Metrics for 2sin (example 3.3)

analyze75.0ms (0.5%)

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: 52.0ms

ival-sin: 28.0ms (53.5% of total)

...c/correct-round.rkt:119:19: 7.0ms (13.4% of total)

ival-mult: 3.0ms (5.7% of total)

ival-<=: 3.0ms (5.7% of total)

ival-<: 3.0ms (5.7% of total)

ival-add: 2.0ms (3.8% of total)

ival-fabs: 2.0ms (3.8% of total)

ival-sub: 2.0ms (3.8% of total)

ival-and: 1.0ms (1.9% of total)

const: 1.0ms (1.9% of total)

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

sample6.7s (48.9%)

Results

3.5s	26135×	0	precondition
1.3s	4460×	1	valid
457.0ms	3796×	0	valid

Precisions

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

...c/correct-round.rkt:119:19: 710.0ms (17.5% of total)

ival-sin: 648.0ms (16% of total)

ival-sub: 550.0ms (13.6% of total)

ival-<: 478.0ms (11.8% of total)

ival-<=: 377.0ms (9.3% of total)

ival-fabs: 355.0ms (8.8% of total)

ival-add: 332.0ms (8.2% of total)

ival-mult: 315.0ms (7.8% of total)

ival-and: 135.0ms (3.3% of total)

backward-pass: 101.0ms (2.5% of total)

const: 48.0ms (1.2% of total)

Bogosity

preprocess52.0ms (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
(- (sin (+ x eps)) (sin x))

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

Call 2

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

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

explain88.0ms (0.6%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
224	3	(2.6568322574247885e-102 1.9401000907893197e-105)	2	(3.056533357342663e-26 7.316052387044661e-28)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	0	-	0	-	`x`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`eps`
0	0	-	0	-	`(sin.f64 (+.f64 x eps))`

Results

35.0ms	252×	1	valid
21.0ms	254×	0	valid
2.0ms	4×	3	valid
0.0ms	2×	2	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-sin: 12.0ms (43.5% of total)

ival-add: 7.0ms (25.4% of total)

backward-pass: 5.0ms (18.1% of total)

ival-sub: 4.0ms (14.5% of total)

const: 0.0ms (0% 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
▶	64.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize34.0ms (0.3%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	64.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

17.0ms	126×	1	valid
8.0ms	127×	0	valid
1.0ms	2×	3	valid
0.0ms	1×	2	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sin: 6.0ms (47.4% of total)

ival-add: 2.0ms (15.8% of total)

backward-pass: 2.0ms (15.8% of total)

ival-sub: 2.0ms (15.8% of total)

const: 0.0ms (0% of total)

series4.0ms (0%)

Counts

4 → 84

Calls

Call 1

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

Outputs
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (- (sin (- eps (* -1 x))) (sin x))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (+ eps x)) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (- (sin (- x (* -1 eps))) (sin x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- 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 (* -1/6 (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)>

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	eps	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	inf	(+ x eps)

rewrite334.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2788×	`-lowering-.f32`
2788×	`-lowering-.f64`
2132×	`/-lowering-/.f32`
2132×	`/-lowering-/.f64`
2068×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	49	16
2	402	16
3	5232	16
0	8309	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 177

Calls

Call 1

Inputs
(- (sin (+ x eps)) (sin x))
(sin (+ x eps))
(+ x eps)
(sin x)

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

simplify259.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

3796×	`-lowering-.f32`
3796×	`-lowering-.f64`
2064×	`+-lowering-+.f64`
2064×	`+-lowering-+.f32`
1456×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	488
1	327	465
2	963	459
3	3572	459
0	8267	459

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(- (sin (- eps (* -1 x))) (sin x))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (+ eps x)) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(- (sin (- x (* -1 eps))) (sin x))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- 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 (* -1/6 (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)

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (.f64 x (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(-.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps))))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))) (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 eps (+.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (.f64 x (cos.f64 eps)) (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+.f64 (.f64 (+.f64 (.f64 x (.f64 x #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 eps)) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))) (cos.f64 eps)) x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(+.f64 (sin.f64 x) (*.f64 eps (cos.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+.f64 (.f64 eps (cos.f64 x)) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64)) (sin.f64 x)) (.f64 (.f64 eps (cos.f64 x)) (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.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 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.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 x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (*.f64 x #s(literal -1/5040 binary64)))))))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

eval30.0ms (0.2%)

Compiler: Compiled 7060 to 730 computations (89.7% saved)

prune31.0ms (0.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	256	5	261
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	257	5	262

Accuracy

100.0%

Counts

262 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.7%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
▶	100.0%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	100.0%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
▶	99.5%	(*.f64 eps (cos.f64 x))
▶	98.4%	(sin.f64 eps)

Compiler

Compiled 116 to 80 computations (31% saved)

simplify191.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))
✓	cost-diff	128	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	cost-diff	256	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	256	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 eps (cos.f64 x))
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
✓	cost-diff	0	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))

Rules

2082×	`fnmadd-define`
1694×	`fma-define`
1502×	`sum3-define`
1484×	`fma-lowering-fma.f32`
1484×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	31	160
1	70	150
2	200	146
3	699	146
4	1284	146
5	2833	146
6	3993	146
7	4574	146
8	4979	142
9	5786	142
10	7747	142
0	8095	142

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize199.0ms (1.5%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	100.0%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.9%	(.f64 x (.f64 x #s(literal -1/6 binary64)))
✓	accuracy	99.6%	(*.f64 x #s(literal -1/6 binary64))
✓	accuracy	64.9%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
✓	accuracy	100.0%	(*.f64 eps (sin.f64 x))
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
✓	accuracy	100.0%	(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))

Results

99.0ms	123×	1	valid
56.0ms	130×	0	valid
2.0ms	2×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 173 to 32 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

ival-mult: 38.0ms (38.7% of total)

ival-sin: 14.0ms (14.2% of total)

...c/correct-round.rkt:119:19: 13.0ms (13.2% of total)

ival-add: 9.0ms (9.2% of total)

backward-pass: 8.0ms (8.1% of total)

ival-cos: 8.0ms (8.1% of total)

ival-div: 5.0ms (5.1% of total)

ival-sub: 2.0ms (2% of total)

const: 1.0ms (1% of total)

series34.0ms (0.3%)

Counts

19 → 360

Calls

Call 1

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

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<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 (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))>
#<alt (* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<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 (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- 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 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))>
#<alt (+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))>
#<alt (+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps x)>
#<alt (* x (+ eps (* -1/6 (* eps (pow x 2)))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))>
#<alt (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (sin x))>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 x)>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (* -1/6 (pow x 2))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>

Calls

90 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(* -1/2 (* eps (sin x)))
3.0ms	eps	@	-inf	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	eps	@	0	(* -1/2 (* eps (sin x)))
1.0ms	eps	@	0	(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
1.0ms	x	@	inf	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)

rewrite348.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4164×	`-lowering-.f32`
4164×	`-lowering-.f64`
2914×	`/-lowering-/.f32`
2914×	`/-lowering-/.f64`
2266×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	122
1	165	113
2	1651	111
0	8609	111

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 298

Calls

Call 1

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

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

simplify284.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

5438×	`-lowering-.f32`
5438×	`-lowering-.f64`
2728×	`+-lowering-+.f64`
2728×	`+-lowering-+.f32`
1498×	`neg-lowering-neg.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	368	2994
1	1233	2729
2	4048	2715
0	8142	2715

