Metrics for 2sin (example 3.3)

analyze64.0ms (0.4%)

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: 36.0ms

ival-sin: 8.0ms (22.2% of total)

ival-add: 7.0ms (19.4% of total)

...c/correct-round.rkt:119:19: 7.0ms (19.4% of total)

ival-mult: 3.0ms (8.3% of total)

ival-fabs: 3.0ms (8.3% of total)

ival-<=: 3.0ms (8.3% of total)

ival-sub: 2.0ms (5.5% of total)

ival-and: 2.0ms (5.5% of total)

ival-<: 2.0ms (5.5% of total)

const: 1.0ms (2.8% of total)

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

sample7.4s (48.2%)

Results

3.7s	26157×	0	precondition
1.5s	4475×	1	valid
553.0ms	3781×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 4.1s

ival-sin: 869.0ms (21.1% of total)

...c/correct-round.rkt:119:19: 811.0ms (19.7% of total)

ival-<: 440.0ms (10.7% of total)

ival-add: 405.0ms (9.8% of total)

ival-mult: 333.0ms (8.1% of total)

ival-<=: 316.0ms (7.7% of total)

ival-fabs: 300.0ms (7.3% of total)

ival-sub: 274.0ms (6.6% of total)

ival-and: 197.0ms (4.8% of total)

backward-pass: 135.0ms (3.3% of total)

const: 46.0ms (1.1% of total)

Bogosity

preprocess50.0ms (0.3%)

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))

explain125.0ms (0.8%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
221	1	(6.525831430160861e-203 3.518018886203367e-205)	4	(9.574255707415447e-127 1.2464922274084292e-128)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
2	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`x`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`eps`

Results

70.0ms	278×	1	valid
20.0ms	232×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-add: 24.0ms (50.3% of total)

ival-sin: 13.0ms (27.3% of total)

backward-pass: 7.0ms (14.7% of total)

ival-sub: 4.0ms (8.4% 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
▶	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify21.0ms (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)

localize45.0ms (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	99.9%	(sin.f64 (+.f64 x eps))
✓	accuracy	62.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

27.0ms	139×	1	valid
10.0ms	116×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

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

ival-sin: 6.0ms (39.9% of total)

backward-pass: 4.0ms (26.6% of total)

ival-add: 3.0ms (20% of total)

ival-sub: 2.0ms (13.3% 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	eps	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	inf	(+ x eps)
0.0ms	x	@	-inf	(- (sin (+ x eps)) (sin x))

rewrite298.0ms (2%)

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	406	16
3	5276	16
0	8497	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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x)))))))
(+.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 #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 (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 (+.f64 x eps)) (sin.f64 x))))))
(-.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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x)))))))
(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 #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))))) (neg.f64 (/.f64 (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 (+.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 #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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x)))))))
(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 #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))))) (neg.f64 (/.f64 (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 (+.f64 x eps)) (sin.f64 x)))))))
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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 6 binary64)) (pow.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) #s(literal 3 binary64)))) (+.f64 (pow.f64 (sin.f64 (+.f64 x eps)) #s(literal 4 binary64)) (.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (-.f64 (.f64 (sin.f64 x) (+.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))) (+.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 (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 eps eps) (.f64 x (-.f64 x eps))))))
(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 eps eps) (.f64 x (-.f64 x eps)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 eps eps))) (-.f64 x eps)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 x (-.f64 x eps))))
(/.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 eps eps) (.f64 x (-.f64 x eps)))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 eps 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 eps eps) (.f64 x (-.f64 x eps))) (+.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 eps eps) (.f64 x (-.f64 x eps))) (-.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 eps (.f64 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 eps eps) (.f64 x (-.f64 x 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)))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 eps eps) (.f64 x (-.f64 x 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)))) #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 eps (.f64 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 eps eps) (*.f64 x (-.f64 x eps))))
(/.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 eps eps) (.f64 x (-.f64 x eps))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 eps 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 eps eps) (.f64 x (-.f64 x eps))))) (+.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 eps eps) (.f64 x (-.f64 x eps))))) (-.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 eps (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 x eps))) (+.f64 (.f64 x x) (*.f64 eps eps)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 x eps)) #s(literal -1 binary64))
(.f64 (+.f64 x eps) (.f64 (-.f64 x eps) (/.f64 #s(literal 1 binary64) (-.f64 x eps))))
(*.f64 (+.f64 x eps) (/.f64 (-.f64 x eps) (-.f64 x eps)))
(.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (*.f64 x (-.f64 x eps)))))
(.f64 (+.f64 (.f64 eps eps) (.f64 x (-.f64 x eps))) (.f64 (+.f64 x eps) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 x (-.f64 x eps))))))
(.f64 (+.f64 (.f64 eps eps) (.f64 x (-.f64 x eps))) (/.f64 (+.f64 x eps) (+.f64 (.f64 eps eps) (*.f64 x (-.f64 x eps)))))
(.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 eps eps) (*.f64 x (-.f64 x eps))))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (*.f64 eps eps))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 eps eps) (.f64 x (-.f64 x eps)))) (+.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (-.f64 (.f64 x x) (*.f64 eps eps)))
(.f64 (-.f64 (.f64 eps eps) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 (.f64 x x) (*.f64 eps eps))) (+.f64 x eps))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (.f64 (-.f64 eps x) (.f64 eps (-.f64 eps x))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 eps (.f64 eps eps))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (.f64 (-.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)

simplify224.0ms (1.5%)

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	459
2	964	455
3	3564	455
0	8263	455

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

eval46.0ms (0.3%)

Compiler: Compiled 7060 to 731 computations (89.6% saved)

prune34.0ms (0.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	251	10	261
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	251	11	262

Accuracy

100.0%

Counts

262 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.1%	(/.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)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))))
	62.3%	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
▶	60.9%	(-.f64 (sin.f64 (+.f64 x eps)) (.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))))))))
	60.7%	(-.f64 (sin.f64 (+.f64 x eps)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	60.5%	(-.f64 (sin.f64 (+.f64 x eps)) x)
▶	99.8%	(.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))
▶	99.6%	(.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 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	99.2%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
	98.6%	(*.f64 eps (cos.f64 x))
▶	97.5%	(sin.f64 eps)

Compiler

Compiled 349 to 234 computations (33% saved)

simplify146.0ms (1%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(.f64 (+.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x))
✓	cost-diff	0	(+.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 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
✓	cost-diff	0	(.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 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
✓	cost-diff	0	(.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)))))))
✓	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 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) x)
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))
✓	cost-diff	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))))
✓	cost-diff	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))
✓	cost-diff	128	(+.f64 eps #s(literal 0 binary64))

Rules

2040×	`fnmadd-define`
1900×	`fma-define`
1720×	`sum4-define`
1694×	`fma-lowering-fma.f32`
1694×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	256
1	112	239
2	407	237
3	1811	237
4	5555	237
5	7445	237
0	8598	237

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (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
(sin eps)
eps
(- (sin (+ x eps)) x)
(sin (+ x eps))
(+ x eps)
x
eps
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))
(sin (+ x eps))
(+ x eps)
x
eps
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120))))))
(+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))
1
(* (* x x) (+ -1/6 (* x (* x 1/120))))
(* x x)
(+ -1/6 (* x (* x 1/120)))
-1/6
(* x (* x 1/120))
(* x 1/120)
1/120
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))))
eps
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)))
(* (+ (* (* eps eps) -1/6) 1) (cos x))
(+ (* (* eps eps) -1/6) 1)
(* (* eps eps) -1/6)
(* eps eps)
-1/6
1
(cos x)
x
(* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))
(* eps (sin x))
(sin x)
(+ (* eps (* eps 1/24)) -1/2)
(* eps (* eps 1/24))
(* eps 1/24)
1/24
-1/2

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

localize334.0ms (2.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/24 binary64))
✓	accuracy	99.9%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/120 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
✓	accuracy	62.8%	(-.f64 (sin.f64 (+.f64 x eps)) (.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))))))))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	99.9%	(sin.f64 (+.f64 x eps))
✓	accuracy	63.1%	(-.f64 (sin.f64 (+.f64 x eps)) x)
✓	accuracy	100.0%	(sin.f64 eps)
✓	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	99.9%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))

Results

187.0ms	137×	1	valid
78.0ms	118×	0	valid
2.0ms	1×	3	valid

Compiler

Compiled 297 to 44 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 115.0ms

ival-mult: 38.0ms (33% of total)

...c/correct-round.rkt:119:19: 17.0ms (14.8% of total)

backward-pass: 16.0ms (13.9% of total)

ival-add: 15.0ms (13% of total)

ival-sin: 11.0ms (9.6% of total)

ival-cos: 7.0ms (6.1% of total)

ival-div: 6.0ms (5.2% of total)

ival-sub: 4.0ms (3.5% of total)

const: 1.0ms (0.9% of total)

series33.0ms (0.2%)

