	0	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-tan: 6.0ms (41% of total)

ival-add: 3.0ms (20.5% of total)

backward-pass: 3.0ms (20.5% of total)

ival-sub: 2.0ms (13.7% of total)

const: 1.0ms (6.8% of total)

series11.0ms (0.1%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (- (tan (+ x eps)) (tan x))>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (tan x)>

Outputs
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))>
#<alt (/ (sin x) (cos x))>
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (+ eps x)) (cos (+ eps x)))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	eps	@	0	(- (tan (+ x eps)) (tan x))
2.0ms	eps	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	inf	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	0	(- (tan (+ x eps)) (tan x))
1.0ms	x	@	-inf	(- (tan (+ x eps)) (tan x))

rewrite371.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

3856×	`-lowering-.f32`
3856×	`-lowering-.f64`
3276×	`/-lowering-/.f32`
3276×	`/-lowering-/.f64`
1940×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	46	16
2	423	16
3	6591	16
0	8698	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 239

Calls

Call 1

Inputs
(- (tan (+ x eps)) (tan x))
(tan (+ x eps))
(+ x eps)
(tan x)

Outputs
(+.f64 (tan.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x) (tan.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (tan.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
(+.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 #s(literal 0 binary64) (-.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
(-.f64 (/.f64 (.f64 (cos.f64 x) (sin.f64 (+.f64 x eps))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))) (/.f64 (.f64 (sin.f64 x) (cos.f64 (+.f64 x eps))) (.f64 (cos.f64 x) (cos.f64 (+.f64 x eps)))))
(-.f64 (/.f64 (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))))
(-.f64 (+.f64 (tan.f64 (+.f64 x eps)) #s(literal 0 binary64)) (tan.f64 x))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (tan.f64 (+.f64 x eps)) #s(literal 2 binary64)) (.f64 (tan.f64 x) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))))
(fma.f64 (tan.f64 (+.f64 x eps)) (/.f64 (tan.f64 (+.f64 x eps)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (neg.f64 (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))))
(fma.f64 (sin.f64 (+.f64 x eps)) (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 #s(literal 1 binary64) (tan.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
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(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x x) (.f64 eps eps)))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (.f64 x x) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x)))))
(.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))))
(.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (/.f64 (+.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x)))))
(.f64 (-.f64 (.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (*.f64 eps (-.f64 eps x))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x)))) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (.f64 x x) (*.f64 eps eps)))
(.f64 (-.f64 (.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (.f64 (-.f64 eps x) (.f64 eps (-.f64 eps x))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (.f64 (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 x x) (*.f64 eps (+.f64 x eps))))
(tan.f64 x)
(neg.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(/.f64 (sin.f64 x) (cos.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (*.f64 (sin.f64 x) #s(literal 1 binary64)) (cos.f64 x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (neg.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) #s(literal -1 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 #s(literal 1 binary64) (tan.f64 x))
(*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

simplify315.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

3412×	`-lowering-.f32`
3412×	`-lowering-.f64`
2990×	`fma-lowering-fma.f32`
2990×	`fma-lowering-fma.f64`
2652×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	1381
1	494	1186
2	1896	1117
3	7762	1117
0	8619	1117

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(/ (sin eps) (cos eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))

Outputs
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+ (* x (- (* x (- (* -1 (* x (+ 1/2 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x (+.f64 (.f64 x (-.f64 (.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (.f64 x (+.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (-.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(* eps (- (+ 1 (* eps (- (* eps (- (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* 1/6 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (/ (* (sin x) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)))))) (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (-.f64 (-.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (.f64 eps (+.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (+ eps x)) (cos (+ eps x))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) (/ (sin x) (cos x)))
(-.f64 (/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (*.f64 (sin.f64 eps) x) (cos.f64 eps))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))))))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (.f64 x (-.f64 (.f64 (sin.f64 eps) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (cos.f64 eps))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (-.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))))))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (-.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
(/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps))))
(/.f64 (sin.f64 (+.f64 eps x)) (cos.f64 (+.f64 eps x)))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64)))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64)))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))

eval38.0ms (0.2%)

Compiler: Compiled 8811 to 993 computations (88.7% saved)

prune46.0ms (0.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	309	14	323
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	309	15	324

Accuracy

100.0%

Counts

324 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.9%	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
	61.6%	(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
	98.7%	(/.f64 (sin.f64 eps) (cos.f64 eps))
▶	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	17.3%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))) (tan.f64 x))
▶	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
▶	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
✓	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) x)
	99.5%	(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
	99.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (-.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
▶	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (-.f64 (-.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (.f64 eps (+.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))

Compiler

Compiled 977 to 422 computations (56.8% saved)

simplify301.0ms (1.6%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(tan.f64 x)
✓	cost-diff	0	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	cost-diff	0	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓	cost-diff	0	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	cost-diff	0	(/.f64 (sin.f64 x) (cos.f64 x))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(tan.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64)))))))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(tan.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(tan.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) x)
✓	cost-diff	19520	(-.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
✓	cost-diff	19776	(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
✓	cost-diff	25984	(+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
✓	cost-diff	26112	(+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))

Rules

3456×	`-lowering-.f32`
3456×	`-lowering-.f64`
2614×	`+-lowering-+.f64`
2614×	`+-lowering-+.f32`
2382×	`--lowering--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1844
1	210	1356
2	854	1142
3	4229	1003
0	8543	1003

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
1
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))))
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (sin x) (cos x))
(sin x)
x
(cos x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
2
(pow (cos x) 2)
(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))
(- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))
(+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6)
(* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))
-1/6
(+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))
-1/2
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))
(/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))
(* -1/2 (pow (sin x) 2))
(/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))
(* 1/6 (pow (sin x) 2))
1/6
(* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))
(+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))
(/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x))
(* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))))
(+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)))
(+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)
-1/3
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
x
eps
(- (tan (+ x eps)) (* x (+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))
(tan (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))
(+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))
1
(* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))
(* x x)
(+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))
1/3
(* (* x x) (+ 2/15 (* x (* x 17/315))))
(+ 2/15 (* x (* x 17/315)))
2/15
(* x (* x 17/315))
(* x 17/315)
17/315
(- (tan (+ x eps)) (/ (sin x) (cos x)))
(tan (+ x eps))
(+ x eps)
x
eps
(/ (sin x) (cos x))
(sin x)
(cos x)
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (tan eps))
(tan x)
x
(tan eps)
eps
(- 1 (* (tan x) (tan eps)))
1
(* (tan x) (tan eps))

Outputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 (.f64 (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))) (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal -1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))) (.f64 #s(literal -1/3 binary64) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))) (.f64 eps eps)) (.f64 (+.f64 (/.f64 (.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3))))))) (/ (pow (sin x) 2) (pow (cos x) 2))))
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#s(literal 1/3 binary64)
(* (* x x) (+ 2/15 (* x (* x 17/315))))
(.f64 x (.f64 x (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))))
(+ 2/15 (* x (* x 17/315)))
(+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))
2/15
#s(literal 2/15 binary64)
(* x (* x 17/315))
(.f64 (.f64 x x) #s(literal 17/315 binary64))
(* x 17/315)
(*.f64 x #s(literal 17/315 binary64))
17/315
#s(literal 17/315 binary64)
(- (tan (+ x eps)) (/ (sin x) (cos x)))
(-.f64 (tan.f64 (+.f64 eps x)) (/.f64 (sin.f64 x) (cos.f64 x)))
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(sin x)
(sin.f64 x)
(cos x)
(cos.f64 x)
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(+ (tan x) (tan eps))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan x)
(tan.f64 x)
x
(tan eps)
(tan.f64 eps)
eps
(- 1 (* (tan x) (tan eps)))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
1
#s(literal 1 binary64)
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))

localize675.0ms (3.6%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(tan.f64 eps)
✓	accuracy	100.0%	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓	accuracy	100.0%	(+.f64 (tan.f64 x) (tan.f64 eps))
✓	accuracy	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(/.f64 (sin.f64 x) (cos.f64 x))
✓	accuracy	99.8%	(tan.f64 (+.f64 x eps))
✓	accuracy	61.9%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (.f64 x #s(literal 17/315 binary64)))))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (.f64 x #s(literal 17/315 binary64)))))))
✓	accuracy	99.5%	(*.f64 x #s(literal 17/315 binary64))
✓	accuracy	62.4%	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	99.8%	(tan.f64 (+.f64 x eps))
✓	accuracy	62.6%	(-.f64 (tan.f64 (+.f64 x eps)) x)
✓	accuracy	99.5%	(.f64 eps (-.f64 (-.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (.f64 eps (+.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (.f64 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64))))))
✓	accuracy	99.4%	(+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	accuracy	98.5%	(-.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (*.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
✓	accuracy	98.4%	(+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))

Results

331.0ms	146×	1	valid
153.0ms	110×	0	valid

Compiler

Compiled 1907 to 66 computations (96.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 212.0ms

ival-mult: 47.0ms (22.2% of total)

ival-add: 38.0ms (17.9% of total)

...c/correct-round.rkt:119:19: 34.0ms (16% of total)

backward-pass: 33.0ms (15.6% of total)

ival-div: 17.0ms (8% of total)

ival-sub: 15.0ms (7.1% of total)

ival-tan: 9.0ms (4.2% of total)

ival-pow: 8.0ms (3.8% of total)

ival-sin: 5.0ms (2.4% of total)

ival-cos: 4.0ms (1.9% of total)

const: 1.0ms (0.5% of total)

series74.0ms (0.4%)

Counts

21 → 360

Calls

Call 1

Inputs
#<alt (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))>
#<alt (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))>
#<alt (- (tan (+ x eps)) x)>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (- (tan (+ x eps)) (* x (+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))>
#<alt (* x (+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))>
#<alt (- (tan (+ x eps)) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))>
#<alt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))>
#<alt (+ (tan x) (tan eps))>
#<alt (tan x)>
#<alt (* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))>
#<alt (* x 17/315)>
#<alt (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))>
#<alt (* (* x x) (+ 2/15 (* x (* x 17/315))))>
#<alt (cos x)>
#<alt (tan eps)>