Stop Event

1×	iter limit
1×	node limit

Counts

360 → 360

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
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)
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
(* -1/2 (* eps (sin x)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- 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 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* -1 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))))
(+ (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/3 (* x (pow (sin (* 1/2 eps)) 2))))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(+ (* -1 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* -1/2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(+ (* x (+ (* -1 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -1/2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* 1/6 (* x (pow (sin (* 1/2 eps)) 2))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* eps (sin x))
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 x)
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(* -1/6 (pow x 2))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 eps eps) (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 eps eps) (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 eps eps) (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 eps eps) (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 eps eps) (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 eps eps) (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x))) (.f64 (.f64 eps (.f64 eps x)) (*.f64 #s(literal 1/12 binary64) x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 eps #s(literal -1/2 binary64))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 eps x) x)))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps x) #s(literal 1/12 binary64)))))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps x))
(.f64 x (.f64 eps #s(literal -1/2 binary64)))
(* x (+ (* -1/2 eps) (* 1/12 (* eps (pow x 2)))))
(.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/12 binary64)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/240 (* eps (pow x 2))) (* 1/12 eps)))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 (.f64 #s(literal -1/240 binary64) (*.f64 x x)) #s(literal 1/12 binary64)))))
(* x (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/12 eps) (* (pow x 2) (+ (* -1/240 eps) (* 1/10080 (* eps (pow x 2)))))))))
(.f64 x (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal 1/12 binary64)) (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/240 binary64) (.f64 (.f64 x x) #s(literal 1/10080 binary64)))))))))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64)))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 eps (*.f64 eps #s(literal 1/120 binary64)))))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/6 binary64) (.f64 eps (.f64 eps (+.f64 #s(literal 1/120 binary64) (.f64 eps (*.f64 eps #s(literal -1/5040 binary64))))))))))
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+.f64 eps (.f64 (.f64 x x) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+.f64 (sin.f64 eps) (*.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps))))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (cos.f64 eps) (.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)))))))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (cos.f64 eps) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (.f64 x (+.f64 #s(literal 1/6 binary64) (*.f64 #s(literal -1/6 binary64) (cos.f64 eps))))))))))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (.f64 x (.f64 x x)))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (.f64 x (.f64 x x)))))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (.f64 x (.f64 x x)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(.f64 (.f64 x (.f64 x x)) (+.f64 (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 x x))) (/.f64 (sin.f64 (+.f64 eps x)) (.f64 x (.f64 x x)))))
(- (sin x) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* -1/6 (pow x 2)))))
(+.f64 (sin.f64 x) (-.f64 (.f64 eps (cos.f64 x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (+.f64 (sin.f64 x) (.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* -1/6 (pow x 2)))))
(+.f64 (sin.f64 x) (-.f64 (.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64)))))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (sin (+ eps x)) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* -1/6 (pow x 2)))))
(-.f64 (sin.f64 (+.f64 eps x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(+.f64 (sin.f64 eps) (*.f64 x (cos.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 (cos.f64 eps) (.f64 x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(+.f64 (sin.f64 eps) (.f64 x (+.f64 (cos.f64 eps) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (.f64 x (*.f64 #s(literal -1/6 binary64) (cos.f64 eps))))))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(+.f64 (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+.f64 (sin.f64 x) (.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(+.f64 (sin.f64 x) (.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
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x
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(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 x)
(*.f64 x #s(literal -1/6 binary64))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(* -1/6 (pow x 2))
(.f64 x (.f64 x #s(literal -1/6 binary64)))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (.f64 eps (-.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/8 binary64))) (.f64 (sin.f64 x) #s(literal 1/2 binary64)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 (sin.f64 x) #s(literal 1/48 binary64))) (.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (-.f64 (.f64 (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (-.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal 1/6 binary64))))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))

eval73.0ms (0.5%)

Compiler: Compiled 13804 to 1342 computations (90.3% saved)

prune56.0ms (0.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	660	11	671
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	663	13	676

Accuracy

100.0%

Counts

676 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
▶	98.4%	(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
▶	98.9%	(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
▶	100.0%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.6%	(.f64 eps (+.f64 (cos.f64 x) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
✓	100.0%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
▶	99.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
	99.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
	98.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
	98.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
	99.8%	(.f64 eps (.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64)))))
✓	99.5%	(*.f64 eps (cos.f64 x))
▶	98.4%	eps

Compiler

Compiled 337 to 221 computations (34.4% saved)

simplify187.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
✓	cost-diff	0	(.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
✓	cost-diff	0	(.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))
✓	cost-diff	0	(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
✓	cost-diff	0	(*.f64 eps #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
✓	cost-diff	0	(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
✓	cost-diff	128	(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
✓	cost-diff	128	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	cost-diff	128	(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	384	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

Rules

2758×	`-lowering-.f32`
2758×	`-lowering-.f64`
2714×	`+-lowering-+.f64`
2714×	`+-lowering-+.f32`
1846×	`sum3-define`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	33	239
1	93	218
2	305	214
3	956	214
4	2562	214
5	4371	214
6	5814	210
7	7262	210
0	8032	210

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(* eps 1/2)
eps
1/2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
eps
(+ eps (* x (* eps (* eps -1/2))))
eps
(* x (* eps (* eps -1/2)))
x
(* eps (* eps -1/2))
(* eps -1/2)
-1/2
(+ eps (* x (* eps (* -1/2 (+ eps x)))))
eps
(* x (* eps (* -1/2 (+ eps x))))
x
(* eps (* -1/2 (+ eps x)))
(* -1/2 (+ eps x))
-1/2
(+ eps x)
(* eps (+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))))
eps
(+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))))
1
(* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))
x
(* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))
(+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))
-1/2
(* (* x x) (+ 1/24 (* (* x x) -1/720)))
(* x x)
(+ 1/24 (* (* x x) -1/720))
1/24
(* (* x x) -1/720)
-1/720

Outputs
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 eps (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(/ (+ eps (* x 2)) 2)
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
eps
(+ eps (* x (* eps (* eps -1/2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
eps
(* x (* eps (* eps -1/2)))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
x
(* eps (* eps -1/2))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(+ eps (* x (* eps (* -1/2 (+ eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
eps
(* x (* eps (* -1/2 (+ eps x))))
(.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x (+.f64 eps x)))
x
(* eps (* -1/2 (+ eps x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
(* -1/2 (+ eps x))
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
-1/2
#s(literal -1/2 binary64)
(+ eps x)
(+.f64 eps x)
(* eps (+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
eps
(+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
1
#s(literal 1 binary64)
(* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
x
(* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))
(.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))
(+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))
-1/2
#s(literal -1/2 binary64)
(* (* x x) (+ 1/24 (* (* x x) -1/720)))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(* x x)
(*.f64 x x)
(+ 1/24 (* (* x x) -1/720))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
1/24
#s(literal 1/24 binary64)
(* (* x x) -1/720)
(.f64 (.f64 x x) #s(literal -1/720 binary64))
-1/720
#s(literal -1/720 binary64)

localize144.0ms (1.1%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
✓	accuracy	100.0%	(.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
✓	accuracy	99.8%	(.f64 (.f64 x x) #s(literal -1/720 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
✓	accuracy	100.0%	(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
✓	accuracy	99.9%	(.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x))))
✓	accuracy	99.8%	(.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))
✓	accuracy	100.0%	(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
✓	accuracy	100.0%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 eps #s(literal -1/2 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	100.0%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))

Results

98.0ms

256×

valid

Compiler

Compiled 242 to 34 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 31.0ms (54.6% of total)