Counts

22 → 396

Calls

Call 1

Inputs
#<alt (+ eps 0)>
#<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 (sin eps)>
#<alt (- (sin (+ x eps)) x)>
#<alt (sin (+ x eps))>
#<alt (+ x eps)>
#<alt (- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))>
#<alt (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120))))))>
#<alt (* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))))>
#<alt (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)))>
#<alt (* (+ (* (* eps eps) -1/6) 1) (cos x))>
#<alt (+ (* (* eps eps) -1/6) 1)>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* x 2)>
#<alt (* (* x x) (+ -1/6 (* x (* x 1/120))))>
#<alt (* x (* x 1/120))>
#<alt (* eps 1/24)>
#<alt (* (* eps eps) -1/6)>
#<alt (* eps (* eps 1/24))>
#<alt (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))>

Outputs
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<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 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 (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)) (* -1/6 (* x (cos eps)))))) 1)))>
#<alt (* -1 x)>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (- (sin x) x)>
#<alt (- (+ (sin x) (* eps (cos x))) x)>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) x)>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) 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 (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 (* -1/120 (pow x 5))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))>
#<alt (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))>
#<alt (* -1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))>
#<alt (- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))>
#<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) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<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 (* 1/24 (* (pow eps 4) (sin x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 4) (sin x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))>
#<alt (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))>
#<alt (* 1/24 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* -1/6 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* (cos x) (+ 1 (* -1/6 (pow eps 2))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<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)>
#<alt (* -1/6 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))>
#<alt (* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))>
#<alt (* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))>
#<alt (* 1/24 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))>
#<alt (* 1/24 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))>
#<alt (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2))))))))>
#<alt (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/120 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))))))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))>

Calls

99 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	inf	(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))
4.0ms	x	@	inf	(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))))
1.0ms	x	@	-inf	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	x	@	inf	(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	x	@	-inf	(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))))

rewrite375.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

5224×	`-lowering-.f32`
5224×	`-lowering-.f64`
2484×	`/-lowering-/.f32`
2484×	`/-lowering-/.f64`
2248×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	178
1	254	167
2	2621	165
0	9581	165

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 495

Calls

Call 1

Inputs
(+ eps 0)
(* (* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (+ eps 0) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (+ eps 0) 2))
(sin eps)
(- (sin (+ x eps)) x)
(sin (+ x eps))
(+ x eps)
(- (sin (+ x eps)) (* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120)))))))
(* x (+ 1 (* (* x x) (+ -1/6 (* x (* x 1/120))))))
(* eps (+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))))
(+ (* (+ (* (* eps eps) -1/6) 1) (cos x)) (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)))
(* (+ (* (* eps eps) -1/6) 1) (cos x))
(+ (* (* eps eps) -1/6) 1)
(cos (/ (+ eps (* x 2)) 2))
(* x 2)
(* (* x x) (+ -1/6 (* x (* x 1/120))))
(* x (* x 1/120))
(* eps 1/24)
(* (* eps eps) -1/6)
(* eps (* eps 1/24))
(* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))

Outputs
eps
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
(exp.f64 (*.f64 (log.f64 eps) #s(literal 1 binary64)))
(exp.f64 (-.f64 (.f64 (log.f64 eps) #s(literal 3 binary64)) (.f64 (log.f64 eps) #s(literal 2 binary64))))
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) (neg.f64 (/.f64 #s(literal 0 binary64) eps)))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) (neg.f64 (/.f64 #s(literal 0 binary64) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (neg.f64 (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(pow.f64 eps #s(literal 1 binary64))
(pow.f64 (/.f64 eps (*.f64 eps eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
(.f64 (.f64 eps eps) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))
(.f64 (pow.f64 (.f64 eps (.f64 eps eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps eps)) #s(literal 1 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))))))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64)) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64)))))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64)))))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 #s(literal 2 binary64) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))))
(/.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x)))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (*.f64 #s(literal 2 binary64) x))))))) #s(literal -1 binary64))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64))))
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 #s(literal 2 binary64) x)) #s(literal -2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (+.f64 (sin.f64 (/.f64 (-.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x))) #s(literal 2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 eps (+.f64 eps (.f64 #s(literal 2 binary64) x)))))) #s(literal 1/2 binary64))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(+.f64 (.f64 (sin.f64 eps) #s(literal 1 binary64)) (.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal 1 binary64) (sin.f64 eps)))
(-.f64 (.f64 (sin.f64 eps) #s(literal 1 binary64)) (.f64 (cos.f64 eps) #s(literal 0 binary64)))
(-.f64 (.f64 (sin.f64 eps) (cos.f64 (/.f64 #s(literal 0 binary64) eps))) (.f64 (cos.f64 eps) (sin.f64 (/.f64 #s(literal 0 binary64) eps))))
(sin.f64 eps)
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (sin.f64 (+.f64 eps x)) (-.f64 #s(literal 0 binary64) x))
(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (sin.f64 eps) (cos.f64 x)) x))
(+.f64 (-.f64 #s(literal 0 binary64) x) (sin.f64 (+.f64 eps x)))
(-.f64 (sin.f64 (+.f64 eps x)) x)
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (.f64 x (+.f64 x (sin.f64 (+.f64 eps x)))))) (/.f64 (.f64 x (.f64 x x)) (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps x))))) (.f64 x (+.f64 x (sin.f64 (+.f64 eps x)))))))
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(/.f64 (+.f64 (.f64 #s(literal -1/216 binary64) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 (.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 x (.f64 x #s(literal -1/6 binary64)))) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64))))) (.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 x (.f64 x #s(literal -1/6 binary64)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64)))))) (-.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) (.f64 (.f64 x x) (.f64 x (.f64 x #s(literal 1/120 binary64))))))
(/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64))))) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64)))) (-.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal -1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728000 binary64)))) (.f64 x x)) (+.f64 #s(literal 1/36 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/120 binary64))) #s(literal -1/6 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/14400 binary64))) (.f64 x x)) (-.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(.f64 (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))) (.f64 x x))
(.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))) #s(literal 1 binary64))
(.f64 (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) x)
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))) (*.f64 x x))
(.f64 x (.f64 x #s(literal 1/120 binary64)))
(.f64 (.f64 x x) #s(literal 1/120 binary64))
(.f64 #s(literal 1/120 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/120 binary64)) x)
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/24 binary64)))
(+.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/24 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/24 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) eps)
(/.f64 (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/24 binary64)) (.f64 eps eps))
(*.f64 eps #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal -1/6 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal -1/6 binary64))) eps)
(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
(.f64 eps (.f64 (*.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps #s(literal -1/6 binary64))))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(.f64 #s(literal -1/6 binary64) (.f64 (*.f64 eps eps) #s(literal 1 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(.f64 (.f64 eps (*.f64 eps #s(literal -1/6 binary64))) #s(literal 1 binary64))
(.f64 (.f64 eps #s(literal -1/6 binary64)) eps)
(+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (.f64 (.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/24 binary64))))
(+.f64 (.f64 (.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64)) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/24 binary64))) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))
(fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) (.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) (.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/24 binary64))))
(fma.f64 #s(literal 0 binary64) (.f64 eps #s(literal 1/24 binary64)) (.f64 eps (*.f64 eps #s(literal 1/24 binary64))))
(fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) (.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) (.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/24 binary64))))
(fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) (.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) (.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/24 binary64))))
(fma.f64 (.f64 eps #s(literal 1/24 binary64)) eps (.f64 (*.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64)))
(fma.f64 (.f64 eps #s(literal 1/24 binary64)) eps (.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/24 binary64))))
(fma.f64 (.f64 eps #s(literal 1/24 binary64)) #s(literal 0 binary64) (.f64 eps (*.f64 eps #s(literal 1/24 binary64))))
(/.f64 (.f64 (.f64 eps #s(literal 1/24 binary64)) (.f64 eps (.f64 eps eps))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 eps eps)) eps)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps #s(literal 1/24 binary64))) (*.f64 eps eps))
(/.f64 (.f64 (.f64 eps eps) (*.f64 eps #s(literal 1/24 binary64))) eps)
(.f64 eps (.f64 eps #s(literal 1/24 binary64)))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(.f64 (.f64 eps #s(literal 1/24 binary64)) eps)
(+.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x)))) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x)))))
(fma.f64 eps (.f64 (sin.f64 x) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (*.f64 eps (sin.f64 x)))))
(fma.f64 eps (.f64 (.f64 eps #s(literal 1/24 binary64)) (.f64 eps (sin.f64 x))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (*.f64 eps (sin.f64 x)))))
(fma.f64 (sin.f64 x) (.f64 eps (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (sin.f64 x)) (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (*.f64 eps (sin.f64 x)))))
(fma.f64 (.f64 eps #s(literal 1/24 binary64)) (.f64 eps (.f64 eps (sin.f64 x))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (.f64 eps (sin.f64 x)) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 eps (sin.f64 x)) (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (*.f64 eps (sin.f64 x)))))
(fma.f64 (.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) (sin.f64 x)) eps (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (*.f64 eps (sin.f64 x)))))
(fma.f64 (.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) eps) (sin.f64 x) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps (sin.f64 x)) eps) (.f64 eps #s(literal 1/24 binary64)) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps eps)) #s(literal 1/24 binary64) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 eps #s(literal 1/24 binary64))) eps (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (*.f64 eps (sin.f64 x)))))
(/.f64 (.f64 (.f64 eps (sin.f64 x)) (.f64 (+.f64 (.f64 eps (*.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps)) eps)
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x)))) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x)))) (.f64 (*.f64 eps (sin.f64 x)) #s(literal -1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x)))) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/24 binary64) (.f64 eps (sin.f64 x)))) (.f64 (.f64 eps (sin.f64 x)) #s(literal -1/2 binary64))))
(/.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/13824 binary64))) #s(literal -1/8 binary64))) (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))))
(/.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/576 binary64)) #s(literal -1/4 binary64))) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 eps eps))
(/.f64 (.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/13824 binary64))) #s(literal -1/8 binary64)) (.f64 eps (sin.f64 x))) (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/576 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 eps (.f64 eps eps)) eps) #s(literal 1/576 binary64)) #s(literal -1/4 binary64)) (.f64 eps (sin.f64 x))) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(.f64 (sin.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))
(.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))
(.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) (.f64 eps (sin.f64 x)))
(.f64 (.f64 (sin.f64 x) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) eps)
(.f64 (.f64 (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) eps) (sin.f64 x))