Outputs
#<alt (* -1/3 (pow x 2))>
#<alt (* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))>
#<alt (* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt 1/6>
#<alt (+ 1/6 (* -5/6 (pow x 2)))>
#<alt (+ 1/6 (* (pow x 2) (- (* -14/9 (pow x 2)) 5/6)))>
#<alt (+ 1/6 (* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt (- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))>
#<alt -1/3>
#<alt (- (* -4/3 (pow x 2)) 1/3)>
#<alt (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt 1/3>
#<alt (+ 1/3 (* 4/3 (pow x 2)))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))>
#<alt (+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (* -1 x)>
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))>
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))>
#<alt (* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))>
#<alt (- (/ (sin x) (cos x)) x)>
#<alt (- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)>
#<alt (- (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)>
#<alt (- (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (+ eps x)) (cos (+ eps x))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)>
#<alt (- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))>
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#<alt (+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (+ x (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* 1/3 (pow x 2)))) (/ (sin eps) (cos eps)))>
#<alt (+ (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))) (/ (sin eps) (cos eps)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (+ eps (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2)))))) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 17/315 x)>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))>
#<alt (* 17/315 (pow x 6))>
#<alt (* (pow x 6) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* 17/315 (pow x 6))>
#<alt (* (pow x 6) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))>
#<alt (* 2/15 (pow x 2))>
#<alt (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))>
#<alt (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))>
#<alt (* 17/315 (pow x 4))>
#<alt (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* 17/315 (pow x 4))>
#<alt (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt eps>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))>
#<alt (* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>

Calls

90 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
5.0ms	eps	@	0	(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
4.0ms	eps	@	inf	(- (tan (+ x eps)) (* x (+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))
4.0ms	x	@	-inf	(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
4.0ms	x	@	-inf	(- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))

rewrite386.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3642×	`-lowering-.f32`
3642×	`-lowering-.f64`
2550×	`/-lowering-/.f32`
2550×	`/-lowering-/.f64`
2044×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	387
1	473	205
2	5987	203
0	8765	203

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 464

Calls

Call 1

Inputs
(+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))
(+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))
(- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)))))
(- (tan (+ x eps)) x)
(tan (+ x eps))
(+ x eps)
(- (tan (+ x eps)) (* x (+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315)))))))))
(* x (+ 1 (* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))))
(- (tan (+ x eps)) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (tan eps))
(tan x)
(* eps (- (- (+ (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))) -1/6) (+ -1/2 (+ (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2)) (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2))))) (* eps (+ (/ (* (sin x) (+ (+ -1/2 (/ (* -1/2 (pow (sin x) 2)) (pow (cos x) 2))) (+ (/ (* 1/6 (pow (sin x) 2)) (pow (cos x) 2)) (- 1/6 (* (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (cos x)) (* (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) -1/3)))))
(* x 17/315)
(* (* x x) (+ 1/3 (* (* x x) (+ 2/15 (* x (* x 17/315))))))
(* (* x x) (+ 2/15 (* x (* x 17/315))))
(cos x)
(tan eps)

Outputs
(+.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(+.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -2/3 binary64))) (/.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -2/3 binary64))))
(fma.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(fma.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (cos.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))) (+.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -2/3 binary64)) (.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -2/3 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/6 binary64)))) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(/.f64 (.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -2/3 binary64))) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -2/3 binary64)))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal -1/6 binary64)))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/6 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal -1/6 binary64)))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/6 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal -1/6 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) #s(literal 1/2 binary64)))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
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(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (.f64 (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))))))) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x x) #s(literal 17/315 binary64)))) #s(literal 1/3 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/9 binary64) (.f64 (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))))))) (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x x) #s(literal 17/315 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 1/27 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (.f64 (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))))))) (.f64 x x)) (+.f64 #s(literal 1/9 binary64) (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x x) #s(literal 17/315 binary64)))) #s(literal 1/3 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/9 binary64) (.f64 (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))))) (.f64 x x)) (-.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x x) #s(literal 17/315 binary64))))))
(.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))))))
(.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x x) #s(literal 17/315 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))))
(.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x x))
(.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x x) #s(literal 17/315 binary64)))))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))))) x)
(.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (*.f64 x x) #s(literal 17/315 binary64))))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))))) (*.f64 x x))
(+.f64 (.f64 (.f64 x x) #s(literal 2/15 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)))))
(+.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (.f64 (.f64 x x) #s(literal 2/15 binary64)))
(fma.f64 (.f64 x x) #s(literal 2/15 binary64) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 17/315 binary64)))))
(fma.f64 #s(literal 2/15 binary64) (.f64 x x) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 17/315 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 x x) #s(literal 2/15 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) #s(literal 2/15 binary64)) (.f64 (.f64 x x) #s(literal 2/15 binary64))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 (.f64 (.f64 x x) #s(literal 2/15 binary64)) (.f64 x (.f64 x (.f64 (*.f64 x x) #s(literal 17/315 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 2/15 binary64)) (.f64 (.f64 x x) #s(literal 2/15 binary64))) (.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)))) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64)))))) (-.f64 (.f64 (.f64 x x) #s(literal 2/15 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 17/315 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 8/3375 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/315 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/99225 binary64))))) (+.f64 #s(literal 4/225 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/315 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 17/315 binary64)) #s(literal 2/15 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 4/225 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/99225 binary64)))) (-.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 8/3375 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/315 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/99225 binary64)))) (.f64 x x)) (+.f64 #s(literal 4/225 binary64) (.f64 (.f64 (.f64 x x) #s(literal 17/315 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 17/315 binary64)) #s(literal 2/15 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 4/225 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 289/99225 binary64))) (.f64 x x)) (-.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))
(.f64 x (.f64 x (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))))
(.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))
(.f64 (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64)))) x)
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(cos.f64 x)
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)) (pow.f64 (cos.f64 x) #s(literal 1/2 binary64)))
(tan.f64 eps)
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 eps) (sin.f64 eps)))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/.f64 (neg.f64 (sin.f64 eps)) (neg.f64 (cos.f64 eps)))
(*.f64 (sin.f64 eps) (/.f64 #s(literal 1 binary64) (cos.f64 eps)))

simplify343.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

3814×	`-lowering-.f32`
3814×	`-lowering-.f64`
2588×	`+-lowering-+.f64`
2588×	`+-lowering-+.f32`
1572×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	493	8479
1	1607	7233
2	6067	6848
0	8022	6848

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

Inputs
(* -1/3 (pow x 2))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
1/6
(+ 1/6 (* -5/6 (pow x 2)))
(+ 1/6 (* (pow x 2) (- (* -14/9 (pow x 2)) 5/6)))
(+ 1/6 (* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
-1/3
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(/ (sin eps) (cos eps))
(+ (/ (sin eps) (cos eps)) (/ (* x (pow (sin eps) 2)) (pow (cos eps) 2)))
(+ (* x (- (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps)) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(* -1 x)
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))
(* x (- (/ (sin (+ eps x)) (* x (cos (+ eps x)))) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) (* x (cos (- eps (* -1 x)))))))))
(- (/ (sin x) (cos x)) x)
(- (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)
(- (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)
(- (+ (* eps (- (+ 1 (* eps (- (* -1 (* eps (+ 1/6 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (+ eps x)) (cos (+ eps x))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)
(- (/ (sin (- x (* -1 eps))) (cos (- x (* -1 eps)))) x)
(/ (sin eps) (cos eps))
(+ (* x (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))) (cos eps))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(+ (* x (- (+ 1 (* x (- (* -1 (* x (+ 1/6 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (pow (cos eps) 2))) (+ (* -1/2 (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* 1/6 (/ (pow (sin eps) 2) (pow (cos eps) 2)))))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (cos eps)))))) (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (/ (sin eps) (cos eps)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (+ eps x)) (cos (+ eps x)))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
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(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 17/315 x)
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))
(* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))
(* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))
(* 17/315 (pow x 6))
(* (pow x 6) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* 17/315 (pow x 6))
(* (pow x 6) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* (pow x 6) (+ 17/315 (+ (/ 1/3 (pow x 4)) (* 2/15 (/ 1 (pow x 2))))))
(* 2/15 (pow x 2))
(* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))
(* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))
(* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))
(* 17/315 (pow x 4))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* 17/315 (pow x 4))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 17/315 (* 2/15 (/ 1 (pow x 2)))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* 2/15 (pow eps 2))))))
(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))
(/ (sin eps) (cos eps))

Outputs
(* -1/3 (pow x 2))
(.f64 #s(literal -1/3 binary64) (.f64 x x))
(* (pow x 2) (- (* -2/9 (pow x 2)) 1/3))
(.f64 (.f64 (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) #s(literal -2/9 binary64))) x) x)
(* (pow x 2) (- (* (pow x 2) (- (* -17/135 (pow x 2)) 2/9)) 1/3))
(.f64 (.f64 x x) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -2/9 binary64) (.f64 (.f64 x x) #s(literal -17/135 binary64))))))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -62/945 (pow x 2)) 17/135)) 2/9)) 1/3))
(.f64 (.f64 x x) (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -2/9 binary64) (.f64 x (.f64 x (+.f64 #s(literal -17/135 binary64) (.f64 (.f64 x x) #s(literal -62/945 binary64)))))))))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
1/6
#s(literal 1/6 binary64)
(+ 1/6 (* -5/6 (pow x 2)))
(+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal -5/6 binary64)))
(+ 1/6 (* (pow x 2) (- (* -14/9 (pow x 2)) 5/6)))
(+.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x (+.f64 #s(literal -5/6 binary64) (.f64 (.f64 x x) #s(literal -14/9 binary64))))))
(+ 1/6 (* (pow x 2) (- (* (pow x 2) (- (* -89/54 (pow x 2)) 14/9)) 5/6)))
(+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -5/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -14/9 binary64) (.f64 (.f64 x x) #s(literal -89/54 binary64)))))))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(+.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(+.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
(+.f64 #s(literal 1/6 binary64) (-.f64 (/.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) #s(literal 1/6 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (+ 1/6 (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))
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(* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (+ (* -1/2 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (* 1/6 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))))))
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(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 #s(literal 2/3 binary64) (.f64 x (.f64 eps eps))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) (.f64 x (.f64 #s(literal 4/3 binary64) eps)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 2/3 binary64)) (.f64 x (+.f64 (.f64 #s(literal 4/3 binary64) eps) (.f64 #s(literal 17/9 binary64) (.f64 x (*.f64 eps eps))))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ (* -1/2 (/ (pow (sin x) 2) (pow (cos x) 2))) (* 1/6 (/ (pow (sin x) 2) (pow (cos x) 2)))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))))))
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(* eps (+ 1 (* (pow eps 2) (+ 1/3 (* (pow eps 2) (+ 2/15 (* 17/315 (pow eps 2))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 2/15 binary64) (.f64 #s(literal 17/315 binary64) (*.f64 eps eps)))))))))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))

eval307.0ms (1.7%)