...c/correct-round.rkt:119:19: 12.0ms (21.1% of total)

ival-add: 9.0ms (15.8% of total)

ival-div: 2.0ms (3.5% of total)

ival-cos: 2.0ms (3.5% of total)

const: 1.0ms (1.8% of total)

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

series29.0ms (0.2%)

Counts

20 → 372

Calls

Call 1

Inputs
#<alt (* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (/ (+ eps (* x 2)) 2)>
#<alt (+ eps (* x (* eps (* eps -1/2))))>
#<alt (* x (* eps (* eps -1/2)))>
#<alt (* eps (* eps -1/2))>
#<alt (* eps -1/2)>
#<alt (+ eps (* x (* eps (* -1/2 (+ eps x)))))>
#<alt (* x (* eps (* -1/2 (+ eps x))))>
#<alt (* eps (* -1/2 (+ eps x)))>
#<alt (* -1/2 (+ eps x))>
#<alt (* eps (+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))))>
#<alt (+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))))>
#<alt (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))>
#<alt (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))>
#<alt (* eps 1/2)>
#<alt (* x 2)>
#<alt (* (* x x) (+ 1/24 (* (* x x) -1/720)))>
#<alt (* (* x x) -1/720)>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (+ eps (* 2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* eps (cos (* 1/2 (- eps (* -2 x)))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 eps))))>
#<alt (+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (+ eps (* 2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt (cos (* 1/2 (- eps (* -2 x))))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/2 (* eps x))))>
#<alt (* eps (+ 1 (* -1/2 (* eps x))))>
#<alt (* eps (+ 1 (* -1/2 (* eps x))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* -1/2 eps)>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))>
#<alt (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))>
#<alt (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* eps (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (* eps (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (* eps (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* eps (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* eps (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1/2 x)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* eps (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 eps)>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (+ (* -1/2 eps) (* -1/2 x))>
#<alt (* -1/2 x)>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* x (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 x)>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))>
#<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 (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* -1/720 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>

Calls

93 calls:

Time	Variable		Point	Expression
5.0ms	x	@	inf	(+ eps (* x (* eps (* -1/2 (+ eps x)))))
1.0ms	eps	@	0	(* eps (+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))))
1.0ms	x	@	-inf	(+ eps (* x (* eps (* -1/2 (+ eps x)))))
1.0ms	eps	@	-inf	(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	eps	@	-inf	(+ eps (* x (* eps (* -1/2 (+ eps x)))))

rewrite349.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

4430×	`-lowering-.f32`
4430×	`-lowering-.f64`
2910×	`/-lowering-/.f32`
2910×	`/-lowering-/.f64`
2302×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	191
1	183	174
2	1593	174
0	8867	174

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 403

Calls

Call 1

Inputs
(* (* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps 1/2) (cos (/ (+ eps (* x 2)) 2)))
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x (* eps (* eps -1/2))))
(* x (* eps (* eps -1/2)))
(* eps (* eps -1/2))
(* eps -1/2)
(+ eps (* x (* eps (* -1/2 (+ eps x)))))
(* x (* eps (* -1/2 (+ eps x))))
(* eps (* -1/2 (+ eps x)))
(* -1/2 (+ eps x))
(* eps (+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))))
(+ 1 (* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))))
(* x (* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720))))))
(* x (+ -1/2 (* (* x x) (+ 1/24 (* (* x x) -1/720)))))
(* eps 1/2)
(* x 2)
(* (* x x) (+ 1/24 (* (* x x) -1/720)))
(* (* x x) -1/720)

Outputs
(.f64 eps (.f64 #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(.f64 eps (.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 (.f64 eps #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) (.f64 eps #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) eps) (.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(.f64 eps (.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 #s(literal 1/2 binary64) (.f64 eps (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 eps #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) eps)
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) eps) #s(literal 1/2 binary64))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 eps eps) (+.f64 eps (.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64)) (/.f64 (/.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (+.f64 eps (*.f64 #s(literal -2 binary64) x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) (+.f64 eps (.f64 #s(literal -2 binary64) x)))) (/.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(neg.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal -2 binary64)))
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -2 binary64))
(/.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) (.f64 #s(literal 2 binary64) (+.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) (.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 #s(literal -2 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps))))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))))
(/.f64 (.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64)) (+.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps))))
(/.f64 (.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/2 binary64)) (+.f64 eps (*.f64 #s(literal -2 binary64) x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64))) #s(literal 1/2 binary64))) (neg.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64))) #s(literal 1/2 binary64))) (neg.f64 (+.f64 eps (*.f64 #s(literal -2 binary64) x))))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 2 binary64) (+.f64 eps (*.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1/2 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64))))
(.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal -1 binary64)))
(.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (+.f64 eps (.f64 #s(literal -2 binary64) x)) (+.f64 eps (.f64 #s(literal -2 binary64) x))))
(.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 eps (.f64 x #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (.f64 eps eps) (.f64 (.f64 x x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 #s(literal -2 binary64) x))))
(.f64 (/.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps))) #s(literal 2 binary64)) (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) (+.f64 (.f64 eps eps) (.f64 (.f64 x #s(literal 2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) eps)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) eps)
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))) (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))))
(-.f64 (/.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))) (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) eps)) (/.f64 (.f64 eps eps) (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) eps)))
(fma.f64 eps #s(literal 1 binary64) (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) x) eps)
(fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 eps x) eps)
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) x eps)
(fma.f64 #s(literal 1 binary64) eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 (.f64 eps eps) (.f64 x #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 eps x) (.f64 eps #s(literal -1/2 binary64)) eps)
(fma.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) eps eps)
(fma.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) eps eps)
(fma.f64 (.f64 x (.f64 eps eps)) #s(literal -1/2 binary64) eps)
(fma.f64 (.f64 (.f64 eps x) eps) #s(literal -1/2 binary64) eps)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) eps))) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
(/.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64))))) (+.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) eps))))
(/.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64))))) (+.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))) (-.f64 (.f64 eps eps) (.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))) (-.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) eps))) (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/8 binary64))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))))))
(/.f64 (neg.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)))))) (neg.f64 (+.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) eps)))))
(/.f64 (neg.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)))))) (neg.f64 (+.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))) (-.f64 (.f64 eps eps) (.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))))) (neg.f64 (-.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))) (.f64 eps eps)) (-.f64 (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) eps))
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(/.f64 (neg.f64 (+.f64 (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))) (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x (.f64 x (*.f64 x #s(literal -1/720 binary64))))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))))) (neg.f64 (-.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)))))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)))) (.f64 x x))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (.f64 x x))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/13824 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))) (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64)))))) (-.f64 (.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 x #s(literal 1/24 binary64)))) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))))) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))) x)
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/720 binary64)) x)

simplify269.0ms (2%)

Algorithm

1×	egg-herbie

Rules

4552×	`-lowering-.f32`
4552×	`-lowering-.f64`
2360×	`+-lowering-+.f64`
2360×	`+-lowering-+.f32`
1872×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	3440
1	999	3156
2	3128	3118
3	6919	3118
0	8040	3118