simplify265.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

4098×	`-lowering-.f32`
4098×	`-lowering-.f64`
2052×	`+-lowering-+.f64`
2052×	`+-lowering-+.f32`
1692×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	471	4357
1	1619	3738
2	5918	3722
0	8088	3722

Stop Event

1×	iter limit
1×	node limit

Counts

396 → 396

Calls

Call 1

Inputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 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))
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)
(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)) (* -1/6 (* x (cos eps)))))) 1)))
(* -1 x)
(* x (- (/ (sin (+ eps x)) x) 1))
(* x (- (/ (sin (+ eps x)) x) 1))
(* x (- (/ (sin (+ eps x)) x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(- (sin x) x)
(- (+ (sin x) (* eps (cos x))) x)
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) x)
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) x)
(- (sin (+ eps x)) x)
(- (sin (+ eps x)) x)
(- (sin (+ eps x)) x)
(- (sin (+ eps x)) x)
(- (sin (- x (* -1 eps))) x)
(- (sin (- x (* -1 eps))) x)
(- (sin (- x (* -1 eps))) x)
(- (sin (- x (* -1 eps))) 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)))
(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)))
(* -1/120 (pow x 5))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
(* -1/120 (pow x 5))
(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2))))))
(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
(- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (+ eps x)) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(- (sin (- x (* -1 eps))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
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) (- (* 1/120 (pow x 2)) 1/6))))
(* 1/120 (pow x 5))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* 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)))))))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(* eps (+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))
(+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x))))))))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1/2 (/ (sin x) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x))) eps)) (* -1/6 (cos x))) eps)) (* -1/24 (sin x)))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/6 (pow eps 2)) (* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 (* x (+ 1 (* -1/6 (pow eps 2))))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* x (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* -1/6 (* eps (* x (- (* 1/24 (pow eps 2)) 1/2))))))))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(cos x)
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(+ (cos x) (* -1/6 (* (pow eps 2) (cos x))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* -1/6 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* 1/24 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/2 (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (+ 1 (* -1/6 (pow eps 2))))))))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
(* (cos x) (+ 1 (* -1/6 (pow eps 2))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(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)
(* -1/6 (pow x 2))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(* 1/24 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))
(* 1/24 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))
(* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2))))))))
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/120 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))

Outputs
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/6 binary64)))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
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(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
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(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 2 (* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #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 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (.f64 eps (cos.f64 x)) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64))))))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 eps)) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))
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(+ (* 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))))
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(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* (cos (* 1/2 (- eps (* -2 x)))) (sin (* 1/2 eps)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3840 binary64))))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
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(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
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(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
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(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)
(sin eps)
(sin.f64 eps)
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(* -1 x)
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(* -1 x)
(-.f64 #s(literal 0 binary64) x)
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(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
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(- (sin x) x)
(-.f64 (sin.f64 x) x)
(- (+ (sin x) (* eps (cos x))) x)
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(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) x)
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(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) x)
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(- (sin (+ eps x)) x)
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(- (sin (+ eps x)) x)
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(- (sin (+ eps x)) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (+ eps x)) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
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(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
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(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
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(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)))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
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(sin (- eps (* -1 x)))
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(sin x)
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(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)
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(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
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(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* x (+ 1 (/ eps x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 #s(literal 0 binary64) x))) #s(literal -1 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 #s(literal 0 binary64) x))) #s(literal -1 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(.f64 x (.f64 (+.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 #s(literal 0 binary64) x))) #s(literal -1 binary64)))
x
(+ eps x)
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(+ eps x)
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(+ eps x)
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eps
(* eps (+ 1 (/ x eps)))
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(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
(* eps (+ 1 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1 binary64) (/.f64 x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(-.f64 #s(literal 0 binary64) (*.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 x (-.f64 #s(literal 0 binary64) eps)))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
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(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
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(* -1/120 (pow x 5))
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(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x))))
(* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4)))))
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(* (pow x 5) (- (+ (* 1/6 (/ 1 (pow x 2))) (/ (sin (+ eps x)) (pow x 5))) (+ 1/120 (/ 1 (pow x 4)))))
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(* -1/120 (pow x 5))
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(* -1 (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2))))))
(-.f64 #s(literal 0 binary64) (.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x)))))
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(* -1 (* (pow x 5) (- (+ 1/120 (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 5))) (/ 1 (pow x 4)))) (* 1/6 (/ 1 (pow x 2))))))
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(- (sin x) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
(-.f64 (sin.f64 x) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 #s(literal 1/120 binary64) (*.f64 x x)))))))
(- (+ (sin x) (* eps (cos x))) (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6)))))
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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))))
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(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
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(* 1/120 (pow x 5))
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(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 5 binary64)) (+.f64 #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (.f64 x x))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
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(* 1/120 (pow x 5))
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(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(.f64 (pow.f64 x #s(literal 5 binary64)) (neg.f64 (+.f64 #s(literal -1/120 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 x x)))))
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(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
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(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
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(* 1/24 (* (pow eps 4) (sin x)))
(.f64 (sin.f64 x) (.f64 #s(literal 1/24 binary64) (pow.f64 eps #s(literal 4 binary64))))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
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(* 1/24 (* (pow eps 4) (sin x)))
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(cos x)
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(* 1/24 (* (pow eps 3) (sin x)))
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(* (pow eps 3) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
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(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
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(* 1/24 (* (pow eps 3) (sin x)))
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(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/6 (/ (cos x) eps)))))
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(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (+ (* -1/2 (sin x)) (* 1/24 (* (pow eps 2) (sin x)))))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* 1/24 (* (pow eps 3) (sin x)))
(.f64 eps (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps (sin.f64 x)))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps eps))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps eps))))
(* (pow eps 3) (+ (* -1/2 (/ (sin x) (pow eps 2))) (* 1/24 (sin x))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 (sin.f64 x) #s(literal 1/24 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps eps))))
(* 1/24 (* (pow eps 3) (sin x)))
(.f64 eps (.f64 #s(literal 1/24 binary64) (.f64 eps (.f64 eps (sin.f64 x)))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))
(.f64 (+.f64 (.f64 (sin.f64 x) #s(literal -1/24 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (sin.f64 x) eps) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))
(.f64 (+.f64 (.f64 (sin.f64 x) #s(literal -1/24 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (sin.f64 x) eps) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))))
(* -1 (* (pow eps 3) (+ (* -1/24 (sin x)) (* 1/2 (/ (sin x) (pow eps 2))))))
(.f64 (+.f64 (.f64 (sin.f64 x) #s(literal -1/24 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 (sin.f64 x) eps) eps))) (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps))))
(* eps (* x (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* x (+ (* -1/6 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* eps (- (* 1/24 (pow eps 2)) 1/2))))
(.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 eps (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) #s(literal -1/6 binary64)))))
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* 1/120 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2))))))))
(.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (.f64 x x) (+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) #s(literal -1/6 binary64))) (.f64 eps (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) #s(literal 1/120 binary64)))))))
(* x (+ (* eps (- (* 1/24 (pow eps 2)) 1/2)) (* (pow x 2) (+ (* -1/6 (* eps (- (* 1/24 (pow eps 2)) 1/2))) (* (pow x 2) (+ (* -1/5040 (* eps (* (pow x 2) (- (* 1/24 (pow eps 2)) 1/2)))) (* 1/120 (* eps (- (* 1/24 (pow eps 2)) 1/2)))))))))
(.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 (.f64 x x) (+.f64 (.f64 eps (.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) #s(literal -1/6 binary64))) (.f64 x (.f64 x (+.f64 (.f64 #s(literal -1/5040 binary64) (.f64 eps (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))) (.f64 #s(literal 1/120 binary64) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))
(* eps (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))

eval138.0ms (0.9%)