Compiler: Compiled 108793 to 5448 computations (95% saved)

prune202.0ms (1.1%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1354	15	1369
Fresh	6	3	9
Picked	3	2	5
Done	0	1	1
Total	1363	21	1384

Accuracy

100.0%

Counts

1384 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	61.9%	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
▶	98.7%	(/.f64 (sin.f64 eps) (cos.f64 eps))
▶	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.2%	(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
	17.3%	(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))) (tan.f64 x))
	23.2%	(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
✓	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
	61.2%	(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
▶	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
✓	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓	61.1%	(-.f64 (tan.f64 (+.f64 x eps)) x)
	5.3%	(-.f64 (tan.f64 x) x)
	7.7%	(-.f64 (tan.f64 eps) x)
▶	7.7%	(-.f64 #s(literal 0 binary64) x)
	99.3%	(+.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (/.f64 (sin.f64 x) (cos.f64 x))))
	99.5%	(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
	100.0%	(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
	99.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
▶	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	5.5%	(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))

Compiler

Compiled 1003 to 519 computations (48.3% saved)

simplify283.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(tan.f64 x)
✓	cost-diff	0	(+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
✓	cost-diff	0	(/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))
✓	cost-diff	0	(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	cost-diff	0	(cos.f64 eps)
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(/.f64 (sin.f64 eps) (cos.f64 eps))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(tan.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) x)
✓	cost-diff	6592	(*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
✓	cost-diff	12800	(+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (tan.f64 x)) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
✓	cost-diff	12992	(+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))
✓	cost-diff	13120	(+.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))

Rules

3876×	`+-lowering-+.f64`
3876×	`+-lowering-+.f32`
2918×	`--lowering--.f32`
2918×	`--lowering--.f64`
2076×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	957
1	183	815
2	691	753
3	3069	679
0	8539	679

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2))))
1
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps)))
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(/ (sin x) (cos x))
(sin x)
x
(cos x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
2
(pow (cos x) 2)
(* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps)
(- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(pow (tan x) 2)
(tan x)
(+ 1 (pow (tan x) 2))
(- 1/3 (* (pow (tan x) 2) -1/3))
1/3
(* (pow (tan x) 2) -1/3)
-1/3
(* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x))
(+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3)))
(- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
1/6
(+ -1/2 (* (pow (tan x) 2) -1/3))
-1/2
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(- 0 x)
0
x
(- (tan (+ x eps)) (* x (+ 1 (* (* x x) 1/3))))
(tan (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* (* x x) 1/3)))
(+ 1 (* (* x x) 1/3))
1
(* (* x x) 1/3)
(* x x)
1/3
(/ (sin eps) (cos eps))
(sin eps)
eps
(cos eps)
(- (/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))
(tan x)
x
(* eps (+ 1 (* 1/3 (* eps eps))))
eps
(+ 1 (* 1/3 (* eps eps)))
1
(* 1/3 (* eps eps))
1/3
(* eps eps)
(- 1 (* (tan x) (tan eps)))
(* (tan x) (tan eps))
(tan eps)

Outputs
(* eps (+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))))
(.f64 eps (+.f64 (.f64 (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (tan.f64 x) (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 eps (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))))) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (.f64 eps #s(literal -1/3 binary64)) (tan.f64 x)))) (.f64 eps eps)) (.f64 (+.f64 (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))
eps
(+ 1 (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (tan.f64 x) (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 eps (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))))) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (.f64 eps #s(literal -1/3 binary64)) (tan.f64 x)))) (.f64 eps eps)) (.f64 (+.f64 (/.f64 (.f64 eps (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
1
#s(literal 1 binary64)
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) eps)) (.f64 eps (+.f64 (.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (tan.f64 x) (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 eps (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))))) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (*.f64 eps #s(literal -1/3 binary64)) (tan.f64 x))))) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))))
(* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps)))
(.f64 eps (+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (tan.f64 x) (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 eps (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))))) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (.f64 eps #s(literal -1/3 binary64)) (tan.f64 x)))))))
(+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))
(+.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64))) (.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (tan.f64 x) (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 eps (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))))) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (*.f64 eps #s(literal -1/3 binary64)) (tan.f64 x))))))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) #s(literal 3 binary64)))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(sin x)
(sin.f64 x)
x
(cos x)
(cos.f64 x)
(+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
2
#s(literal 2 binary64)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps)
(.f64 eps (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (tan.f64 x) (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 eps (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))))) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (*.f64 eps #s(literal -1/3 binary64)) (tan.f64 x)))))
(- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))))
(-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (tan.f64 x) (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 eps (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))))) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (-.f64 (.f64 eps #s(literal -1/3 binary64)) (tan.f64 x))))
(+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))
(-.f64 #s(literal 1/3 binary64) (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(pow (tan x) 2)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan x)
(tan.f64 x)
(+ 1 (pow (tan x) 2))
(+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))
(- 1/3 (* (pow (tan x) 2) -1/3))
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* (pow (tan x) 2) -1/3)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))
(.f64 eps (+.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 (tan.f64 x) (+.f64 (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64)))))
(+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3))
(+.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 (tan.f64 x) (+.f64 (+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)) #s(literal -1/3 binary64))))
(* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x))
(.f64 (tan.f64 x) (+.f64 (-.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64)))
(+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3)))
(+.f64 (-.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -4/3 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal -1/3 binary64))
(- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))))
(-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
1/6
#s(literal 1/6 binary64)
(+ -1/2 (* (pow (tan x) 2) -1/3))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(+ (tan x) (pow (tan x) 3))
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow (tan x) 3)
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
x
(- (tan (+ x eps)) (* x (+ 1 (* (* x x) 1/3))))
(+.f64 (tan.f64 (+.f64 eps x)) (.f64 x (-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))))
(tan (+ x eps))
(tan.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(* x (+ 1 (* (* x x) 1/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x))))
(+ 1 (* (* x x) 1/3))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
1
#s(literal 1 binary64)
(* (* x x) 1/3)
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(* x x)
(*.f64 x x)
1/3
#s(literal 1/3 binary64)
(/ (sin eps) (cos eps))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(sin eps)
(sin.f64 eps)
eps
(cos eps)
(cos.f64 eps)
(- (/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps)))) (tan x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps))))
(/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))
(+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))
(+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(tan x)
(tan.f64 x)
x
(* eps (+ 1 (* 1/3 (* eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
eps
(+ 1 (* 1/3 (* eps eps)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
1
#s(literal 1 binary64)
(* 1/3 (* eps eps))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(- 1 (* (tan x) (tan eps)))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))
(tan eps)
(tan.f64 eps)

localize588.0ms (3.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
✓	accuracy	100.0%	(+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
✓	accuracy	99.7%	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
✓	accuracy	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	100.0%	(/.f64 (sin.f64 eps) (cos.f64 eps))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64))))
✓	accuracy	99.8%	(tan.f64 (+.f64 x eps))
✓	accuracy	99.6%	(.f64 (.f64 x x) #s(literal 1/3 binary64))
✓	accuracy	62.5%	(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) x)
✓	accuracy	99.5%	(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
✓	accuracy	99.5%	(.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (tan.f64 x))
✓	accuracy	99.5%	(.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (tan.f64 x)) (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps)
✓	accuracy	98.5%	(+.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))

Results

353.0ms	145×	1	valid
106.0ms	111×	0	valid

Compiler

Compiled 998 to 63 computations (93.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 230.0ms

ival-add: 41.0ms (17.9% of total)

ival-mult: 41.0ms (17.9% of total)

ival-pow: 28.0ms (12.2% of total)

backward-pass: 27.0ms (11.8% of total)

ival-tan: 25.0ms (10.9% of total)

ival-div: 19.0ms (8.3% of total)

...c/correct-round.rkt:119:19: 17.0ms (7.4% of total)

ival-sub: 13.0ms (5.7% of total)

ival-sin: 9.0ms (3.9% of total)

ival-cos: 7.0ms (3% of total)

const: 2.0ms (0.9% of total)

series49.0ms (0.3%)

Counts

22 → 360

Calls

Call 1

Inputs
#<alt (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3)))>
#<alt (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))>
#<alt (+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- 0 x)>
#<alt (- (tan (+ x eps)) (* x (+ 1 (* (* x x) 1/3))))>
#<alt (tan (+ x eps))>
#<alt (+ x eps)>
#<alt (* x (+ 1 (* (* x x) 1/3)))>
#<alt (/ (sin eps) (cos eps))>
#<alt (sin eps)>
#<alt (cos eps)>
#<alt (- (/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps)))) (tan x))>
#<alt (/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps))))>
#<alt (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))>
#<alt (tan x)>
#<alt (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps)>
#<alt (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x))>
#<alt (* (+ (tan x) (pow (tan x) 3)) -1/3)>
#<alt (* (* x x) 1/3)>
#<alt (* 1/3 (* eps eps))>
#<alt (* eps (+ 1 (* 1/3 (* eps eps))))>