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(* eps (cos (* 1/2 eps)))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* 1/2 (* eps (cos (* 1/2 eps))))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
(cos (* 1/2 (- eps (* -2 x))))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
eps
(* eps (+ 1 (* -1/2 (* eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* -1/2 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 (pow eps 2))
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* -1/2 eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))
(* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))
(* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1/2 (* eps (pow x 2)))
(* eps (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* eps (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* (pow eps 2) (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1/2 (* eps x))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* -1/2 x)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 eps)
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* eps (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 eps)
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))
(* -1/2 eps)
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(+ (* -1/2 eps) (* -1/2 x))
(* -1/2 x)
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* x (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 x)
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
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)))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/2 x)
(* x (- (* 1/24 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* -1/720 (pow x 5))
(* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 5) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 5))
(* -1 (* (pow x 5) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2))))))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/48 binary64))) #s(literal -1/2 binary64)))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 eps)))
(.f64 eps (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(.f64 eps (-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+.f64 (.f64 eps (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (.f64 eps (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(+.f64 (.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal 1/6 binary64))))) (.f64 x x)) (.f64 eps (-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (+ eps (* 2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 (- eps (* -2 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos x)))
(.f64 (cos.f64 x) (.f64 eps #s(literal 1/2 binary64)))
(* eps (+ (* -1/4 (* eps (sin x))) (* 1/2 (cos x))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 (sin.f64 x) (.f64 eps #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* -1/16 (* eps (cos x)))))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) (.f64 eps #s(literal -1/4 binary64))) (.f64 (cos.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal -1/16 binary64))) #s(literal 1/2 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* 1/96 (* eps (sin x)))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/16 binary64))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/96 binary64))) #s(literal -1/4 binary64)))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 eps))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
(+ (* -1/2 (* eps (* x (sin (* 1/2 eps))))) (* 1/2 (* eps (cos (* 1/2 eps)))))
(.f64 eps (+.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* -1/4 (* eps (* x (cos (* 1/2 eps))))))))
(+.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal -1/4 binary64))))))
(+ (* 1/2 (* eps (cos (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/4 (* eps (cos (* 1/2 eps)))) (* 1/12 (* eps (* x (sin (* 1/2 eps))))))))))
(+.f64 (.f64 (.f64 eps (+.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -1/4 binary64)) (.f64 (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 1/12 binary64)))) (.f64 x x)) (.f64 eps (+.f64 (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (+ eps (* 2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 (* eps (cos (* 1/2 (- eps (* -2 x))))))
(.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal -1/8 binary64))) #s(literal 1 binary64)) (cos.f64 x)))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/48 binary64))) #s(literal -1/2 binary64))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 eps))
(cos.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (-.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(+.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (+.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64))))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (+ eps (* 2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (* 1/2 (- eps (* -2 x))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
x
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (/ x eps)))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* eps (+ 1/2 (/ x eps)))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* eps (+ 1/2 (/ x eps)))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+ x (* 1/2 eps))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
(* x (+ 1 (* 1/2 (/ eps x))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
eps
(* eps (+ 1 (* -1/2 (* eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 eps x))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 eps x)))
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(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))

eval89.0ms (0.7%)

Compiler: Compiled 19776 to 1871 computations (90.5% saved)

prune80.0ms (0.6%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	767	8	775
Fresh	4	2	6
Picked	3	2	5
Done	0	2	2
Total	774	14	788

Accuracy

100.0%

Counts

788 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.5%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
	99.0%	(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
	98.8%	(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
✓	98.4%	(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
✓	100.0%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
▶	99.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
	99.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
	99.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))) x) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))))
▶	98.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
▶	98.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
	99.8%	(.f64 eps (.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64)))))
▶	100.0%	(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
✓	99.5%	(*.f64 eps (cos.f64 x))
✓	98.4%	eps

Compiler

Compiled 443 to 260 computations (41.3% saved)

simplify210.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))
✓	cost-diff	256	(-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))))
✓	cost-diff	1152	(/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
✓	cost-diff	0	(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (.f64 x x)))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
✓	cost-diff	0	(*.f64 (+.f64 eps x) x)
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 (+.f64 eps x) x))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 eps x) x)))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
✓	cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
✓	cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
✓	cost-diff	0	(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
✓	cost-diff	0	(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
✓	cost-diff	0	(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))

Rules

4902×	`-lowering-.f32`
4902×	`-lowering-.f64`
1292×	`/-lowering-/.f32`
1292×	`/-lowering-/.f64`
1230×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	336
1	121	313
2	378	301
3	1740	279
4	4988	269
0	8214	269

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* eps (cos (+ x (* eps 1/2))))
eps
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
(* eps 1/2)
1/2
(* eps (+ 1 (* x (* x -1/2))))
eps
(+ 1 (* x (* x -1/2)))
1
(* x (* x -1/2))
x
(* x -1/2)
-1/2
(* eps (+ 1 (* -1/2 (* (+ eps x) x))))
eps
(+ 1 (* -1/2 (* (+ eps x) x)))
1
(* -1/2 (* (+ eps x) x))
-1/2
(* (+ eps x) x)
(+ eps x)
x
(* eps (+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))))
eps
(+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x)))
1
(* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))
(+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720))))))
-1/2
(* x (* x (+ 1/24 (* x (* x -1/720)))))
x
(* x (+ 1/24 (* x (* x -1/720))))
(+ 1/24 (* x (* x -1/720)))
1/24
(* x (* x -1/720))
(* x -1/720)
-1/720
(* x x)
(/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))
1
(/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))))
(- eps (* x (* eps (* eps -1/2))))
eps
(* x (* eps (* eps -1/2)))
x
(* eps (* eps -1/2))
(* eps -1/2)
-1/2
(- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))
(* eps eps)
(* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))
(* x (* x (* eps (* eps -1/2))))

Outputs
(* eps (cos (+ x (* eps 1/2))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
eps
(cos (+ x (* eps 1/2)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(+ x (* eps 1/2))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
x
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(* eps (+ 1 (* x (* x -1/2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
eps
(+ 1 (* x (* x -1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
1
#s(literal 1 binary64)
(* x (* x -1/2))
(.f64 x (.f64 x #s(literal -1/2 binary64)))
x
(* x -1/2)
(*.f64 x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(* eps (+ 1 (* -1/2 (* (+ eps x) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
eps
(+ 1 (* -1/2 (* (+ eps x) x)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x)))
1
#s(literal 1 binary64)
(* -1/2 (* (+ eps x) x))
(.f64 (.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))
-1/2
#s(literal -1/2 binary64)
(* (+ eps x) x)
(*.f64 x (+.f64 eps x))
(+ eps x)
(+.f64 eps x)
x
(* eps (+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))))) (*.f64 x x))))
eps
(+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x)))
(+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))))) (.f64 x x)))
1
#s(literal 1 binary64)
(* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))
(.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))))) (.f64 x x))
(+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720))))))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x))))))
-1/2
#s(literal -1/2 binary64)
(* x (* x (+ 1/24 (* x (* x -1/720)))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))))
x
(* x (+ 1/24 (* x (* x -1/720))))
(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (*.f64 x x))))
(+ 1/24 (* x (* x -1/720)))
(+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (.f64 x x)))
1/24
#s(literal 1/24 binary64)
(* x (* x -1/720))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(* x -1/720)
(*.f64 x #s(literal -1/720 binary64))
-1/720
#s(literal -1/720 binary64)
(* x x)
(*.f64 x x)
(/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
1
#s(literal 1 binary64)
(/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))))
(/.f64 (/.f64 #s(literal 1 binary64) eps) (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(- eps (* x (* eps (* eps -1/2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 eps (*.f64 x #s(literal 1/2 binary64)))))
eps
(* x (* eps (* eps -1/2)))
(.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
x
(* eps (* eps -1/2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 eps eps) #s(literal -1/4 binary64)))))
(* eps eps)
(*.f64 eps eps)
(* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))
(.f64 (.f64 eps eps) (.f64 (.f64 x x) (.f64 (.f64 eps eps) #s(literal 1/4 binary64))))
(* x (* x (* eps (* eps -1/2))))
(.f64 eps (.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64)))))

localize163.0ms (1.2%)