Compiler: Compiled 30768 to 2442 computations (92.1% saved)

prune105.0ms (0.7%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	962	18	980
Fresh	1	4	5
Picked	4	1	5
Done	0	1	1
Total	967	24	991

Accuracy

100.0%

Counts

991 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.1%	(/.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)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))))
▶	35.5%	(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (.f64 eps eps))
	54.0%	(/.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
	62.3%	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	8.1%	(-.f64 #s(literal 0 binary64) x)
▶	98.0%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
	98.0%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))))))))
	99.5%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 binary64)))))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	99.6%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
	99.2%	(.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 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))) #s(literal 2 binary64))
	54.1%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	98.0%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
	98.0%	(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
✓	99.6%	(.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 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	49.3%	(.f64 eps (+.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	99.2%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
	97.5%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
	97.5%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
	34.1%	(.f64 eps (.f64 (-.f64 (.f64 (sin.f64 x) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (/.f64 (cos.f64 x) eps)) eps)) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps)))))
	98.6%	(*.f64 eps (cos.f64 x))
▶	97.6%	eps

Compiler

Compiled 1162 to 721 computations (38% saved)

simplify180.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (*.f64 eps eps))
✓	cost-diff	0	(.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 eps eps)) eps)
✓	cost-diff	384	(+.f64 (.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (*.f64 eps eps))))
✓	cost-diff	512	(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (.f64 eps eps))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
✓	cost-diff	0	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
✓	cost-diff	128	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
✓	cost-diff	256	(+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))
✓	cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
✓	cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))

Rules

3568×	`-lowering-.f32`
3568×	`-lowering-.f64`
2052×	`+-lowering-+.f64`
2052×	`+-lowering-+.f32`
1364×	`times-frac`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	458
1	175	416
2	581	401
3	2266	397
4	5373	394
5	6240	394
6	7442	394
0	8247	394

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
eps
1/2
(cos (+ x (* eps 1/2)))
(+ x (* eps 1/2))
x
2
eps
(+ (* eps (+ 1 (* (* eps eps) -1/6))) (* x (+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))))
(* eps (+ 1 (* (* eps eps) -1/6)))
eps
(+ 1 (* (* eps eps) -1/6))
1
(* (* eps eps) -1/6)
(* eps eps)
-1/6
(* x (+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps)))))))
x
(+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))
(* (* eps x) (+ -1/2 (* (* eps eps) 1/12)))
(* eps x)
(+ -1/2 (* (* eps eps) 1/12))
-1/2
(* (* eps eps) 1/12)
1/12
(* eps (* eps (+ -1/2 (* 1/24 (* eps eps)))))
(* eps (+ -1/2 (* 1/24 (* eps eps))))
(+ -1/2 (* 1/24 (* eps eps)))
(* 1/24 (* eps eps))
1/24
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
eps
(+ 1/2 (* -1/48 (* eps eps)))
1/2
(* -1/48 (* eps eps))
-1/48
(* eps eps)
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x
2
(/ (+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))) (* eps eps))
(+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps))))
(* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps)
(* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps))
(* (+ 1 (* eps (* eps -1/6))) (cos x))
(+ 1 (* eps (* eps -1/6)))
1
(* eps (* eps -1/6))
eps
(* eps -1/6)
-1/6
(cos x)
x
(* eps eps)
(* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))
(* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps))
(* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))
(* eps (sin x))
(sin x)
(+ (* eps (* eps 1/24)) -1/2)
(* eps (* eps 1/24))
(* eps 1/24)
1/24
-1/2

Outputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(sin (* eps 1/2))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(cos (+ x (* eps 1/2)))
(cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(+ x (* eps 1/2))
(+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
x
2
#s(literal 2 binary64)
eps
(+ (* eps (+ 1 (* (* eps eps) -1/6))) (* x (+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/12 binary64))))))))))
(* eps (+ 1 (* (* eps eps) -1/6)))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
eps
(+ 1 (* (* eps eps) -1/6))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
1
#s(literal 1 binary64)
(* (* eps eps) -1/6)
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* eps eps)
(*.f64 eps eps)
-1/6
#s(literal -1/6 binary64)
(* x (+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps)))))))
(.f64 (.f64 eps x) (+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/12 binary64))))))))
x
(+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))
(.f64 eps (+.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 (.f64 eps #s(literal 1/24 binary64)) (.f64 x #s(literal 1/12 binary64))))))))
(* (* eps x) (+ -1/2 (* (* eps eps) 1/12)))
(.f64 x (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))))
(* eps x)
(*.f64 eps x)
(+ -1/2 (* (* eps eps) 1/12))
(+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))
-1/2
#s(literal -1/2 binary64)
(* (* eps eps) 1/12)
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
1/12
#s(literal 1/12 binary64)
(* eps (* eps (+ -1/2 (* 1/24 (* eps eps)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64))))
(* eps (+ -1/2 (* 1/24 (* eps eps))))
(.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal 1/24 binary64))))
(+ -1/2 (* 1/24 (* eps eps)))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))
(* 1/24 (* eps eps))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 #s(literal 2 binary64) (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))))
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/48 binary64))))
eps
(+ 1/2 (* -1/48 (* eps eps)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) #s(literal -1/48 binary64)))
1/2
#s(literal 1/2 binary64)
(* -1/48 (* eps eps))
(.f64 (.f64 eps eps) #s(literal -1/48 binary64))
-1/48
#s(literal -1/48 binary64)
(* eps eps)
(*.f64 eps eps)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ 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)
(/ (+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))) (* eps eps))
(.f64 eps (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (cos.f64 x)) (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (sin.f64 x))))
(+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps))))
(.f64 eps (.f64 (.f64 eps eps) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (cos.f64 x)) (.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (sin.f64 x)))))
(* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps)
(.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (cos.f64 x))))
(* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps))
(.f64 (.f64 eps eps) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) (cos.f64 x)))
(* (+ 1 (* eps (* eps -1/6))) (cos x))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))) (cos.f64 x))
(+ 1 (* eps (* eps -1/6)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
1
#s(literal 1 binary64)
(* eps (* eps -1/6))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
eps
(* eps -1/6)
(*.f64 eps #s(literal -1/6 binary64))
-1/6
#s(literal -1/6 binary64)
(cos x)
(cos.f64 x)
x
(* eps eps)
(*.f64 eps eps)
(* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))
(.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (.f64 eps (*.f64 eps (sin.f64 x))))
(* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps))
(.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (.f64 eps (.f64 eps (sin.f64 x))))
(* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2))
(.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))) (sin.f64 x))
(* eps (sin x))
(*.f64 eps (sin.f64 x))
(sin x)
(sin.f64 x)
(+ (* eps (* eps 1/24)) -1/2)
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/24 binary64)))
(* eps (* eps 1/24))
(.f64 (.f64 eps eps) #s(literal 1/24 binary64))
(* eps 1/24)
(*.f64 eps #s(literal 1/24 binary64))
1/24
#s(literal 1/24 binary64)
-1/2
#s(literal -1/2 binary64)

localize334.0ms (2.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/24 binary64))
✓	accuracy	99.4%	(*.f64 eps #s(literal -1/6 binary64))
✓	accuracy	36.7%	(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (.f64 eps eps))
✓	accuracy	100.0%	(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps))))
✓	accuracy	100.0%	(.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	99.9%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	99.8%	(.f64 #s(literal -1/48 binary64) (.f64 eps eps))
✓	accuracy	99.8%	(+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
✓	accuracy	99.8%	(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) #s(literal 1/12 binary64))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64)))))
✓	accuracy	99.9%	(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))

Results

219.0ms

256×

valid

Compiler

Compiled 519 to 58 computations (88.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 105.0ms

ival-mult: 48.0ms (45.9% of total)

...c/correct-round.rkt:119:19: 20.0ms (19.1% of total)

ival-add: 14.0ms (13.4% of total)

ival-sin: 12.0ms (11.5% of total)

ival-cos: 6.0ms (5.7% of total)

ival-div: 4.0ms (3.8% of total)

const: 1.0ms (1% of total)

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

series43.0ms (0.3%)

Counts

25 → 444

Calls

Call 1

Inputs
#<alt (* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)>
#<alt (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))>
#<alt (sin (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))>
#<alt (+ (* eps (+ 1 (* (* eps eps) -1/6))) (* x (+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))))>
#<alt (* eps (+ 1 (* (* eps eps) -1/6)))>
#<alt (+ 1 (* (* eps eps) -1/6))>
#<alt (* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (* eps (+ 1/2 (* -1/48 (* eps eps))))>
#<alt (+ 1/2 (* -1/48 (* eps eps)))>
#<alt (/ (+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))) (* eps eps))>
#<alt (+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps))))>
#<alt (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps)>
#<alt (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps))>
#<alt (cos (+ x (* eps 1/2)))>
#<alt (* (* eps eps) 1/12)>
#<alt (* 1/24 (* eps eps))>
#<alt (* (* eps eps) -1/6)>
#<alt (* -1/48 (* eps eps))>
#<alt (cos (/ (+ eps (* x 2)) 2))>
#<alt (* eps -1/6)>
#<alt (* eps 1/24)>
#<alt (* eps (* eps -1/6))>