Outputs
#<alt -1/3>
#<alt (- (* -4/3 (pow x 2)) 1/3)>
#<alt (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))>
#<alt 1/3>
#<alt (+ 1/3 (* 4/3 (pow x 2)))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))>
#<alt (+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))>
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#<alt eps>
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#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt (/ (sin eps) (cos eps))>
#<alt eps>
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#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt 1>
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#<alt (cos eps)>
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#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (* eps (* x (* (sin eps) (+ 1 (* 1/3 (pow eps 2)))))) (cos eps)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (* eps (* (pow (sin eps) 2) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 2)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* eps (* (pow (sin eps) 3) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 3))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1/3 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (* eps (* (pow (sin eps) 2) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 2)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))>
#<alt (* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))>
#<alt (* (pow eps 3) (- (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))) (/ (sin x) (* (pow eps 3) (cos x)))))>
#<alt (* (pow eps 3) (- (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))) (/ (sin x) (* (pow eps 3) (cos x)))))>
#<alt (* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))>
#<alt (* (pow eps 3) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (- (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x))) (pow eps 3))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (- (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x))) (pow eps 3))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps)))))) (cos eps))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))) (pow (cos eps) 2))) (* -1/3 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))) (cos eps)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))>
#<alt (/ (sin x) (cos x))>
#<alt (+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))>
#<alt (* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))>
#<alt (* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))>
#<alt (* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))>
#<alt (* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))>
#<alt (* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))>
#<alt (* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ x (* eps (+ 1 (* 1/3 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* 1/3 (pow x 2)))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (+ eps (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (/ (sin x) (cos x))>
#<alt (* 1/3 eps)>
#<alt (+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))>
#<alt (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))>
#<alt (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))>
#<alt (* -1/3 x)>
#<alt (* x (- (* -13/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))>
#<alt (* -1/3 x)>
#<alt (* x (- (* -4/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt eps>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>

Calls

90 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3)))
4.0ms	x	@	inf	(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))
3.0ms	x	@	-inf	(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))
2.0ms	x	@	inf	(+ x eps)
2.0ms	eps	@	0	(* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps)

rewrite344.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2886×	`-lowering-.f32`
2886×	`-lowering-.f64`
2138×	`fma-lowering-fma.f32`
2138×	`fma-lowering-fma.f64`
1936×	`fmsub-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	60	336
1	452	272
2	5395	267
0	8792	267

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 392

Calls

Call 1

Inputs
(+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3)))
(+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3)))
(+ (* eps (+ (* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps))) (/ (pow (sin x) 2) (pow (cos x) 2)))
(* (/ (sin x) (cos x)) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- 0 x)
(- (tan (+ x eps)) (* x (+ 1 (* (* x x) 1/3))))
(tan (+ x eps))
(+ x eps)
(* x (+ 1 (* (* x x) 1/3)))
(/ (sin eps) (cos eps))
(sin eps)
(cos eps)
(- (/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps)))) (tan x))
(/ (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps))))) (- 1 (* (tan x) (tan eps))))
(+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))
(tan x)
(* (- (+ (* (pow (tan x) 2) (+ 1 (pow (tan x) 2))) (- 1/3 (* (pow (tan x) 2) -1/3))) (* eps (+ (* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x)) (* (+ (tan x) (pow (tan x) 3)) -1/3)))) eps)
(* (+ (- 1/6 (* (pow (tan x) 2) (+ 1 (pow (tan x) 2)))) (+ -1/2 (* (pow (tan x) 2) -1/3))) (tan x))
(* (+ (tan x) (pow (tan x) 3)) -1/3)
(* (* x x) 1/3)
(* 1/3 (* eps eps))
(* eps (+ 1 (* 1/3 (* eps eps))))

Outputs
(+.f64 #s(literal 1/6 binary64) (neg.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))))
(+.f64 #s(literal 1/6 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))
(+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal -1/2 binary64)))
(+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(+.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal -1/2 binary64)) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))
(+.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal -1/2 binary64))
(+.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(-.f64 #s(literal 1/6 binary64) (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))) (/.f64 (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))))
(-.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 1/6 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (-.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))
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(/.f64 (.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (/.f64 #s(literal 1 binary64) (tan.f64 x))))
(/.f64 (.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64))) (sin.f64 x)) (.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (cos.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (sin.f64 x)) (cos.f64 x))
(/.f64 (.f64 (tan.f64 x) (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))
(/.f64 (.f64 (tan.f64 x) (-.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64)))) (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(/.f64 (.f64 (sin.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (cos.f64 x))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(/.f64 (.f64 (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (tan.f64 x)) (+.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))))))
(/.f64 (.f64 (-.f64 (pow.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64))) (tan.f64 x)) (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))))
(.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (tan.f64 x))
(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))))
(.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(+.f64 (.f64 #s(literal -1/3 binary64) (tan.f64 x)) (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(+.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 #s(literal -1/3 binary64) (tan.f64 x)))
(+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)))
(+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) #s(literal -1/3 binary64)) (.f64 (tan.f64 x) #s(literal -1/3 binary64)))
(/.f64 (*.f64 #s(literal -1/3 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64)))) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(/.f64 (*.f64 #s(literal -1/3 binary64) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64)))) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 9 binary64))) #s(literal -1/3 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 6 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(/.f64 (*.f64 (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 6 binary64))) #s(literal -1/3 binary64)) (-.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(.f64 (.f64 #s(literal 1/3 binary64) (*.f64 x x)) #s(literal 1 binary64))
(.f64 (.f64 x #s(literal 1/3 binary64)) x)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/3 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(.f64 eps (.f64 #s(literal 1/3 binary64) eps))
(.f64 (.f64 eps eps) #s(literal 1/3 binary64))
(.f64 (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 1/3 binary64) eps) eps)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 1/3 binary64))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) eps)) eps)
(+.f64 eps (.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps))))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps))) eps)
(fma.f64 #s(literal 1 binary64) eps (.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps))))
(fma.f64 eps #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps))))
(/.f64 (+.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps))) #s(literal 3 binary64))) (+.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps)))) (.f64 eps (.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)))))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 eps eps))))) (-.f64 eps (.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)))))
(/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 #s(literal 1/9 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (-.f64 (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64)))))
(/.f64 (.f64 eps (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/9 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (*.f64 eps eps))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 #s(literal 1/9 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))))) eps) (+.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (-.f64 (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/9 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))) eps) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) eps)

simplify338.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

5580×	`-lowering-.f32`
5580×	`-lowering-.f64`
3330×	`+-lowering-+.f64`
3330×	`+-lowering-+.f32`
1252×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	605	9772
1	2066	8394
0	8334	8394

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

Inputs
-1/3
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
1/3
(+ 1/3 (* 4/3 (pow x 2)))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (* eps (* (pow (sin eps) 2) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 2)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* eps (* (pow (sin eps) 3) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 3))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1/3 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (* eps (* (pow (sin eps) 2) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 2)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))
(* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* -1 (* eps (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1 (* eps (- (* eps (- (+ 1/3 (* -1 (* eps (+ (* -1 (/ (* (sin x) (- 1/3 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x))) (+ (* -1/3 (/ (sin x) (cos x))) (+ (* -1/3 (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (* (sin x) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))))) (+ (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ (* -1 (/ (pow (sin x) 4) (pow (cos x) 4))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))))) (+ (* -1 (/ (sin x) (cos x))) (* -1 (/ (pow (sin x) 3) (pow (cos x) 3))))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))
(* (pow eps 3) (- (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))) (/ (sin x) (* (pow eps 3) (cos x)))))
(* (pow eps 3) (- (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))) (/ (sin x) (* (pow eps 3) (cos x)))))
(* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(* (pow eps 3) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x))) (pow eps 3))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (- (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x))) (pow eps 3))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (+ 1 (/ (* x (* (sin eps) (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps)))))) (cos eps))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (+ 1 (* x (- (* x (- 1/3 (+ (* -1 (/ (* (pow (sin eps) 2) (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))) (pow (cos eps) 2))) (* -1/3 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps)))))) (* -1 (/ (* (sin eps) (- 1 (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))) (cos eps)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))
(/ (sin x) (cos x))
(+ (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (/ (* eps (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (cos x))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(+ (* eps (- (+ 1 (* eps (- (* eps (- 1/3 (+ (* -1 (/ (* (pow (sin x) 2) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))) (* -1 (/ (* (sin x) (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)))))) (* -1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (sin x) (cos x)))
(* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))
(* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))
(* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (+ (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))
(* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
(* (pow eps 3) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))))) (+ (/ 1 (* (pow eps 2) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (* 1/3 (/ 1 (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ x (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* 1/3 (pow x 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))
(* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 2/15 (* 17/315 (pow x 2))))))))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(/ (sin x) (cos x))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))))
(* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1/3 x)
(* x (- (* -13/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(* -1/3 x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow x 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
(* 1/3 (pow eps 2))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))

Outputs
-1/3
#s(literal -1/3 binary64)
(- (* -4/3 (pow x 2)) 1/3)
(+.f64 #s(literal -1/3 binary64) (.f64 #s(literal -4/3 binary64) (.f64 x x)))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -4/3 binary64) (.f64 x (.f64 x #s(literal -17/9 binary64))))))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -4/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -17/9 binary64) (.f64 x (.f64 x #s(literal -248/135 binary64)))))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))
(-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 4/3 (pow x 2)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x #s(literal 4/3 binary64))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* 17/9 (pow x 2)))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4/3 binary64) (.f64 x (.f64 x #s(literal 17/9 binary64))))))
(+ 1/3 (* (pow x 2) (+ 4/3 (* (pow x 2) (+ 17/9 (* 248/135 (pow x 2)))))))
(+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 4/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/9 binary64) (.f64 (.f64 x x) #s(literal 248/135 binary64))))))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(+.f64 (.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (/ (* eps (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))) (cos x)) (/ (pow (sin x) 2) (pow (cos x) 2)))
(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 eps (/.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (cos.f64 x))))
(+ (* eps (+ (* eps (- (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))) (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x)))) (/ (pow (sin x) 2) (pow (cos x) 2)))
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(* 1/3 (/ (pow eps 3) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x))))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))))) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (pow (cos x) 2))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(* x (- (* -13/9 (pow x 2)) 1/3))
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(* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))
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(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(.f64 (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(.f64 (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(.f64 (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(.f64 (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(.f64 (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(.f64 (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (/ (* (pow (sin x) 2) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (pow (cos x) 2))))) (cos x))
(.f64 (-.f64 (+.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal -1/3 binary64)) (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (/.f64 (sin.f64 x) (cos.f64 x)))
(* -1/3 x)
(*.f64 #s(literal -1/3 binary64) x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (*.f64 x x) #s(literal -4/9 binary64))))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -4/9 binary64) (.f64 x (*.f64 x #s(literal -17/45 binary64)))))))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -4/9 binary64) (.f64 x (.f64 x (+.f64 #s(literal -17/45 binary64) (.f64 (*.f64 x x) #s(literal -248/945 binary64)))))))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(*.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
(* 1/3 (pow eps 2))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(* 1/3 (pow eps 3))
(.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* 1/3 (pow eps 3))
(.f64 #s(literal 1/3 binary64) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))

eval447.0ms (2.4%)