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64)))))
✓	accuracy	99.9%	(.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
✓	accuracy	53.1%	(/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))))))
✓	accuracy	99.8%	(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal -1/720 binary64)))
✓	accuracy	99.6%	(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
✓	accuracy	99.6%	(*.f64 x #s(literal -1/720 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 (+.f64 eps x) x)))
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (.f64 (+.f64 eps x) x))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
✓	accuracy	99.8%	(*.f64 (+.f64 eps x) x)
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
✓	accuracy	100.0%	(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))

Results

106.0ms

256×

valid

Compiler

Compiled 343 to 41 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-mult: 37.0ms (59.1% of total)

ival-add: 9.0ms (14.4% of total)

...c/correct-round.rkt:119:19: 7.0ms (11.2% of total)

ival-sub: 3.0ms (4.8% of total)

ival-div: 3.0ms (4.8% of total)

ival-cos: 2.0ms (3.2% of total)

const: 1.0ms (1.6% of total)

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

series27.0ms (0.2%)

Counts

26 → 492

Calls

Call 1

Inputs
#<alt (* eps (cos (+ x (* eps 1/2))))>
#<alt (cos (+ x (* eps 1/2)))>
#<alt (+ x (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (* eps (+ 1 (* x (* x -1/2))))>
#<alt (+ 1 (* x (* x -1/2)))>
#<alt (* x (* x -1/2))>
#<alt (* x -1/2)>
#<alt (* eps (+ 1 (* -1/2 (* (+ eps x) x))))>
#<alt (+ 1 (* -1/2 (* (+ eps x) x)))>
#<alt (* -1/2 (* (+ eps x) x))>
#<alt (* (+ eps x) x)>
#<alt (* eps (+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))))>
#<alt (+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x)))>
#<alt (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))>
#<alt (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720))))))>
#<alt (/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))>
#<alt (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))))>
#<alt (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))>
#<alt (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))>
#<alt (* x -1/720)>
#<alt (* x (+ 1/24 (* x (* x -1/720))))>
#<alt (* x (* x -1/720))>
#<alt (* x (* x (+ 1/24 (* x (* x -1/720)))))>
#<alt (* x (* eps (* eps -1/2)))>
#<alt (* x (* x (* eps (* eps -1/2))))>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))>
#<alt (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (- x (* -1/2 eps))))>
#<alt (* eps (cos (* 1/2 eps)))>
#<alt (+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))>
#<alt (+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (+ x (* 1/2 eps))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (* eps (cos (- (* 1/2 eps) (* -1 x))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos (- (* 1/2 eps) (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (+ x (* 1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (cos (- x (* -1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (/ 1 (pow x 2)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))>
#<alt (pow x 2)>
#<alt (+ (* eps x) (pow x 2))>
#<alt (+ (* eps x) (pow x 2))>
#<alt (+ (* eps x) (pow x 2))>
#<alt (* eps x)>
#<alt (* eps (+ x (/ (pow x 2) eps)))>
#<alt (* eps (+ x (/ (pow x 2) eps)))>
#<alt (* eps (+ x (/ (pow x 2) eps)))>
#<alt (* eps x)>
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))>
#<alt (* eps x)>
#<alt (* x (+ eps x))>
#<alt (* x (+ eps x))>
#<alt (* x (+ eps x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* (pow x 2) (+ 1 (/ eps x)))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))>
#<alt (* -1/720 (* eps (pow x 6)))>
#<alt (* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))>
#<alt (* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))>
#<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 (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt -1/2>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/2 (* eps x))))>
#<alt (* eps (+ 1 (* -1/2 (* eps x))))>
#<alt (* eps (+ 1 (* -1/2 (* eps x))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ eps x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))>
#<alt (/ 1 eps)>
#<alt (/ (+ 1 (* 1/2 (* eps x))) eps)>
#<alt (/ (+ 1 (* eps (+ (* 1/4 (* eps (pow x 2))) (* 1/2 x)))) eps)>
#<alt (/ (+ 1 (* eps (+ (* 1/2 x) (* eps (- (* 1/8 (* eps (pow x 3))) (* -1/4 (pow x 2))))))) eps)>
#<alt (/ -2 (* (pow eps 2) x))>
#<alt (* -1 (/ (+ (* 2 (/ 1 x)) (* 4 (/ 1 (* eps (pow x 2))))) (pow eps 2)))>
#<alt (/ (- (* -1 (/ (+ (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* eps (pow x 3))))) eps)) (* 2 (/ 1 x))) (pow eps 2))>
#<alt (/ (- (* -1 (/ (+ (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* eps (pow x 4))))) (pow eps 2))) (+ (* 2 (/ 1 x)) (/ 4 (* eps (pow x 2))))) (pow eps 2))>
#<alt (/ -2 (* (pow eps 2) x))>
#<alt (* -1 (/ (+ (* 2 (/ 1 x)) (* 4 (/ 1 (* eps (pow x 2))))) (pow eps 2)))>
#<alt (/ (- (* -1 (/ (+ (* 8 (/ 1 (* eps (pow x 3)))) (* 4 (/ 1 (pow x 2)))) eps)) (* 2 (/ 1 x))) (pow eps 2))>
#<alt (/ (- (* -1 (/ (+ (* 4 (/ 1 (pow x 2))) (+ (/ 8 (* eps (pow x 3))) (/ 16 (* (pow eps 2) (pow x 4))))) eps)) (* 2 (/ 1 x))) (pow eps 2))>
#<alt (/ 1 eps)>
#<alt (+ (* 1/2 x) (/ 1 eps))>
#<alt (+ (* x (+ 1/2 (* 1/4 (* eps x)))) (/ 1 eps))>
#<alt (+ (* x (+ 1/2 (* x (- (* 1/8 (* (pow eps 2) x)) (* -1/4 eps))))) (/ 1 eps))>
#<alt (/ -2 (* (pow eps 2) x))>
#<alt (* -1 (/ (+ (* 4 (/ 1 (* (pow eps 3) x))) (* 2 (/ 1 (pow eps 2)))) x))>
#<alt (/ (- (* -1 (/ (+ (* 4 (/ 1 (pow eps 3))) (* 8 (/ 1 (* (pow eps 4) x)))) x)) (* 2 (/ 1 (pow eps 2)))) x)>
#<alt (/ (- (* -1 (/ (+ (* 8 (/ 1 (pow eps 4))) (* 16 (/ 1 (* (pow eps 5) x)))) (pow x 2))) (+ (* 2 (/ 1 (pow eps 2))) (/ 4 (* (pow eps 3) x)))) x)>
#<alt (/ -2 (* (pow eps 2) x))>
#<alt (* -1 (/ (+ (* 4 (/ 1 (* (pow eps 3) x))) (* 2 (/ 1 (pow eps 2)))) x))>
#<alt (* -1 (/ (+ (* 2 (/ 1 (pow eps 2))) (+ (/ 4 (* (pow eps 3) x)) (/ 8 (* (pow eps 4) (pow x 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 16 (/ 1 (* (pow eps 5) x))) (* 8 (/ 1 (pow eps 4)))) x)) (* 4 (/ 1 (pow eps 3)))) x)) (* 2 (/ 1 (pow eps 2)))) x))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* -1/4 (* (pow eps 2) (pow x 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -1/4 (* (pow eps 2) (pow x 2)))))>
#<alt (* (pow eps 2) (+ 1 (* -1/4 (* (pow eps 2) (pow x 2)))))>
#<alt (* -1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))>
#<alt (* -1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))>
#<alt (* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))>
#<alt (pow eps 2)>
#<alt (+ (* -1/4 (* (pow eps 4) (pow x 2))) (pow eps 2))>
#<alt (+ (* -1/4 (* (pow eps 4) (pow x 2))) (pow eps 2))>
#<alt (+ (* -1/4 (* (pow eps 4) (pow x 2))) (pow eps 2))>
#<alt (* -1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))>
#<alt (* -1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))>
#<alt (* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* 1/4 (* (pow eps 4) (pow x 2)))>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* 1/24 x)>
#<alt (* x (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* x (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* x (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* -1/720 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* -1/720 (pow x 2))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>
#<alt (* -1/2 (* (pow eps 2) (pow x 2)))>