Outputs
#<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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))>
#<alt (* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))>
#<alt (* (cos (- (* 1/2 eps) (* -1 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 (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))>
#<alt (* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))>
#<alt (* 1/24 (pow eps 4))>
#<alt (* (pow eps 4) (+ 1/24 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 4) (- (+ 1/24 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))>
#<alt (* (pow eps 4) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (* 1/12 (/ x eps)))) (/ 1/2 (pow eps 2))))>
#<alt (* 1/24 (pow eps 4))>
#<alt (* (pow eps 4) (+ 1/24 (* 1/12 (/ x eps))))>
#<alt (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))>
#<alt (* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/2) eps)) (* -1/12 x)) eps))))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))>
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#<alt (* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* -1 (* x (+ (* -1 (* eps (- (* 1/12 (pow eps 2)) 1/2))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (- (* 1/12 (pow eps 2)) 1/2))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))>
#<alt (* -1 (* x (+ (* -1 (* eps (- (* 1/12 (pow eps 2)) 1/2))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 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 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))>
#<alt (* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))>
#<alt (* 1/24 (* (pow eps 4) x))>
#<alt (* (pow eps 4) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))>
#<alt (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))>
#<alt (* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))>
#<alt (* 1/24 (* (pow eps 4) x))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1/12 (pow x 2))) eps)) (* 1/24 x)))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/24 x)))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)) eps)) (* -1/12 (pow x 2)))) eps)) (* 1/24 x)))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))>
#<alt (* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (+ (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))))>
#<alt (* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (+ (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))))>
#<alt (* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))>
#<alt (* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt (* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))>
#<alt 1>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (+ 1 (* -1/6 (pow eps 2)))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))>
#<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 (* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))>
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))>
#<alt (* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))>
#<alt (* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))>
#<alt (+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))>
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#<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 (* -1/48 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))>
#<alt (* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))>
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#<alt (* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))>
#<alt (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))>
#<alt (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* -1/48 (pow eps 3))>
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<alt (* -1/48 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (+ 1/2 (* -1/48 (pow eps 2)))>
#<alt (* -1/48 (pow eps 2))>
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#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<alt (* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))>
#<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 (* 1/24 (* (pow eps 4) (sin x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))>
#<alt (* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 4) (sin x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))>
#<alt (* (pow eps 3) (cos x))>
#<alt (* (pow eps 3) (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* (pow eps 3) (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))>
#<alt (* (pow eps 3) (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))>
#<alt (* 1/24 (* (pow eps 6) (sin x)))>
#<alt (* (pow eps 6) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))>
#<alt (* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))>
#<alt (* 1/24 (* (pow eps 6) (sin x)))>
#<alt (* (pow eps 6) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 6) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 6) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))>
#<alt (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 4) (* x (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* x (+ (* -1/2 (* (pow eps 3) (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 4) (- (* 1/24 (pow eps 2)) 1/2)))) (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 4) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 4) (- (* 1/24 (pow eps 2)) 1/2)))) (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))>
#<alt (* (pow eps 3) (cos x))>
#<alt (* (pow eps 3) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* (pow eps 3) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* (pow eps 3) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* -1/6 (* (pow eps 5) (cos x)))>
#<alt (* (pow eps 5) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 5) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 5) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* -1/6 (* (pow eps 5) (cos x)))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))>
#<alt (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 3) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* (pow eps 3) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* (pow eps 3) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))))))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (cos x))>
#<alt (* (pow eps 2) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* (pow eps 2) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* (pow eps 2) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))>
#<alt (* -1/6 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* -1/6 (* (pow eps 4) (cos x)))>
#<alt (* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))>
#<alt (+ (* -1/2 (* (pow eps 2) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (+ (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* (pow eps 2) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))>
#<alt (+ (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* (pow eps 2) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))))))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))>
#<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 (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/12 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* 1/24 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 2))>
#<alt (* -1/48 (pow eps 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 (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* -1/6 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* 1/24 eps)>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>
#<alt (* -1/6 (pow eps 2))>

Calls

111 calls:

Time	Variable		Point	Expression
9.0ms	eps	@	inf	(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
2.0ms	x	@	inf	(/ (+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))) (* eps eps))
1.0ms	x	@	-inf	(/ (+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))) (* eps eps))
1.0ms	x	@	inf	(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
1.0ms	eps	@	0	(+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))

rewrite438.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4194×	`-lowering-.f32`
4194×	`-lowering-.f64`
2550×	`/-lowering-/.f32`
2550×	`/-lowering-/.f64`
1520×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	272
1	338	244
2	2900	244
0	8609	244

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 506

Calls

Call 1

Inputs
(* (* (sin (* eps 1/2)) (cos (+ x (* eps 1/2)))) 2)
(* (sin (* eps 1/2)) (cos (+ x (* eps 1/2))))
(sin (* eps 1/2))
(* eps 1/2)
(+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))
(+ (* eps (+ 1 (* (* eps eps) -1/6))) (* x (+ (* (* eps x) (+ -1/2 (* (* eps eps) 1/12))) (* eps (* eps (+ -1/2 (* 1/24 (* eps eps))))))))
(* eps (+ 1 (* (* eps eps) -1/6)))
(+ 1 (* (* eps eps) -1/6))
(* (* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (* eps (+ 1/2 (* -1/48 (* eps eps)))) (cos (/ (+ eps (* x 2)) 2)))
(* eps (+ 1/2 (* -1/48 (* eps eps))))
(+ 1/2 (* -1/48 (* eps eps)))
(/ (+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps)))) (* eps eps))
(+ (* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps) (* eps (* (* (* eps (sin x)) (+ (* eps (* eps 1/24)) -1/2)) (* eps eps))))
(* (* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps)) eps)
(* (* (+ 1 (* eps (* eps -1/6))) (cos x)) (* eps eps))
(cos (+ x (* eps 1/2)))
(* (* eps eps) 1/12)
(* 1/24 (* eps eps))
(* (* eps eps) -1/6)
(* -1/48 (* eps eps))
(cos (/ (+ eps (* x 2)) 2))
(* eps -1/6)
(* eps 1/24)
(* eps (* eps -1/6))

Outputs
(/.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal 2 binary64))
(/.f64 (.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))
(.f64 (.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) #s(literal 2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))))
(/.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 2 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))))
(/.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -2 binary64))
(/.f64 (neg.f64 (neg.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))))) #s(literal -1 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(.f64 (cos.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))
(.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (+.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))) #s(literal 1/2 binary64))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(*.f64 eps #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) eps)
(+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))))
(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))) (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64))))))
(+.f64 (.f64 x (.f64 eps #s(literal -1/2 binary64))) (+.f64 (.f64 (.f64 eps x) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))))))
(+.f64 (+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64))))) (.f64 x (.f64 eps #s(literal -1/2 binary64)))) (.f64 (.f64 eps x) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))
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(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)) #s(literal 1/24 binary64))
(.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps #s(literal 1/24 binary64))) eps)
(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 eps #s(literal -1/6 binary64))
(*.f64 #s(literal -1/6 binary64) eps)
(*.f64 eps #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) eps)
(.f64 eps (.f64 eps #s(literal -1/6 binary64)))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(.f64 #s(literal -1/6 binary64) (.f64 eps eps))
(.f64 (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(.f64 (.f64 eps #s(literal -1/6 binary64)) eps)
(.f64 (.f64 #s(literal 1 binary64) (*.f64 eps #s(literal -1/6 binary64))) eps)

simplify377.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

6318×	`-lowering-.f32`
6318×	`-lowering-.f64`
3022×	`+-lowering-+.f64`
3022×	`+-lowering-+.f32`
1628×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	564	6051
1	2038	5176
2	7782	5173
0	8298	5173