Compiler: Compiled 78397 to 6167 computations (92.1% saved)

prune134.0ms (0.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	1138	10	1148
Fresh	12	1	13
Picked	4	1	5
Done	1	2	3
Total	1155	14	1169

Accuracy

100.0%

Counts

1169 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.9%	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	61.6%	(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
✓	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.3%	(+.f64 (/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (/.f64 (sin.f64 x) (cos.f64 x))))
▶	99.5%	(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
	99.8%	(.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
▶	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	98.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
▶	98.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
	98.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
▶	98.7%	eps

Compiler

Compiled 778 to 407 computations (47.7% saved)

simplify236.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 (tan.f64 x) (tan.f64 eps))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
✓	cost-diff	6528	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓	cost-diff	0	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
✓	cost-diff	0	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
✓	cost-diff	0	(+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
✓	cost-diff	0	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
✓	cost-diff	256	(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))
✓	cost-diff	6400	(+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))
✓	cost-diff	6464	(-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))
✓	cost-diff	6528	(+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))
✓	cost-diff	13120	(+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))

Rules

2902×	`+-lowering-+.f64`
2902×	`+-lowering-+.f32`
2896×	`--lowering--.f32`
2896×	`--lowering--.f64`
2368×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	897
1	208	804
2	870	757
3	4273	687
0	8077	687

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps (+ 1 (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))))))))
eps
(+ 1 (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))))))
1
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))))))
(pow (tan x) 2)
(tan x)
x
2
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))))
(+ (tan x) (pow (tan x) 3))
(pow (tan x) 3)
3
(* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))
(+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))
(+ (pow (tan x) 2) (pow (tan x) 4))
(pow (tan x) 4)
4
(- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))
(- 1/3 (* (pow (tan x) 2) -1/3))
1/3
(* (pow (tan x) 2) -1/3)
-1/3
(* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))
(+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))
(* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3))))
(+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))
(- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4)))
1/6
(+ -1/2 (* (pow (tan x) 2) -1/3))
-1/2
(* -1/3 (+ (tan x) (pow (tan x) 3)))
eps
(* eps (+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))))
eps
(+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3))))))
1
(+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))
(* 1/3 (* eps eps))
1/3
(* eps eps)
(* eps (* x (+ 1 (* (* eps eps) 2/3))))
(* x (+ 1 (* (* eps eps) 2/3)))
x
(+ 1 (* (* eps eps) 2/3))
(* (* eps eps) 2/3)
2/3
(* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps)
(+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(sin x)
x
2
(pow (cos x) 2)
(cos x)
1
eps
(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))) (- 0 (tan x)))
(/ 1 (- 1 (* (tan x) (tan eps))))
1
(- 1 (* (tan x) (tan eps)))
(* (tan x) (tan eps))
(tan x)
x
(tan eps)
eps
(+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))
(* eps (+ 1 (* 1/3 (* eps eps))))
(+ 1 (* 1/3 (* eps eps)))
(* 1/3 (* eps eps))
1/3
(* eps eps)
(- 0 (tan x))
0

Outputs
(* eps (+ 1 (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (tan.f64 x) (+.f64 eps (tan.f64 x))) (.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))))))))))
eps
(+ 1 (+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))))))
(+.f64 #s(literal 1 binary64) (+.f64 (.f64 (tan.f64 x) (+.f64 eps (tan.f64 x))) (.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))))))))
1
#s(literal 1 binary64)
(+ (pow (tan x) 2) (* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))))))
(+.f64 (.f64 (tan.f64 x) (+.f64 eps (tan.f64 x))) (.f64 eps (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))))))))
(pow (tan x) 2)
(pow.f64 (tan.f64 x) #s(literal 2 binary64))
(tan x)
(tan.f64 x)
x
2
#s(literal 2 binary64)
(* eps (+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))))
(.f64 eps (+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))))))))
(+ (+ (tan x) (pow (tan x) 3)) (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))))
(+.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 3 binary64)) (.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))))))
(+ (tan x) (pow (tan x) 3))
(+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))
(pow (tan x) 3)
(pow.f64 (tan.f64 x) #s(literal 3 binary64))
3
#s(literal 3 binary64)
(* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))
(.f64 eps (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))))
(+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))
(-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))) (.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))))
(+ (pow (tan x) 2) (pow (tan x) 4))
(+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(pow (tan x) 4)
(pow.f64 (tan.f64 x) #s(literal 4 binary64))
4
#s(literal 4 binary64)
(- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))
(+.f64 (.f64 eps (.f64 (tan.f64 x) (+.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) #s(literal 1/3 binary64))))) (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/3 binary64) (.f64 eps (.f64 (tan.f64 x) #s(literal -1/3 binary64))))))
(- 1/3 (* (pow (tan x) 2) -1/3))
(+.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal 1/3 binary64)))
1/3
#s(literal 1/3 binary64)
(* (pow (tan x) 2) -1/3)
(*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))
-1/3
#s(literal -1/3 binary64)
(* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))
(.f64 eps (.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))))
(+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))
(.f64 (tan.f64 x) (+.f64 (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (*.f64 #s(literal -1/3 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))))
(* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3))))
(.f64 (tan.f64 x) (-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))))
(+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))
(-.f64 (-.f64 #s(literal -1/3 binary64) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 #s(literal 4/3 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4)))
(-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
1/6
#s(literal 1/6 binary64)
(+ -1/2 (* (pow (tan x) 2) -1/3))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* -1/3 (+ (tan x) (pow (tan x) 3)))
(*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))
eps
(* eps (+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 (.f64 (*.f64 x #s(literal 2/3 binary64)) eps) #s(literal 1/3 binary64)))))))
eps
(+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3))))))
(+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 (.f64 (.f64 x #s(literal 2/3 binary64)) eps) #s(literal 1/3 binary64))))))
1
#s(literal 1 binary64)
(+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))
(.f64 eps (+.f64 x (.f64 eps (+.f64 (.f64 (.f64 x #s(literal 2/3 binary64)) eps) #s(literal 1/3 binary64)))))
(* 1/3 (* eps eps))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(* eps (* x (+ 1 (* (* eps eps) 2/3))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))) (.f64 eps x))
(* x (+ 1 (* (* eps eps) 2/3)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))
x
(+ 1 (* (* eps eps) 2/3))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))
(* (* eps eps) 2/3)
(.f64 (.f64 eps eps) #s(literal 2/3 binary64))
2/3
#s(literal 2/3 binary64)
(* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)
(+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/ (pow (sin x) 2) (pow (cos x) 2))
(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
(pow (sin x) 2)
(pow.f64 (sin.f64 x) #s(literal 2 binary64))
(sin x)
(sin.f64 x)
x
2
#s(literal 2 binary64)
(pow (cos x) 2)
(pow.f64 (cos.f64 x) #s(literal 2 binary64))
(cos x)
(cos.f64 x)
1
#s(literal 1 binary64)
eps
(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))) (- 0 (tan x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/ 1 (- 1 (* (tan x) (tan eps))))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
1
#s(literal 1 binary64)
(- 1 (* (tan x) (tan eps)))
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(* (tan x) (tan eps))
(*.f64 (tan.f64 x) (tan.f64 eps))
(tan x)
(tan.f64 x)
x
(tan eps)
(tan.f64 eps)
eps
(+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))
(+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(* eps (+ 1 (* 1/3 (* eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+ 1 (* 1/3 (* eps eps)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))
(* 1/3 (* eps eps))
(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
1/3
#s(literal 1/3 binary64)
(* eps eps)
(*.f64 eps eps)
(- 0 (tan x))
(-.f64 #s(literal 0 binary64) (tan.f64 x))
0
#s(literal 0 binary64)

localize873.0ms (4.7%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
✓	accuracy	99.8%	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
✓	accuracy	94.1%	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(pow.f64 (sin.f64 x) #s(literal 2 binary64))
✓	accuracy	100.0%	(/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
✓	accuracy	99.9%	(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal 2/3 binary64))
✓	accuracy	99.8%	(.f64 #s(literal 1/3 binary64) (.f64 eps eps))
✓	accuracy	99.8%	(*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))
✓	accuracy	99.8%	(.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
✓	accuracy	99.7%	(.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))))))))
✓	accuracy	99.3%	(+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))

Results

617.0ms	143×	5	exit
106.0ms	108×	0	valid
5.0ms	3×	1	valid
5.0ms	2×	2	valid

Compiler

Compiled 947 to 61 computations (93.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 312.0ms

backward-pass: 131.0ms (41.9% of total)

ival-mult: 50.0ms (16% of total)

ival-add: 30.0ms (9.6% of total)

ival-pow: 27.0ms (8.6% of total)

...c/correct-round.rkt:119:19: 24.0ms (7.7% of total)

ival-cos: 15.0ms (4.8% of total)

ival-sub: 10.0ms (3.2% of total)

compiled-spec: 7.0ms (2.2% of total)

ival-tan: 7.0ms (2.2% of total)

ival-div: 6.0ms (1.9% of total)

ival-sin: 3.0ms (1% of total)

const: 2.0ms (0.6% of total)

series57.0ms (0.3%)