Calls

123 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(* x -1/2)
1.0ms	eps	@	inf	(/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))
1.0ms	x	@	inf	(/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))
1.0ms	x	@	0	(/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))
1.0ms	eps	@	0	(/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))

rewrite406.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

4032×	`-lowering-.f32`
4032×	`-lowering-.f64`
3592×	`/-lowering-/.f32`
3592×	`/-lowering-/.f64`
1992×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	282
1	257	213
2	2202	209
0	8482	209

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 727

Calls

Call 1

Inputs
(* eps (cos (+ x (* eps 1/2))))
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
(* eps 1/2)
(* eps (+ 1 (* x (* x -1/2))))
(+ 1 (* x (* x -1/2)))
(* x (* x -1/2))
(* x -1/2)
(* eps (+ 1 (* -1/2 (* (+ eps x) x))))
(+ 1 (* -1/2 (* (+ eps x) x)))
(* -1/2 (* (+ eps x) x))
(* (+ eps x) x)
(* eps (+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))))
(+ 1 (* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x)))
(* (+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720)))))) (* x x))
(+ -1/2 (* x (* x (+ 1/24 (* x (* x -1/720))))))
(/ 1 (/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))))
(/ (- eps (* x (* eps (* eps -1/2)))) (- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))))
(- (* eps eps) (* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2))))))
(* (* eps (* eps -1/2)) (* x (* x (* eps (* eps -1/2)))))
(* x -1/720)
(* x (+ 1/24 (* x (* x -1/720))))
(* x (* x -1/720))
(* x (* x (+ 1/24 (* x (* x -1/720)))))
(* x (* eps (* eps -1/2)))
(* x (* x (* eps (* eps -1/2))))

Outputs
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) eps)
(+.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (+.f64 (.f64 (neg.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 x)) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (neg.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (cos.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) (cos.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (.f64 eps #s(literal -1/2 binary64)))))) (.f64 (sin.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) (sin.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (.f64 eps #s(literal -1/2 binary64)))))))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))))
(fma.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (neg.f64 (.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (neg.f64 (.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (neg.f64 (sin.f64 x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (+.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 4 binary64))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (cos.f64 (+.f64 x (*.f64 eps #s(literal -1/2 binary64))))))
(+.f64 x (*.f64 eps #s(literal 1/2 binary64)))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (+.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (/.f64 (.f64 x x) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(fma.f64 eps #s(literal 1/2 binary64) x)
(fma.f64 #s(literal 1/2 binary64) eps x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 eps #s(literal 1/2 binary64)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 eps #s(literal 1/2 binary64)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/8 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))) (-.f64 (.f64 x x) (.f64 (.f64 eps eps) #s(literal 1/4 binary64))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (+.f64 (.f64 x x) (.f64 (.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))) (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 x x) (.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps eps) #s(literal 1/4 binary64))) (+.f64 x (.f64 eps #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 (.f64 x x) (.f64 (.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64)))) (neg.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 x x) (.f64 x (.f64 eps #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)))) (neg.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (.f64 eps #s(literal -1/2 binary64)))) (.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))) (.f64 (.f64 eps eps) #s(literal 1/4 binary64)))) (.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 x (.f64 eps #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/8 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 x x) (.f64 (.f64 eps #s(literal 1/2 binary64)) (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))))
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(.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x))) x)
(.f64 (.f64 (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))) x)
(.f64 (.f64 (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 eps x)) (*.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) eps) (*.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (*.f64 eps eps)) #s(literal -1/2 binary64))
(.f64 (pow.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) #s(literal 2 binary64)) (.f64 eps eps))
(.f64 (pow.f64 (.f64 x (*.f64 eps eps)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(.f64 (pow.f64 (.f64 (*.f64 eps x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 eps eps))
(*.f64 x #s(literal -1/720 binary64))
(*.f64 #s(literal -1/720 binary64) x)
(+.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) (.f64 x #s(literal 1/24 binary64)))
(+.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)))
(-.f64 (/.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)))) (/.f64 (.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x))) (-.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)))))
(fma.f64 x #s(literal 1/24 binary64) (.f64 (.f64 x #s(literal -1/720 binary64)) (*.f64 x x)))
(fma.f64 x (.f64 x (.f64 x #s(literal -1/720 binary64))) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 #s(literal 1/24 binary64) x (.f64 (.f64 x #s(literal -1/720 binary64)) (*.f64 x x)))
(fma.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) x (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal -1/720 binary64)) (*.f64 x #s(literal 1/24 binary64)))
(fma.f64 (.f64 x (.f64 x x)) #s(literal -1/720 binary64) (*.f64 x #s(literal 1/24 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64)))) (+.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x))) (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal -1/720 binary64)) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)))) (-.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x))))
(/.f64 (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64)))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))) (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64))) x) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) x) (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(/.f64 (neg.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64))))) (neg.f64 (+.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (-.f64 (.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x))) (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal -1/720 binary64)) (*.f64 x x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 x #s(literal 1/24 binary64))) (.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x))))) (neg.f64 (-.f64 (.f64 x #s(literal 1/24 binary64)) (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64))))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64))) x)) (neg.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) x)) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64))))))
(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))) x)
(.f64 x (.f64 x #s(literal -1/720 binary64)))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal -1/720 binary64)) x)
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(+.f64 (.f64 x (.f64 x #s(literal 1/24 binary64))) (.f64 x (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x))))
(+.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
(+.f64 (.f64 (.f64 x #s(literal 1/24 binary64)) x) (.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (.f64 x x)) x))
(+.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 x x)))
(+.f64 (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 x x)) (.f64 #s(literal 1/24 binary64) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/24 binary64)) (.f64 x (.f64 (.f64 x #s(literal -1/720 binary64)) (*.f64 x x))))
(fma.f64 #s(literal 1/24 binary64) (.f64 x x) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (*.f64 x x)))
(fma.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 x x) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))
(fma.f64 (.f64 x x) #s(literal 1/24 binary64) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))
(fma.f64 (.f64 x x) (.f64 x (.f64 x #s(literal -1/720 binary64))) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))
(fma.f64 (.f64 x #s(literal 1/24 binary64)) x (.f64 (.f64 (.f64 x #s(literal -1/720 binary64)) (*.f64 x x)) x))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64)))) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))) (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/13824 binary64) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/373248000 binary64))))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x #s(literal -1/720 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal -1/720 binary64))) #s(literal 1/24 binary64))))))
(/.f64 (neg.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))
(.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))
(.f64 (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))) x)
(.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))
(.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 eps x))
(.f64 (.f64 eps (*.f64 eps #s(literal -1/2 binary64))) x)
(.f64 (.f64 eps eps) (*.f64 x #s(literal -1/2 binary64)))
(.f64 (.f64 eps x) (*.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 x (*.f64 eps #s(literal -1/2 binary64))) eps)
(.f64 (.f64 x (*.f64 eps eps)) #s(literal -1/2 binary64))
(.f64 (.f64 (*.f64 eps x) eps) #s(literal -1/2 binary64))
(.f64 (.f64 (*.f64 eps x) #s(literal -1/2 binary64)) eps)
(.f64 x (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x x))
(.f64 (.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) x)) x)
(.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (.f64 x x))) eps)
(.f64 (.f64 eps x) (.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 (.f64 (.f64 x x) (.f64 eps eps)) #s(literal -1/2 binary64))
(.f64 (.f64 x (.f64 eps x)) (.f64 eps #s(literal -1/2 binary64)))
(.f64 (.f64 (.f64 x x) eps) (.f64 eps #s(literal -1/2 binary64)))