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

Inputs
(* 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- x (* -1/2 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 (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps)))
(* (cos (- (* 1/2 eps) (* -1 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)
(* -1/2 (* eps x))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/12 (/ x eps))))
(* (pow eps 4) (- (+ 1/24 (* 1/12 (/ x eps))) (/ 1/2 (pow eps 2))))
(* (pow eps 4) (- (+ 1/24 (+ (* -1/2 (/ x (pow eps 3))) (* 1/12 (/ x eps)))) (/ 1/2 (pow eps 2))))
(* 1/24 (pow eps 4))
(* (pow eps 4) (+ 1/24 (* 1/12 (/ x eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1/12 x) (* 1/2 (/ 1 eps))) eps))))
(* (pow eps 4) (+ 1/24 (* -1 (/ (+ (* -1 (/ (- (* -1/2 (/ x eps)) 1/2) eps)) (* -1/12 x)) eps))))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))
(* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* x (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* eps (* x (- (* 1/12 (pow eps 2)) 1/2)))
(* -1 (* x (+ (* -1 (* eps (- (* 1/12 (pow eps 2)) 1/2))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/12 (pow eps 2)) 1/2))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))))
(* -1 (* x (+ (* -1 (* eps (- (* 1/12 (pow eps 2)) 1/2))) (* -1 (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 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 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(* 1/24 (* (pow eps 4) x))
(* (pow eps 4) (- (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps))) (* 1/6 (/ 1 eps))))
(* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* 1/24 x) (* 1/12 (/ (pow x 2) eps)))) (* 1/6 (/ 1 eps))))
(* (pow eps 4) (- (+ (* -1/2 (/ x (pow eps 2))) (+ (* -1/2 (/ (pow x 2) (pow eps 3))) (+ (* 1/24 x) (+ (* 1/12 (/ (pow x 2) eps)) (/ 1 (pow eps 3)))))) (* 1/6 (/ 1 eps))))
(* 1/24 (* (pow eps 4) x))
(* (pow eps 4) (+ (* -1 (/ (+ 1/6 (* -1/12 (pow x 2))) eps)) (* 1/24 x)))
(* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1/12 (pow x 2)) (* 1/2 (/ x eps)))) eps)) (* 1/24 x)))
(* (pow eps 4) (+ (* -1 (/ (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)) eps)) (* -1/12 (pow x 2)))) eps)) (* 1/24 x)))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (+ (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))))
(* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (+ (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)) x)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))) (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* -1/6 (pow eps 3))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 3) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
(* -1 (* (pow eps 3) (- 1/6 (/ 1 (pow eps 2)))))
1
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (* -1/6 (pow eps 2)))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* -1/6 (pow eps 2))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* (pow eps 2) (- (/ 1 (pow eps 2)) 1/6))
(* 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))))))))))
(* -1/24 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(* (pow eps 3) (+ (* -1/24 (cos (* 1/2 (+ eps (* 2 x))))) (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2))))
(* -1/24 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/24 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(+ (* -2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+ (* 2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/3 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 2 (* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2))))))
(* 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))))))))))
(* -1/48 (* (pow eps 3) (cos (* 1/2 (+ eps (* 2 x))))))
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* (pow eps 3) (+ (* -1/48 (cos (* 1/2 (+ eps (* 2 x))))) (* 1/2 (/ (cos (* 1/2 (+ eps (* 2 x)))) (pow eps 2)))))
(* -1/48 (* (pow eps 3) (cos (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* -1 (* (pow eps 3) (+ (* -1/2 (/ (cos (* 1/2 (- (* 2 x) (* -1 eps)))) (pow eps 2))) (* 1/48 (cos (* 1/2 (- (* 2 x) (* -1 eps))))))))
(* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))
(+ (* -1 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* -1/2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))
(+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))) (* x (+ (* -1 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* x (+ (* -1/2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2)))))) (* 1/6 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* -1/48 (pow eps 2))))))))))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (+ eps (* 2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* eps (* (cos (* 1/2 (- eps (* -2 x)))) (+ 1/2 (* -1/48 (pow eps 2)))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* -1/48 (pow eps 3))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 3))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
1/2
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* -1/48 (pow eps 2)))
(+ 1/2 (* -1/48 (pow eps 2)))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* -1/48 (pow eps 2))
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* (pow eps 2) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(* 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)))))))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 4) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 4) (sin x)))
(* (pow eps 4) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 4) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (* eps (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* x (+ (* -1/2 (* eps (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 2) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(/ (+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2)))) (pow eps 2))
(* (pow eps 3) (cos x))
(* (pow eps 3) (+ (cos x) (* -1/2 (* eps (sin x)))))
(* (pow eps 3) (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(* (pow eps 3) (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(* 1/24 (* (pow eps 6) (sin x)))
(* (pow eps 6) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x)))))
(* (pow eps 6) (+ (* -1/2 (/ (sin x) (pow eps 2))) (+ (* -1/6 (/ (cos x) eps)) (+ (* 1/24 (sin x)) (/ (cos x) (pow eps 3))))))
(* 1/24 (* (pow eps 6) (sin x)))
(* (pow eps 6) (+ (* -1/6 (/ (cos x) eps)) (* 1/24 (sin x))))
(* (pow eps 6) (+ (* -1 (/ (+ (* 1/6 (cos x)) (* 1/2 (/ (sin x) eps))) eps)) (* 1/24 (sin x))))
(* (pow eps 6) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sin x)) (/ (cos x) eps)) eps)) (* 1/6 (cos x))) eps)) (* 1/24 (sin x))))
(* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))
(+ (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))) (* (pow eps 4) (* x (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* x (+ (* -1/2 (* (pow eps 3) (* x (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 4) (- (* 1/24 (pow eps 2)) 1/2)))) (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* x (+ (* x (+ (* -1/2 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))) (* -1/6 (* (pow eps 4) (* x (- (* 1/24 (pow eps 2)) 1/2)))))) (* (pow eps 4) (- (* 1/24 (pow eps 2)) 1/2)))) (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(+ (* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2))))) (* (pow eps 4) (* (sin x) (- (* 1/24 (pow eps 2)) 1/2))))
(* (pow eps 3) (cos x))
(* (pow eps 3) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* (pow eps 3) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* (pow eps 3) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* -1/6 (* (pow eps 5) (cos x)))
(* (pow eps 5) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 5) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 5) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* -1/6 (* (pow eps 5) (cos x)))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))
(* -1 (* (pow eps 5) (+ (* -1 (/ (cos x) (pow eps 2))) (* 1/6 (cos x)))))
(* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 3) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* (pow eps 3) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(+ (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* (pow eps 3) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* (pow eps 3) (+ 1 (* -1/6 (pow eps 2))))))))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 3) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (cos x))
(* (pow eps 2) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* (pow eps 2) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* (pow eps 2) (+ (cos x) (* -1/6 (* (pow eps 2) (cos x)))))
(* -1/6 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* -1/6 (* (pow eps 4) (cos x)))
(* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 4) (+ (* -1/6 (cos x)) (/ (cos x) (pow eps 2))))
(* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2)))))
(+ (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))) (* 1/24 (* (pow eps 2) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))))))
(+ (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2)))) (* (pow x 2) (+ (* -1/2 (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))) (* (pow x 2) (+ (* -1/720 (* (pow eps 2) (* (pow x 2) (+ 1 (* -1/6 (pow eps 2)))))) (* 1/24 (* (pow eps 2) (+ 1 (* -1/6 (pow eps 2))))))))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(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)))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/12 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* 1/24 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 2))
(* -1/48 (pow eps 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))))
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* -1/6 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* 1/24 eps)
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 2))
(* -1/6 (pow eps 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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 eps (+.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/6 binary64))) (.f64 (sin.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64))))
(+ (* 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))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (-.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(+ (* 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))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (+.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (-.f64 (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
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eps
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1
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(* 1/2 (* eps (cos x)))
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(+.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 x (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 (.f64 eps eps) #s(literal -1/720 binary64))) (.f64 #s(literal 1/24 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))))))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(* (pow eps 2) (* (cos x) (+ 1 (* -1/6 (pow eps 2)))))
(.f64 (cos.f64 x) (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 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 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 (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- (* 1/2 eps) (* -1 x)))
(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 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 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 (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (+ x (* 1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- x (* -1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- x (* -1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- x (* -1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(cos (- x (* -1/2 eps)))
(cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/12 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 1/12 binary64)))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* 1/24 (pow eps 2))
(.f64 #s(literal 1/24 binary64) (.f64 eps eps))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 binary64)))
(* -1/48 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -1/48 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 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 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 (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 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))))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* -1/6 eps)
(*.f64 eps #s(literal -1/6 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* 1/24 eps)
(*.f64 eps #s(literal 1/24 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))

eval141.0ms (0.9%)

Compiler: Compiled 56217 to 2731 computations (95.1% saved)

prune366.0ms (2.4%)

Pruning

27 alts after pruning (23 fresh and 4 done)

	Pruned	Kept	Total
New	949	15	964
Fresh	9	8	17
Picked	3	2	5
Done	0	2	2
Total	961	27	988

Accuracy

100.0%

Counts

988 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.1%	(/.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)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))))
	35.1%	(/.f64 (+.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (*.f64 eps eps))
	35.1%	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))) (.f64 eps eps))
	62.3%	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	8.1%	(-.f64 #s(literal 0 binary64) x)
	33.8%	(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
	97.9%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))
	98.0%	(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
	97.9%	(+.f64 eps (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
	99.6%	(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (+.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)))))))) #s(literal 2 binary64))
	99.2%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
▶	54.1%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64))
✓	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	51.0%	(.f64 (.f64 x x) (+.f64 (.f64 (.f64 eps eps) (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) x)) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x x))))))
	99.6%	(.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	35.3%	(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
✓	99.6%	(.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 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	49.3%	(.f64 eps (+.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	99.2%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
	97.5%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
▶	98.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
	97.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
	97.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
▶	98.6%	(*.f64 eps (cos.f64 x))
✓	97.6%	eps