Counts

24 → 432

Calls

Call 1

Inputs
#<alt (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))>
#<alt (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))>
#<alt (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))>
#<alt (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))>
#<alt (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))>
#<alt (* eps (+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))))>
#<alt (+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3))))))>
#<alt (* 1/3 (* eps eps))>
#<alt (* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps)>
#<alt (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (pow (sin x) 2)>
#<alt (+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))) (- 0 (tan x)))>
#<alt (/ 1 (- 1 (* (tan x) (tan eps))))>
#<alt (- 1 (* (tan x) (tan eps)))>
#<alt (* (tan x) (tan eps))>
#<alt (* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))>
#<alt (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3))))>
#<alt (* -1/3 (+ (tan x) (pow (tan x) 3)))>
#<alt (* (* eps eps) 2/3)>
#<alt (cos x)>
#<alt (sin x)>
#<alt (* eps (+ 1 (* 1/3 (* eps eps))))>
#<alt (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))>

Outputs
#<alt -1/3>
#<alt (- (* -4/3 (pow x 2)) 1/3)>
#<alt (- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)>
#<alt (- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))>
#<alt 1/3>
#<alt (+ 1/3 (* 2/3 (* eps x)))>
#<alt (+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))>
#<alt (+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))>
#<alt (* eps (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (* eps (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (* eps (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))>
#<alt 1/3>
#<alt (+ 1/3 (* 2/3 (* eps x)))>
#<alt (+ 1/3 (* x (- (* 1/3 x) (* -2/3 eps))))>
#<alt (+ 1/3 (* x (- (* x (+ 1/3 (* 17/9 (* eps x)))) (* -2/3 eps))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (- (+ 1/3 (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))>
#<alt (* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))>
#<alt (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))>
#<alt (* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))>
#<alt (* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))>
#<alt (* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))>
#<alt (* -2/3 x)>
#<alt (* x (- (* -17/9 (pow x 2)) 2/3))>
#<alt (* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))>
#<alt (* eps x)>
#<alt (* eps (+ x (* 1/3 eps)))>
#<alt (* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))>
#<alt (* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* (pow eps 3) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))>
#<alt (* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* -1 (* (pow eps 3) (- (* -2/3 x) (* 1/3 (/ 1 eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (/ x eps)) eps)) (* -2/3 x))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (/ x eps)) eps)) (* -2/3 x))))>
#<alt (* 1/3 (pow eps 2))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))>
#<alt (* x (+ (* 1/3 (/ (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (* x (+ (* 1/3 (/ (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (* x (+ (* 1/3 (/ (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1/3 (/ (pow eps 2) x)))))>
#<alt eps>
#<alt (* eps (+ 1 (* eps x)))>
#<alt (* eps (+ 1 (* eps (+ x (* 1/3 eps)))))>
#<alt (* eps (+ 1 (* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))))>
#<alt (* 2/3 (* (pow eps 4) x))>
#<alt (* (pow eps 4) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))>
#<alt (* (pow eps 4) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))>
#<alt (* (pow eps 4) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (/ x (pow eps 2))))))>
#<alt (* 2/3 (* (pow eps 4) x))>
#<alt (* (pow eps 4) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/3) eps)) (* 2/3 x)))>
#<alt (* (pow eps 4) (+ (* -1 (/ (- (* -1 (/ (+ x (/ 1 eps)) eps)) 1/3) eps)) (* 2/3 x)))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))>
#<alt (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))>
#<alt (* x (+ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x)))>
#<alt (* x (+ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x)))>
#<alt (* x (+ (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x)))>
#<alt (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x)))))>
#<alt (* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x)))))>
#<alt (* -1 (* x (+ (* -1 (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) x)))))>
#<alt 1>
#<alt (+ 1 (* eps x))>
#<alt (+ 1 (* eps (+ x (* 1/3 eps))))>
#<alt (+ 1 (* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x)))))))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* (pow eps 3) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))>
#<alt (* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (+ (/ 1 (pow eps 3)) (/ x (pow eps 2))))))>
#<alt (* 2/3 (* (pow eps 3) x))>
#<alt (* -1 (* (pow eps 3) (- (* -2/3 x) (* 1/3 (/ 1 eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (/ x eps)) eps)) (* -2/3 x))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ 1/3 (* -1 (/ (- (* -1 x) (/ 1 eps)) eps))) eps)) (* -2/3 x))))>
#<alt (+ 1 (* 1/3 (pow eps 2)))>
#<alt (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))>
#<alt (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))>
#<alt (* x (+ (* 1/3 (/ (pow eps 2) x)) (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (/ 1 x))))>
#<alt (* x (+ (* 1/3 (/ (pow eps 2) x)) (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (/ 1 x))))>
#<alt (* x (+ (* 1/3 (/ (pow eps 2) x)) (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (/ 1 x))))>
#<alt (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (+ 1 (* 2/3 (pow eps 2))))) (* -1 (/ (+ 1 (* 1/3 (pow eps 2))) x)))))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt (* 1/3 (pow eps 2))>
#<alt eps>
#<alt (+ eps (* eps (pow x 2)))>
#<alt (+ eps (* (pow x 2) (+ eps (* 2/3 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ eps (* (pow x 2) (+ (* 17/45 (* eps (pow x 2))) (* 2/3 eps))))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt (* eps (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2))))>
#<alt 1>
#<alt (+ 1 (pow x 2))>
#<alt (+ 1 (* (pow x 2) (+ 1 (* 2/3 (pow x 2)))))>
#<alt (+ 1 (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2)))))))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* 17/45 (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 17/45 (* 62/315 (pow x 2))))))))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (/ (pow (sin x) 2) (pow (cos x) 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* 2/45 (pow x 2)) 1/3))))>
#<alt (* (pow x 2) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 2/45 (* -1/315 (pow x 2)))) 1/3))))>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (pow (sin x) 2)>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (* eps (* x (* (sin eps) (+ 1 (* 1/3 (pow eps 2)))))) (cos eps)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (* -1 (* x (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (* eps (* (pow (sin eps) 2) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 2)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (- (* x (- (* -1 (* x (+ (* -1 (/ (* eps (* (pow (sin eps) 3) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 3))) (+ (* -1 (/ (pow (sin eps) 2) (pow (cos eps) 2))) (* -1/3 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (* eps (* (pow (sin eps) 2) (+ 1 (* 1/3 (pow eps 2))))) (pow (cos eps) 2)))))) (* -1 (/ (* eps (* (sin eps) (+ 1 (* 1/3 (pow eps 2))))) (cos eps))))))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
#<alt (- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (* eps (+ 1 (* 1/3 (pow eps 2)))) (- 1 (/ (* (sin eps) (sin x)) (* (cos eps) (cos x)))))) (/ (sin x) (cos x)))>
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#<alt (* -1/3 x)>
#<alt (* x (- (* -13/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))>
#<alt (* -1/3 x)>
#<alt (* x (- (* -4/9 (pow x 2)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))>
#<alt (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt (* 2/3 (pow eps 2))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt eps>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* eps (+ 1 (* 1/3 (pow eps 2))))>
#<alt (+ x (* eps (+ 1 (* 1/3 (pow eps 2)))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* 1/3 (pow x 2)))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (/ (sin x) (cos x))>
#<alt (+ eps (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))>
#<alt (* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))>
#<alt (* 1/3 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))>

Calls

108 calls:

Time	Variable		Point	Expression
17.0ms	x	@	-inf	(* eps (+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))))
4.0ms	eps	@	0	(* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))
3.0ms	eps	@	0	(+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))
2.0ms	x	@	inf	(+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))
1.0ms	x	@	-inf	(+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))

rewrite315.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2656×	`-lowering-.f32`
2656×	`-lowering-.f64`
2122×	`fma-lowering-fma.f32`
2122×	`fma-lowering-fma.f64`
1936×	`fmm-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	392
1	432	338
2	5060	336
0	8033	336

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 456

Calls

Call 1

Inputs
(+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))
(+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3)))))))
(- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))
(+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))
(+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))
(* eps (+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3)))))))
(+ 1 (+ (* 1/3 (* eps eps)) (* eps (* x (+ 1 (* (* eps eps) 2/3))))))
(* 1/3 (* eps eps))
(* (+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1) eps)
(+ (/ (pow (sin x) 2) (pow (cos x) 2)) 1)
(/ (pow (sin x) 2) (pow (cos x) 2))
(pow (sin x) 2)
(+ (* (/ 1 (- 1 (* (tan x) (tan eps)))) (+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))) (- 0 (tan x)))
(/ 1 (- 1 (* (tan x) (tan eps))))
(- 1 (* (tan x) (tan eps)))
(* (tan x) (tan eps))
(* eps (+ (+ (pow (tan x) 2) (pow (tan x) 4)) (- (- 1/3 (* (pow (tan x) 2) -1/3)) (* eps (+ (* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3)))) (* -1/3 (+ (tan x) (pow (tan x) 3))))))))
(* (tan x) (+ (- 1/6 (+ (pow (tan x) 2) (pow (tan x) 4))) (+ -1/2 (* (pow (tan x) 2) -1/3))))
(* -1/3 (+ (tan x) (pow (tan x) 3)))
(* (* eps eps) 2/3)
(cos x)
(sin x)
(* eps (+ 1 (* 1/3 (* eps eps))))
(+ (tan x) (* eps (+ 1 (* 1/3 (* eps eps)))))

Outputs
(+.f64 #s(literal 1/6 binary64) (neg.f64 (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))))
(+.f64 #s(literal 1/6 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(+.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))
(+.f64 #s(literal -1/2 binary64) (+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal -1/2 binary64))))
(+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(+.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) #s(literal -1/2 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))
(+.f64 (+.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal -1/2 binary64))
(+.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 1/6 binary64)) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))
(-.f64 #s(literal 1/6 binary64) (-.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (-.f64 (pow.f64 (tan.f64 x) #s(literal 4 binary64)) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))
(-.f64 (/.f64 (pow.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))) (/.f64 (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))))))
(-.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 1/6 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))))
(-.f64 (+.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))) (+.f64 (pow.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (-.f64 (pow.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 3 binary64)) (pow.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (-.f64 (-.f64 #s(literal 1/6 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))
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simplify425.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