simplify304.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

5386×	`-lowering-.f32`
5386×	`-lowering-.f64`
2618×	`+-lowering-+.f64`
2618×	`+-lowering-+.f32`
1558×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	402	4615
1	1313	4421
2	3818	4331
0	8409	4331

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (- x (* -1/2 eps))))
(* eps (cos (* 1/2 eps)))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* x (+ (* -1/2 (* eps (cos (* 1/2 eps)))) (* 1/6 (* eps (* x (sin (* 1/2 eps))))))))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (+ x (* 1/2 eps))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(* eps (cos (- (* 1/2 eps) (* -1 x))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos (- (* 1/2 eps) (* -1 x)))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (+ x (* 1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(cos (- x (* -1/2 eps)))
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* -1/2 (pow x 2)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* eps (+ (* -1/2 x) (* -1/2 (/ (pow x 2) eps))))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps)))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* x (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))
(pow x 2)
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(+ (* eps x) (pow x 2))
(* eps x)
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(* eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(* eps x)
(* x (+ eps x))
(* x (+ eps x))
(* x (+ eps x))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
(* -1/720 (* eps (pow x 6)))
(* (pow x 6) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2)))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (* 1/24 (/ eps (pow x 2))))))
(* (pow x 6) (+ (* -1/2 (/ eps (pow x 4))) (+ (* -1/720 eps) (+ (* 1/24 (/ eps (pow x 2))) (/ eps (pow x 6))))))
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)))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
eps
(* eps (+ 1 (* -1/2 (* eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(* eps (+ 1 (* -1/2 (* eps x))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ 1 eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* x (+ (* -1/2 (pow eps 2)) (/ eps x)))
(* -1/2 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2)))))
(/ 1 eps)
(/ (+ 1 (* 1/2 (* eps x))) eps)
(/ (+ 1 (* eps (+ (* 1/4 (* eps (pow x 2))) (* 1/2 x)))) eps)
(/ (+ 1 (* eps (+ (* 1/2 x) (* eps (- (* 1/8 (* eps (pow x 3))) (* -1/4 (pow x 2))))))) eps)
(/ -2 (* (pow eps 2) x))
(* -1 (/ (+ (* 2 (/ 1 x)) (* 4 (/ 1 (* eps (pow x 2))))) (pow eps 2)))
(/ (- (* -1 (/ (+ (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* eps (pow x 3))))) eps)) (* 2 (/ 1 x))) (pow eps 2))
(/ (- (* -1 (/ (+ (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* eps (pow x 4))))) (pow eps 2))) (+ (* 2 (/ 1 x)) (/ 4 (* eps (pow x 2))))) (pow eps 2))
(/ -2 (* (pow eps 2) x))
(* -1 (/ (+ (* 2 (/ 1 x)) (* 4 (/ 1 (* eps (pow x 2))))) (pow eps 2)))
(/ (- (* -1 (/ (+ (* 8 (/ 1 (* eps (pow x 3)))) (* 4 (/ 1 (pow x 2)))) eps)) (* 2 (/ 1 x))) (pow eps 2))
(/ (- (* -1 (/ (+ (* 4 (/ 1 (pow x 2))) (+ (/ 8 (* eps (pow x 3))) (/ 16 (* (pow eps 2) (pow x 4))))) eps)) (* 2 (/ 1 x))) (pow eps 2))
(/ 1 eps)
(+ (* 1/2 x) (/ 1 eps))
(+ (* x (+ 1/2 (* 1/4 (* eps x)))) (/ 1 eps))
(+ (* x (+ 1/2 (* x (- (* 1/8 (* (pow eps 2) x)) (* -1/4 eps))))) (/ 1 eps))
(/ -2 (* (pow eps 2) x))
(* -1 (/ (+ (* 4 (/ 1 (* (pow eps 3) x))) (* 2 (/ 1 (pow eps 2)))) x))
(/ (- (* -1 (/ (+ (* 4 (/ 1 (pow eps 3))) (* 8 (/ 1 (* (pow eps 4) x)))) x)) (* 2 (/ 1 (pow eps 2)))) x)
(/ (- (* -1 (/ (+ (* 8 (/ 1 (pow eps 4))) (* 16 (/ 1 (* (pow eps 5) x)))) (pow x 2))) (+ (* 2 (/ 1 (pow eps 2))) (/ 4 (* (pow eps 3) x)))) x)
(/ -2 (* (pow eps 2) x))
(* -1 (/ (+ (* 4 (/ 1 (* (pow eps 3) x))) (* 2 (/ 1 (pow eps 2)))) x))
(* -1 (/ (+ (* 2 (/ 1 (pow eps 2))) (+ (/ 4 (* (pow eps 3) x)) (/ 8 (* (pow eps 4) (pow x 2))))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 16 (/ 1 (* (pow eps 5) x))) (* 8 (/ 1 (pow eps 4)))) x)) (* 4 (/ 1 (pow eps 3)))) x)) (* 2 (/ 1 (pow eps 2)))) x))
(pow eps 2)
(* (pow eps 2) (+ 1 (* -1/4 (* (pow eps 2) (pow x 2)))))
(* (pow eps 2) (+ 1 (* -1/4 (* (pow eps 2) (pow x 2)))))
(* (pow eps 2) (+ 1 (* -1/4 (* (pow eps 2) (pow x 2)))))
(* -1/4 (* (pow eps 4) (pow x 2)))
(* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))
(* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))
(* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))
(* -1/4 (* (pow eps 4) (pow x 2)))
(* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))
(* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))
(* (pow eps 4) (- (/ 1 (pow eps 2)) (* 1/4 (pow x 2))))
(pow eps 2)
(+ (* -1/4 (* (pow eps 4) (pow x 2))) (pow eps 2))
(+ (* -1/4 (* (pow eps 4) (pow x 2))) (pow eps 2))
(+ (* -1/4 (* (pow eps 4) (pow x 2))) (pow eps 2))
(* -1/4 (* (pow eps 4) (pow x 2)))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))
(* -1/4 (* (pow eps 4) (pow x 2)))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))
(* (pow x 2) (- (/ (pow eps 2) (pow x 2)) (* 1/4 (pow eps 4))))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* 1/24 x)
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 3))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 3))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* -1/720 (pow x 2))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 4))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) x))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))
(* -1/2 (* (pow eps 2) (pow x 2)))