Compiler

Compiled 1132 to 707 computations (37.5% saved)

simplify212.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #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	384	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 eps (cos.f64 x))
✓	cost-diff	0	(.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x)))
✓	cost-diff	0	(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64)))))
✓	cost-diff	0	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) x)
✓	cost-diff	0	(*.f64 eps #s(literal 1/2 binary64))
✓	cost-diff	0	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
✓	cost-diff	0	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))
✓	cost-diff	0	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64))

Rules

2936×	`+-lowering-+.f64`
2936×	`+-lowering-+.f32`
2498×	`-lowering-.f32`
2498×	`-lowering-.f64`
1866×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	274
1	111	255
2	295	253
3	1288	253
4	5297	253
0	8136	253

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)
(* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x))))
(sin (* eps 1/2))
(* eps 1/2)
eps
1/2
(- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))
(* (cos x) (cos (* eps 1/2)))
(cos x)
x
(cos (* eps 1/2))
(* (sin (* eps 1/2)) (sin x))
(sin x)
2
(- 0 x)
0
x
(* eps (+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))))
eps
(+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6))))
1
(+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))
(* -1/2 (* x (+ eps x)))
-1/2
(* x (+ eps x))
x
(+ eps x)
(* (* eps eps) (+ (* x (* x 1/12)) -1/6))
(* eps eps)
(+ (* x (* x 1/12)) -1/6)
(* x (* x 1/12))
(* x 1/12)
1/12
-1/6
(* eps (cos x))
eps
(cos x)
x
(* (* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (* (* eps eps) (/ 1 eps)) 2))
(/ (* (* eps eps) (/ 1 eps)) 2)
(* (* eps eps) (/ 1 eps))
(* eps eps)
eps
(/ 1 eps)
1
2
(cos (/ (+ eps (* x 2)) 2))
(/ (+ eps (* x 2)) 2)
(+ eps (* x 2))
(* x 2)
x

Outputs
(* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)
(.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x))))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))))
(sin (* eps 1/2))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(* eps 1/2)
(/.f64 eps #s(literal 2 binary64))
eps
1/2
#s(literal 1/2 binary64)
(- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))
(-.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)))
(* (cos x) (cos (* eps 1/2)))
(*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))))
(cos x)
(cos.f64 x)
x
(cos (* eps 1/2))
(cos.f64 (/.f64 eps #s(literal 2 binary64)))
(* (sin (* eps 1/2)) (sin x))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))
(sin x)
(sin.f64 x)
2
#s(literal 2 binary64)
(- 0 x)
(-.f64 #s(literal 0 binary64) x)
0
#s(literal 0 binary64)
x
(* eps (+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal -1/6 binary64))))))
eps
(+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6))))
(+.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64)))))
1
#s(literal 1 binary64)
(+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))
(+.f64 (.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64))) (.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64))))
(* -1/2 (* x (+ eps x)))
(.f64 (+.f64 eps x) (.f64 x #s(literal -1/2 binary64)))
-1/2
#s(literal -1/2 binary64)
(* x (+ eps x))
(*.f64 x (+.f64 eps x))
x
(+ eps x)
(+.f64 eps x)
(* (* eps eps) (+ (* x (* x 1/12)) -1/6))
(.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64)))
(* eps eps)
(*.f64 eps eps)
(+ (* x (* x 1/12)) -1/6)
(+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64))
(* x (* x 1/12))
(.f64 #s(literal 1/12 binary64) (.f64 x x))
(* x 1/12)
(*.f64 x #s(literal 1/12 binary64))
1/12
#s(literal 1/12 binary64)
-1/6
#s(literal -1/6 binary64)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(cos x)
(cos.f64 x)
x
(* (* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(.f64 (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2)))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
(sin (/ (* (* eps eps) (/ 1 eps)) 2))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(/ (* (* eps eps) (/ 1 eps)) 2)
(/.f64 eps #s(literal 2 binary64))
(* (* eps eps) (/ 1 eps))
eps
(* eps eps)
(*.f64 eps eps)
eps
(/ 1 eps)
(/.f64 #s(literal 1 binary64) eps)
1
#s(literal 1 binary64)
2
#s(literal 2 binary64)
(cos (/ (+ eps (* x 2)) 2))
(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
(/ (+ eps (* x 2)) 2)
(/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))
(+ eps (* x 2))
(+.f64 eps (*.f64 x #s(literal 2 binary64)))
(* x 2)
(*.f64 x #s(literal 2 binary64))
x

localize239.0ms (1.6%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))))
✓	accuracy	99.9%	(cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))
✓	accuracy	54.3%	(.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	99.8%	(*.f64 x (+.f64 eps x))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/12 binary64)))
✓	accuracy	99.7%	(.f64 (.f64 eps eps) (+.f64 (.f64 x (.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64)))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/12 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) x)
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))
✓	accuracy	100.0%	(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x))))

Results

174.0ms

256×

valid

Compiler

Compiled 318 to 43 computations (86.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-mult: 31.0ms (47.1% of total)

...c/correct-round.rkt:119:19: 8.0ms (12.2% of total)

ival-add: 6.0ms (9.1% of total)

ival-sin: 6.0ms (9.1% of total)

ival-cos: 6.0ms (9.1% of total)

ival-div: 5.0ms (7.6% of total)

ival-sub: 2.0ms (3% of total)

const: 1.0ms (1.5% of total)

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

series29.0ms (0.2%)

Counts

23 → 456

Calls

Call 1

Inputs
#<alt (* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)>
#<alt (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x))))>
#<alt (sin (* eps 1/2))>
#<alt (* eps 1/2)>
#<alt (- 0 x)>
#<alt (* eps (+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))))>
#<alt (+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6))))>
#<alt (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))>
#<alt (* -1/2 (* x (+ eps x)))>
#<alt (* eps (cos x))>
#<alt (cos x)>
#<alt (* (* eps eps) (/ 1 eps))>
#<alt (* (* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)>
#<alt (* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2)))>
#<alt (sin (/ (* (* eps eps) (/ 1 eps)) 2))>
#<alt (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))>
#<alt (* (cos x) (cos (* eps 1/2)))>
#<alt (* (sin (* eps 1/2)) (sin x))>
#<alt (* x 1/12)>
#<alt (* (* eps eps) (+ (* x (* x 1/12)) -1/6))>
#<alt (* x (* x 1/12))>
#<alt (* x (+ eps x))>
#<alt (cos (/ (+ eps (* x 2)) 2))>

Outputs
#<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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
#<alt (* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))>
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#<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 (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) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<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) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))>
#<alt (cos (* 1/2 eps))>
#<alt (+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))>
#<alt (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))>
#<alt (+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* (cos x) (cos (* 1/2 eps)))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* x (sin (* 1/2 eps)))>
#<alt (* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))>
#<alt (* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))>
#<alt (* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* (sin x) (sin (* 1/2 eps)))>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* 1/12 x)>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow eps 2))>
#<alt (+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))>
#<alt (+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))>
#<alt (+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* 1/12 (* (pow eps 2) (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<alt (* 1/12 (pow x 2))>
#<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 (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 (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))))>

Calls

114 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	(- 0 x)
2.0ms	x	@	inf	(* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)
1.0ms	eps	@	inf	(* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)
1.0ms	x	@	-inf	(* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)
1.0ms	eps	@	-inf	(* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)

rewrite385.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

5400×	`-lowering-.f32`
5400×	`-lowering-.f64`
2898×	`/-lowering-/.f32`
2898×	`/-lowering-/.f64`
2538×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	216
1	239	172
2	2127	170
0	9476	170

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 458

Calls

Call 1

Inputs
(* (* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))) 2)
(* (sin (* eps 1/2)) (- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x))))
(sin (* eps 1/2))
(* eps 1/2)
(- 0 x)
(* eps (+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))))
(+ 1 (+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6))))
(+ (* -1/2 (* x (+ eps x))) (* (* eps eps) (+ (* x (* x 1/12)) -1/6)))
(* -1/2 (* x (+ eps x)))
(* eps (cos x))
(cos x)
(* (* eps eps) (/ 1 eps))
(* (* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2))) 2)
(* (sin (/ (* (* eps eps) (/ 1 eps)) 2)) (cos (/ (+ eps (* x 2)) 2)))
(sin (/ (* (* eps eps) (/ 1 eps)) 2))
(- (* (cos x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (sin x)))
(* (cos x) (cos (* eps 1/2)))
(* (sin (* eps 1/2)) (sin x))
(* x 1/12)
(* (* eps eps) (+ (* x (* x 1/12)) -1/6))
(* x (* x 1/12))
(* x (+ eps x))
(cos (/ (+ eps (* x 2)) 2))