5970×	`-lowering-.f32`
5970×	`-lowering-.f64`
2964×	`+-lowering-+.f64`
2964×	`+-lowering-+.f32`
1396×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	626	10993
1	2175	9707
0	8278	9707

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 432

Calls

Call 1

Inputs
-1/3
(- (* -4/3 (pow x 2)) 1/3)
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))
(+ 1/3 (* x (- (* x (+ 4/3 (* 17/9 (* eps x)))) (* -2/3 eps))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* eps (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* eps (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* eps (- (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4))))) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* -1 (* eps (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* -1 (* eps (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* -1 (* eps (- (* -1 (/ (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
1/3
(+ 1/3 (* 2/3 (* eps x)))
(+ 1/3 (* x (- (* 1/3 x) (* -2/3 eps))))
(+ 1/3 (* x (- (* x (+ 1/3 (* 17/9 (* eps x)))) (* -2/3 eps))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(- (+ 1/3 (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
(* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* -2/3 x)
(* x (- (* -17/9 (pow x 2)) 2/3))
(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
(* eps x)
(* eps (+ x (* 1/3 eps)))
(* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))
(* eps (+ x (* eps (+ 1/3 (* 2/3 (* eps x))))))
(* 2/3 (* (pow eps 3) x))
(* (pow eps 3) (+ (* 2/3 x) (* 1/3 (/ 1 eps))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* (pow eps 3) (+ (* 2/3 x) (+ (* 1/3 (/ 1 eps)) (/ x (pow eps 2)))))
(* 2/3 (* (pow eps 3) x))
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1
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1
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1
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1
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(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* eps (- (+ 1/3 (+ (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))) (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* -1 (* (pow eps 2) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
(* 1/3 eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))
(+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* 17/9 (* (pow eps 2) x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
(* -1/3 x)
(* x (- (* -13/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
(* -1/3 x)
(* x (- (* -4/9 (pow x 2)) 1/3))
(* x (- (* (pow x 2) (- (* -17/45 (pow x 2)) 4/9)) 1/3))
(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -248/945 (pow x 2)) 17/45)) 4/9)) 1/3))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
(* 2/3 (pow eps 2))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
eps
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(+ x (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* 1/3 (pow x 2)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(/ (sin x) (cos x))
(+ eps (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))
(* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))
(* 1/3 (pow eps 3))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))

Outputs
-1/3
#s(literal -1/3 binary64)
(- (* -4/3 (pow x 2)) 1/3)
(+.f64 #s(literal -1/3 binary64) (.f64 #s(literal -4/3 binary64) (.f64 x x)))
(- (* (pow x 2) (- (* -17/9 (pow x 2)) 4/3)) 1/3)
(+.f64 #s(literal -1/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -4/3 binary64) (.f64 (.f64 x x) #s(literal -17/9 binary64))))))
(- (* (pow x 2) (- (* (pow x 2) (- (* -248/135 (pow x 2)) 17/9)) 4/3)) 1/3)
(+.f64 #s(literal -1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -4/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal -17/9 binary64) (.f64 (.f64 x x) #s(literal -248/135 binary64))))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))
(-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
1/3
#s(literal 1/3 binary64)
(+ 1/3 (* 2/3 (* eps x)))
(+.f64 #s(literal 1/3 binary64) (.f64 x (.f64 #s(literal 2/3 binary64) eps)))
(+ 1/3 (* x (- (* 4/3 x) (* -2/3 eps))))
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(- (+ 1/3 (* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))) (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))))
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(* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
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(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
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(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
(.f64 eps (-.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) eps) (.f64 #s(literal -1/3 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))) (.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (+.f64 #s(literal 1/3 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (/.f64 (sin.f64 x) (cos.f64 x)))))
(* eps (- (* 1/3 (/ 1 eps)) (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (+ (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))))))
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(* -1 (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))
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(* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
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(* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
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(* -1 (* eps (- (* -1 (/ (- 1/3 (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2)))) eps)) (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
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(* -2/3 x)
(*.f64 x #s(literal -2/3 binary64))
(* x (- (* -17/9 (pow x 2)) 2/3))
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(* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))
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(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))
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(+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* (pow eps 2) (- (+ (* -1 (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))) (+ (* 1/3 (/ 1 eps)) (+ (/ (pow (sin x) 2) (* eps (pow (cos x) 2))) (/ (pow (sin x) 4) (* eps (pow (cos x) 4)))))) (* -1/3 (/ (pow (sin x) 2) (* eps (pow (cos x) 2))))))
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(* 1/3 eps)
(*.f64 #s(literal 1/3 binary64) eps)
(+ (* 1/3 eps) (* 2/3 (* (pow eps 2) x)))
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(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
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(* eps (- (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))) (+ (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (* eps (+ (* -1/3 (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3)))) (/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x)))))))
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(*.f64 #s(literal -1/3 binary64) x)
(* x (- (* -13/9 (pow x 2)) 1/3))
(.f64 x (+.f64 #s(literal -1/3 binary64) (.f64 (*.f64 x x) #s(literal -13/9 binary64))))
(* x (- (* (pow x 2) (- (* -107/45 (pow x 2)) 13/9)) 1/3))
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(* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2516/945 (pow x 2)) 107/45)) 13/9)) 1/3))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
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(/ (* (sin x) (- (* -1/3 (/ (pow (sin x) 2) (pow (cos x) 2))) (+ 1/3 (+ (/ (pow (sin x) 2) (pow (cos x) 2)) (/ (pow (sin x) 4) (pow (cos x) 4)))))) (cos x))
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(* x (- (* -4/9 (pow x 2)) 1/3))
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1
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(cos x)
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x
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(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* eps (+ 1 (* 1/3 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(+ x (* eps (+ 1 (* 1/3 (pow eps 2)))))
(+.f64 x (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* 1/3 (pow x 2)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/3 binary64)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ 1 (* (pow x 2) (+ 1/3 (* 2/15 (pow x 2)))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) #s(literal 2/15 binary64))))))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(/ (sin x) (cos x))
(/.f64 (sin.f64 x) (cos.f64 x))
(+ eps (/ (sin x) (cos x)))
(+.f64 eps (/.f64 (sin.f64 x) (cos.f64 x)))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (/ (sin x) (cos x)))
(+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))))
(* 1/3 (pow eps 3))
(.f64 eps (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (.f64 eps (.f64 eps eps)))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
(* (pow eps 3) (+ 1/3 (+ (/ 1 (pow eps 2)) (/ (sin x) (* (pow eps 3) (cos x))))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (.f64 eps (.f64 eps eps)))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)))))
(* 1/3 (pow eps 3))
(.f64 eps (.f64 #s(literal 1/3 binary64) (*.f64 eps eps)))
(* (pow eps 3) (+ 1/3 (/ 1 (pow eps 2))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (/.f64 (/.f64 (.f64 (sin.f64 x) #s(literal -1 binary64)) (cos.f64 x)) (.f64 eps (.f64 eps eps))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (sin x) (* (pow eps 3) (cos x)))) (+ 1/3 (/ 1 (pow eps 2))))))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 eps (.f64 eps eps)) (-.f64 (/.f64 (/.f64 (.f64 (sin.f64 x) #s(literal -1 binary64)) (cos.f64 x)) (.f64 eps (.f64 eps eps))) (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))))))

eval150.0ms (0.8%)

Compiler: Compiled 48365 to 4028 computations (91.7% saved)

prune130.0ms (0.7%)

Pruning

25 alts after pruning (20 fresh and 5 done)

	Pruned	Kept	Total
New	891	17	908
Fresh	3	3	6
Picked	2	3	5
Done	1	2	3
Total	897	25	922

Accuracy

100.0%

Counts

922 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	61.9%	(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
✓	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
	61.9%	(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓	61.7%	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
	99.3%	(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
	99.5%	(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
	98.7%	(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
	98.8%	(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
	99.0%	(.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
	99.5%	(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
	98.9%	(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
	98.9%	(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
	98.8%	(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
	52.2%	(.f64 (+.f64 (exp.f64 (-.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))))) #s(literal 1 binary64)) eps)
	98.7%	(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
	98.7%	(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
✓	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
	99.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
	98.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
	98.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
	98.7%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
✓	98.7%	eps

Compiler

Compiled 2329 to 762 computations (67.3% saved)

regimes56.0ms (0.3%)

Counts

57 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
(-.f64 (tan.f64 eps) x)
(-.f64 (tan.f64 x) x)
(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 (+.f64 (exp.f64 (-.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(+.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 eps (+.f64 #s(literal 1/3 binary64) (-.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 4 binary64)) (pow.f64 (cos.f64 x) #s(literal 4 binary64))))))) (*.f64 #s(literal 1 binary64) (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (-.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 (+.f64 (-.f64 #s(literal 1/6 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 eps (-.f64 (-.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) #s(literal -1/6 binary64)) (+.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))) (.f64 eps (+.f64 (/.f64 (.f64 (sin.f64 x) (+.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (+.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 #s(literal 1/6 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))) (cos.f64 x)) (.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) #s(literal -1/3 binary64)))))))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))

Outputs

(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))

Calls

3 calls:

17.0ms	x
16.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes50.0ms (0.3%)

Counts

52 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
(-.f64 (tan.f64 eps) x)
(-.f64 (tan.f64 x) x)
(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 (+.f64 (exp.f64 (-.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(+.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (.f64 (-.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)))) (.f64 eps (+.f64 (.f64 #s(literal -1/3 binary64) (tan.f64 x)) (*.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64))))) eps))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))

Outputs

(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (*.f64 eps (+.f64 (*.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))

Calls

3 calls:

15.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
15.0ms	x
14.0ms	eps

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes49.0ms (0.3%)