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/8 (* eps (cos x)))))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) #s(literal 1 binary64)) (cos.f64 x))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x)))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 binary64))) (.f64 (sin.f64 x) (+.f64 (.f64 eps (*.f64 eps #s(literal 1/48 binary64))) #s(literal -1/2 binary64)))))))
(* eps (cos (+ x (* 1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (+ x (* 1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (+ x (* 1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (+ x (* 1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (- x (* -1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (- x (* -1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (- x (* -1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (- x (* -1/2 eps))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(* eps (cos (* 1/2 eps)))
(.f64 eps (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (* -1 (* eps (* x (sin (* 1/2 eps))))) (* eps (cos (* 1/2 eps))))
(.f64 eps (-.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+ (* eps (cos (* 1/2 eps))) (* x (+ (* -1 (* eps (sin (* 1/2 eps)))) (* -1/2 (* eps (* x (cos (* 1/2 eps))))))))
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(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(* 1/4 (* (pow eps 4) (pow x 2)))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
(* x (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64))))
(* -1/720 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/720 binary64)))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* (pow x 3) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1/720 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/720 binary64)))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1 (* (pow x 3) (- 1/720 (* 1/24 (/ 1 (pow x 2))))))
(.f64 (.f64 x x) (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (.f64 x x)))))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* -1/720 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/720 binary64))
(* 1/24 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(* (pow x 2) (+ 1/24 (* -1/720 (pow x 2))))
(.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(* -1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* -1/720 (pow x 4))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* (pow x 4) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) x))
(.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))
(* -1/2 (* (pow eps 2) (pow x 2)))
(.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps (.f64 x x))))

eval185.0ms (1.4%)

Compiler: Compiled 43258 to 2949 computations (93.2% saved)

prune125.0ms (0.9%)

Pruning

16 alts after pruning (9 fresh and 7 done)

	Pruned	Kept	Total
New	1247	6	1253
Fresh	2	3	5
Picked	2	3	5
Done	0	4	4
Total	1251	16	1267

Accuracy

100.0%

Counts

1267 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	25.0%	(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x (.f64 (.f64 eps eps) #s(literal 1/2 binary64))))) (.f64 (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))) (.f64 eps (-.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))) (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))
	98.0%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
	98.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
	99.0%	(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
	99.0%	(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)
	98.8%	(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
✓	98.4%	(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
✓	100.0%	(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
	99.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
	99.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))) x) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))))
✓	98.8%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
✓	98.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
	99.8%	(.f64 eps (.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64)))))
✓	100.0%	(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
✓	99.5%	(*.f64 eps (cos.f64 x))
✓	98.4%	eps

Compiler

Compiled 801 to 331 computations (58.7% saved)

regimes30.0ms (0.2%)

Counts

31 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)
(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))) x) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x (.f64 (.f64 eps eps) #s(literal 1/2 binary64))))) (.f64 (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))) (.f64 eps (-.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))) (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(.f64 eps (.f64 eps (-.f64 (/.f64 (cos.f64 x) eps) (*.f64 (sin.f64 x) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes26.0ms (0.2%)

Counts

28 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)
(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))) x) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x (.f64 (.f64 eps eps) #s(literal 1/2 binary64))))) (.f64 (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))) (.f64 eps (-.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))) (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 x (*.f64 eps #s(literal -1/2 binary64)))))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

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

Calls

3 calls:

8.0ms	x
7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
7.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes16.0ms (0.1%)

Counts

23 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)
(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))) x) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x (.f64 (.f64 eps eps) #s(literal 1/2 binary64))))) (.f64 (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))) (.f64 eps (-.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))) (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))

Outputs
(*.f64 eps (cos.f64 x))

Calls

2 calls:

7.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes36.0ms (0.3%)

Counts

22 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)
(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
(+.f64 eps (.f64 (.f64 x x) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps (.f64 x x)) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))))) (-.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (.f64 x (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))))) x) (-.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))))))))))
(/.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x (.f64 (.f64 eps eps) #s(literal 1/2 binary64))))) (.f64 (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))) (.f64 eps (-.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))) (.f64 eps (+.f64 eps (.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))))))
(sin.f64 eps)

Outputs
(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)

Calls

2 calls:

6.0ms	eps
6.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

16 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)

Outputs
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)

Calls

2 calls:

5.0ms	eps
5.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

15 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`eps`
99.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes13.0ms (0.1%)

Counts

14 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))

Calls

2 calls:

8.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes9.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

Inputs
eps
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 eps #s(literal -1/2 binary64)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 eps (.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal 1/24 binary64))) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps x) #s(literal 1/4 binary64)))))) eps))

Outputs
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))

Calls

2 calls:

4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes8.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
3.0ms	eps

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	eps
2.0ms	x

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 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
eps

Outputs
eps

Calls

2 calls:

3.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

76×	`*-commutative_binary64`
36×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	163
1	126	163

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 x))
(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
eps

Outputs
(.f64 eps (+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps (sin.f64 x)))))
(.f64 eps (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))
(*.f64 eps (cos.f64 x))
(+.f64 (.f64 x (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))) eps)) eps)
(+.f64 eps (.f64 x (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal -1/720 binary64)))))))))))
(+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (.f64 x x))) (*.f64 x x))) eps)
(+.f64 eps (.f64 eps (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64)))) (*.f64 x x))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x #s(literal -1/720 binary64))))))) (*.f64 x x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/720 binary64)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 #s(literal -1/720 binary64) (*.f64 x x)))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/24 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x)))))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(+.f64 eps (.f64 x (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x))))
eps

soundness2.0s (15%)

Rules

5438×	`-lowering-.f32`
5438×	`-lowering-.f64`
4552×	`-lowering-.f32`
4552×	`-lowering-.f64`
4430×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	368	2994
1	1233	2729
2	4048	2715
0	8142	2715
0	6	16
1	49	16
2	402	16
3	5232	16
0	8309	16
0	40	282
1	257	213
2	2202	209
0	8482	209
0	33	191
1	183	174
2	1593	174
0	8867	174
0	299	3440
1	999	3156
2	3128	3118
3	6919	3118
0	8040	3118
0	107	488
1	327	465
2	963	459
3	3572	459
0	8267	459

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

Compiler

Compiled 523 to 310 computations (40.7% saved)

preprocess72.0ms (0.5%)

Compiler: Compiled 378 to 164 computations (56.6% 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

analyze75.0ms (0.5%)

sample6.7s (48.9%)

preprocess52.0ms (0.4%)

explain88.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify18.0ms (0.1%)

localize34.0ms (0.3%)

series4.0ms (0%)

rewrite334.0ms (2.4%)

simplify259.0ms (1.9%)

eval30.0ms (0.2%)

prune31.0ms (0.2%)

simplify191.0ms (1.4%)

localize199.0ms (1.5%)

series34.0ms (0.3%)

rewrite348.0ms (2.5%)

simplify284.0ms (2.1%)

eval73.0ms (0.5%)

prune56.0ms (0.4%)

simplify187.0ms (1.4%)

localize144.0ms (1.1%)

series29.0ms (0.2%)

rewrite349.0ms (2.6%)

simplify269.0ms (2%)

eval89.0ms (0.7%)

prune80.0ms (0.6%)

simplify210.0ms (1.5%)

localize163.0ms (1.2%)

series27.0ms (0.2%)

rewrite406.0ms (3%)

simplify304.0ms (2.2%)

eval185.0ms (1.4%)

prune125.0ms (0.9%)

regimes30.0ms (0.2%)

regimes26.0ms (0.2%)

regimes16.0ms (0.1%)

regimes36.0ms (0.3%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes4.0ms (0%)

simplify10.0ms (0.1%)

soundness2.0s (15%)

preprocess72.0ms (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