Counts

50 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
(-.f64 (tan.f64 eps) x)
(-.f64 (tan.f64 x) x)
(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 (+.f64 (exp.f64 (-.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (/.f64 (sin.f64 x) (cos.f64 x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(+.f64 (/.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps))) (cos.f64 x)))) (/.f64 (sin.f64 x) (cos.f64 x))))

Outputs

(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (*.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))

Calls

3 calls:

15.0ms	eps
14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
13.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`eps`
100.0%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes45.0ms (0.2%)

Counts

48 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
(-.f64 (tan.f64 eps) x)
(-.f64 (tan.f64 x) x)
(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 (+.f64 (exp.f64 (-.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(+.f64 (+.f64 (-.f64 #s(literal 0 binary64) (tan.f64 x)) (/.f64 (tan.f64 x) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 eps (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (/.f64 (*.f64 eps (sin.f64 x)) (cos.f64 x))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps)))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (-.f64 (/.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 x) (cos.f64 eps))))) (/.f64 (sin.f64 x) (cos.f64 x))))

Outputs

(*.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))

Calls

3 calls:

14.0ms	x
14.0ms	eps
13.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`eps`
99.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes42.0ms (0.2%)

Counts

40 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
(-.f64 (tan.f64 eps) x)
(-.f64 (tan.f64 x) x)
(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
(-.f64 (tan.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 eps (.f64 eps eps)))) (.f64 (-.f64 x eps) (+.f64 (.f64 x x) (*.f64 eps eps))))) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 x eps)) (/.f64 (sin.f64 x) (cos.f64 x)))
(.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))
(*.f64 eps (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) eps) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(fma.f64 (/.f64 #s(literal 1 binary64) (cos.f64 (+.f64 x eps))) (sin.f64 (+.f64 x eps)) (-.f64 #s(literal 0 binary64) (tan.f64 x)))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(.f64 (+.f64 (exp.f64 (-.f64 (.f64 #s(literal 2 binary64) (log.f64 (sin.f64 x))) (*.f64 #s(literal 2 binary64) (log.f64 (cos.f64 x))))) #s(literal 1 binary64)) eps)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

Outputs

(*.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)

Calls

3 calls:

15.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms	x
11.0ms	eps

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.1%)

Counts

28 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
(-.f64 (tan.f64 eps) x)
(-.f64 (tan.f64 x) x)
(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)

Outputs
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)

Calls

3 calls:

9.0ms	x
8.0ms	eps
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.1%)

Counts

27 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 4/3 binary64) (.f64 eps eps)))))))))
(.f64 eps (-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))))) (/.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64)))))) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))))))
(-.f64 (tan.f64 eps) x)
(-.f64 (tan.f64 x) x)
(*.f64 #s(literal -17/315 binary64) (pow.f64 x #s(literal 7 binary64)))
(-.f64 (tan.f64 (+.f64 x eps)) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/3 binary64))))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))))
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x #s(literal 2/15 binary64))))))))
(-.f64 (tan.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) x)
(-.f64 (tan.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 x (*.f64 x #s(literal 17/315 binary64))))))))))
(-.f64 (tan.f64 (+.f64 x eps)) (+.f64 (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))) x))
(-.f64 (-.f64 (tan.f64 (+.f64 x eps)) x) (.f64 (+.f64 #s(literal 1/3 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/15 binary64) (.f64 (.f64 x x) #s(literal 17/315 binary64))))) (.f64 x (*.f64 x x))))
(/.f64 (sin.f64 eps) (cos.f64 eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Outputs

(*.f64 (+.f64 (*.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) (+.f64 #s(literal 2/3 binary64) (*.f64 x (*.f64 x (+.f64 #s(literal 17/45 binary64) (*.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)

Calls

3 calls:

9.0ms	x
8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
8.0ms	eps

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes8.0ms (0%)

Counts

11 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)

Outputs
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes7.0ms (0%)

Counts

10 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (.f64 eps (+.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))))
(+.f64 (.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/3 binary64) eps) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal 2/3 binary64))))))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 1/3 binary64) (.f64 eps eps)) (.f64 eps (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal 2/3 binary64))))))))

Outputs
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))

Calls

2 calls:

3.0ms	x
3.0ms	eps

Results

Accuracy	Segments	Branch
98.8%	1	`eps`
98.8%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0%)

Counts

6 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 eps eps))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (+.f64 x (*.f64 #s(literal 1/3 binary64) eps)))))

Outputs
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)

Calls

2 calls:

6.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Accuracy

Total -58.3b remaining (-7061.7%)

Threshold costs -58.3b (-7061.7%)

Counts

3 → 1

Calls

Call 1

Inputs
eps
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 (.f64 x eps) #s(literal 1 binary64)))

Outputs
eps

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify191.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1654×	`unsub-neg_binary64`
976×	`distribute-lft-neg-in_binary64`
960×	`neg-mul-1_binary64`
506×	`neg-sub0_binary64`
398×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	297
1	206	297
2	258	297
3	304	297
4	354	297
5	382	297
6	409	297
7	442	297
8	491	297
9	542	297
10	795	297
11	1401	297
12	1858	297
13	1943	297
14	2141	297
15	2476	297
16	2791	297
17	3192	297
18	3436	297
19	3647	297
20	3788	297
21	3930	297
22	4068	297
23	4119	297
24	4121	297
25	4121	297
26	4132	297
27	4138	297
28	4148	297
29	4151	297
30	4151	297

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
eps

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) (+.f64 (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))))) (.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) (.f64 (tan.f64 x) (+.f64 (+.f64 (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64)) #s(literal -1/2 binary64)) (-.f64 #s(literal 1/6 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64)))))))))))))) #s(literal 1 binary64)))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (tan.f64 x) #s(literal -1/3 binary64)) (*.f64 #s(literal -1/3 binary64) (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))))))))))))))
(.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 (-.f64 #s(literal 1/3 binary64) (.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) #s(literal -1/3 binary64))) (.f64 eps (+.f64 (.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) #s(literal -1/3 binary64)) (*.f64 (tan.f64 x) #s(literal -1/3 binary64)))))))))) #s(literal 1 binary64)))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))))))))))
(.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 4 binary64))) (-.f64 #s(literal 1/3 binary64) (/.f64 (.f64 #s(literal -1/3 binary64) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))))))) #s(literal 1 binary64)))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64)))))))
(.f64 eps (+.f64 (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (.f64 eps (+.f64 (+.f64 (tan.f64 x) (pow.f64 (tan.f64 x) #s(literal 3 binary64))) (*.f64 eps #s(literal 1/3 binary64))))) #s(literal 1 binary64)))
(.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 x #s(literal 2 binary64)))))) #s(literal 1 binary64)))
(+.f64 (*.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) eps) eps)
(+.f64 eps (*.f64 eps (pow.f64 (tan.f64 x) #s(literal 2 binary64))))
(.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 (.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x (+.f64 #s(literal 17/45 binary64) (.f64 (*.f64 x x) #s(literal 62/315 binary64))))))) #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (+.f64 (.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64)))))))) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 (.f64 x (.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 2/3 binary64) (.f64 x (*.f64 x #s(literal 17/45 binary64))))) #s(literal 1 binary64)))) #s(literal 1 binary64)))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 #s(literal 2/3 binary64) eps))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 eps (.f64 x (.f64 x (*.f64 eps #s(literal 2/3 binary64)))))))
(.f64 (+.f64 (.f64 x x) #s(literal 1 binary64)) eps)
(.f64 eps (+.f64 (.f64 x x) #s(literal 1 binary64)))
eps

soundness2.8s (14.9%)

Rules

5970×	`-lowering-.f32`
5970×	`-lowering-.f64`
5580×	`-lowering-.f32`
5580×	`-lowering-.f64`
3856×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	493	8479
1	1607	7233
2	6067	6848
0	8022	6848
0	60	336
1	452	272
2	5395	267
0	8792	267
0	56	392
1	432	338
2	5060	336
0	8033	336
0	6	16
1	46	16
2	423	16
3	6591	16
0	8698	16
0	60	387
1	473	205
2	5987	203
0	8765	203
0	157	1381
1	494	1186
2	1896	1117
3	7762	1117
0	8619	1117
0	605	9772
1	2066	8394
0	8334	8394
0	626	10993
1	2175	9707
0	8278	9707

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 888 to 464 computations (47.7% saved)

preprocess99.0ms (0.5%)

Compiler: Compiled 640 to 240 computations (62.5% saved)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

analyze114.0ms (0.6%)

sample7.3s (39.5%)

preprocess68.0ms (0.4%)

explain138.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify17.0ms (0.1%)

localize62.0ms (0.3%)

series11.0ms (0.1%)

rewrite371.0ms (2%)

simplify315.0ms (1.7%)

eval38.0ms (0.2%)

prune46.0ms (0.2%)

simplify301.0ms (1.6%)

localize675.0ms (3.6%)

series74.0ms (0.4%)

rewrite386.0ms (2.1%)

simplify343.0ms (1.9%)

eval307.0ms (1.7%)

prune202.0ms (1.1%)

simplify283.0ms (1.5%)

localize588.0ms (3.2%)

series49.0ms (0.3%)

rewrite344.0ms (1.9%)

simplify338.0ms (1.8%)

eval447.0ms (2.4%)

prune134.0ms (0.7%)

simplify236.0ms (1.3%)

localize873.0ms (4.7%)

series57.0ms (0.3%)

rewrite315.0ms (1.7%)

simplify425.0ms (2.3%)

eval150.0ms (0.8%)

prune130.0ms (0.7%)

regimes56.0ms (0.3%)

regimes50.0ms (0.3%)

regimes49.0ms (0.3%)

regimes45.0ms (0.2%)

regimes42.0ms (0.2%)

regimes27.0ms (0.1%)

regimes25.0ms (0.1%)

regimes8.0ms (0%)

regimes7.0ms (0%)

regimes8.0ms (0%)

regimes4.0ms (0%)

simplify191.0ms (1%)

soundness2.8s (14.9%)

preprocess99.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	21	18
4	31	18
5	63	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18