Outputs
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) #s(literal 2 binary64)))
(.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))))
(.f64 (.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) #s(literal 2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))
(+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)))))
(+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) (.f64 (+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(+.f64 (.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(fma.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)))))
(fma.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (.f64 (+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(fma.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(fma.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)))))
(fma.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)) #s(literal 3 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 eps #s(literal 2 binary64))))))) (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))))))
(/.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 eps #s(literal 2 binary64))))))) (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))))))
(/.f64 (.f64 (.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))))
(/.f64 (+.f64 (sin.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) (sin.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))) #s(literal 2 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))
(*.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(sin.f64 (/.f64 eps #s(literal 2 binary64)))
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 eps #s(literal -2 binary64)))
(/.f64 eps #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) eps))
(/.f64 (.f64 eps eps) (.f64 #s(literal 2 binary64) eps))
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(exp.f64 (+.f64 (.f64 (log.f64 eps) #s(literal 2 binary64)) (.f64 (log.f64 eps) #s(literal -1 binary64))))
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(/.f64 eps #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (-.f64 #s(literal 0 binary64) eps) #s(literal -1 binary64))
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(/.f64 (.f64 (.f64 eps eps) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 eps eps)) (-.f64 #s(literal 0 binary64) eps))
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(pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64))
(*.f64 eps #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) eps)
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(.f64 (/.f64 #s(literal 1 binary64) eps) (.f64 eps eps))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal 1 binary64)) (.f64 eps eps))
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(fma.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
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(fma.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 eps #s(literal 2 binary64))) (*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))))
(fma.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))))
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(fma.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64) (neg.f64 (-.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)) (+.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))))))
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(/.f64 (neg.f64 (*.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))) (neg.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64))))))
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(pow.f64 (/.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (*.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))) #s(literal -1 binary64))
(.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 x #s(literal 2 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (/.f64 eps #s(literal 2 binary64))))))) (.f64 (.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64))))))))
(.f64 (.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))))))
(/.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64))))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))))) #s(literal -1 binary64))
(*.f64 (cos.f64 x) (cos.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (cos.f64 (/.f64 eps #s(literal 2 binary64))) (cos.f64 x))
(*.f64 (+.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(-.f64 (/.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))))
(/.f64 (-.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x)))) #s(literal -1 binary64))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 x))
(*.f64 (sin.f64 x) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(*.f64 (-.f64 (cos.f64 (-.f64 x (/.f64 eps #s(literal 2 binary64)))) (cos.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) x))) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/12 binary64))
(*.f64 #s(literal 1/12 binary64) x)
(+.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x))) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))
(+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x))))
(fma.f64 eps (.f64 eps (.f64 #s(literal 1/12 binary64) (.f64 x x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (*.f64 x x))))
(fma.f64 x (.f64 (.f64 x #s(literal 1/12 binary64)) (.f64 eps eps)) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x)) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (*.f64 x x))))
(fma.f64 (.f64 x #s(literal 1/12 binary64)) (.f64 x (.f64 eps eps)) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (*.f64 x x))))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/12 binary64) (.f64 eps eps)) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (.f64 x x)) #s(literal 1/12 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) eps) eps (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (.f64 #s(literal -1/6 binary64) eps) eps (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (*.f64 x x))))
(fma.f64 (.f64 (.f64 eps eps) x) (.f64 x #s(literal 1/12 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (.f64 x #s(literal 1/12 binary64))) x (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64))) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps)))) (.f64 #s(literal -1/216 binary64) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 eps eps))))) (+.f64 (.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x)))) (-.f64 (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x))) (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x)))) (.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (-.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/12 binary64) (.f64 x x))) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))))
(/.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64))) #s(literal -1/216 binary64))) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/72 binary64)))))
(/.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64)) #s(literal -1/36 binary64))) (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/6 binary64)))
(/.f64 (.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/1728 binary64))) #s(literal -1/216 binary64)) (.f64 eps eps)) (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64)) (-.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) #s(literal -1/72 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/144 binary64)) #s(literal -1/36 binary64)) (.f64 eps eps)) (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/6 binary64)))
(.f64 eps (.f64 eps (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64))))
(.f64 (.f64 eps eps) (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64)))
(.f64 (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64)) (.f64 eps eps))
(.f64 (.f64 eps (+.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal -1/6 binary64))) eps)
(.f64 x (.f64 x #s(literal 1/12 binary64)))
(.f64 #s(literal 1/12 binary64) (.f64 x x))
(.f64 (.f64 x #s(literal 1/12 binary64)) x)
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(+.f64 (.f64 x x) (.f64 eps x))
(+.f64 (.f64 eps x) (.f64 x x))
(fma.f64 eps x (*.f64 x x))
(fma.f64 x eps (*.f64 x x))
(fma.f64 x x (*.f64 eps x))
(/.f64 (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 eps eps) (.f64 x x)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 eps x) (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 eps x) (.f64 x x)))
(/.f64 (.f64 x (+.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x)))) (+.f64 (.f64 eps eps) (*.f64 x (-.f64 x eps))))
(/.f64 (.f64 x (-.f64 (.f64 eps eps) (*.f64 x x))) (-.f64 eps x))
(/.f64 (.f64 (+.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) x) (+.f64 (.f64 eps eps) (*.f64 x (-.f64 x eps))))
(/.f64 (.f64 (-.f64 (.f64 eps eps) (*.f64 x x)) x) (-.f64 eps x))
(*.f64 x (+.f64 eps x))
(*.f64 (+.f64 eps x) 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)))

simplify300.0ms (2%)

Algorithm

1×	egg-herbie

Rules

5916×	`-lowering-.f32`
5916×	`-lowering-.f64`
2956×	`+-lowering-+.f64`
2956×	`+-lowering-+.f32`
1634×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	427	5330
1	1453	4786
2	5031	4647
0	8632	4647

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 456

Calls

Call 1

Inputs
(* 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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (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 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin 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))))))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (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))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin 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)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 3) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 3) (- (* 1/12 (pow x 2)) 1/6))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* 1/2 (/ x eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (- (* 1/12 (pow x 2)) 1/6)) (* -1 (/ (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))) eps)))))
(* eps (+ 1 (* -1/6 (pow eps 2))))
(+ (* -1/2 (* (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ (* eps (+ 1 (* -1/6 (pow eps 2)))) (* x (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (+ (* eps (- (* 1/12 (pow eps 2)) 1/2)) (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) (pow x 2)))))
(* eps (* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2)))
(* (pow x 2) (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (* eps (+ 1 (* -1/6 (pow eps 2)))) x)) (* 1/2 (pow eps 2))) x)) (* eps (- (* 1/12 (pow eps 2)) 1/2))))
(+ 1 (* -1/6 (pow eps 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(+ 1 (+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2))))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (+ (* 1/12 (pow eps 2)) (/ 1 (pow x 2))))) 1/2))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/6 (pow eps 2))) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6))))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (+ (* 1/12 (pow x 2)) (/ 1 (pow eps 2))))) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x)) eps)) (* 1/12 (pow x 2))) 1/6))
(* -1/6 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/6 (pow eps 2)))
(+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
(+ (* -1/6 (pow eps 2)) (* x (+ (* -1/2 eps) (* x (- (* 1/12 (pow eps 2)) 1/2)))))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2)))) 1/2))
(* (pow x 2) (- (* 1/12 (pow eps 2)) 1/2))
(* (pow x 2) (- (+ (* -1/2 (/ eps x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* (pow x 2) (- (+ (* -1 (/ (+ (* 1/6 (/ (pow eps 2) x)) (* 1/2 eps)) x)) (* 1/12 (pow eps 2))) 1/2))
(* -1/2 (pow x 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))
(+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (+ (* -1/2 (/ (pow x 2) (pow eps 2))) (* 1/12 (pow x 2)))) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (+ (* -1/2 (/ x eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))
(* (pow eps 2) (- (+ (* -1 (/ (+ (* 1/2 x) (* 1/2 (/ (pow x 2) eps))) eps)) (* 1/12 (pow x 2))) 1/6))
(* -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))
(* -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)))))
(* 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))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* 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))
(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) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(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) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
(cos (* 1/2 eps))
(+ (cos (* 1/2 eps)) (* -1/2 (* (pow x 2) (cos (* 1/2 eps)))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* 1/24 (* (pow x 2) (cos (* 1/2 eps)))))))
(+ (cos (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (cos (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos (* 1/2 eps)))) (* 1/24 (cos (* 1/2 eps))))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(cos x)
(+ (cos x) (* -1/8 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* 1/384 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/8 (cos x)) (* (pow eps 2) (+ (* -1/46080 (* (pow eps 2) (cos x))) (* 1/384 (cos x)))))))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* (cos x) (cos (* 1/2 eps)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* x (sin (* 1/2 eps)))
(* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* (sin x) (sin (* 1/2 eps)))
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* 1/12 x)
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(* -1/6 (pow eps 2))
(+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))
(+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))
(+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 1/12 (pow x 2))
(* 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)))
(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)))))
(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))))

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)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos 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)))))))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 eps (.f64 #s(literal 1/24 binary64) (sin.f64 x))) (*.f64 (cos.f64 x) #s(literal -1/6 binary64))))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (*.f64 x #s(literal -2 binary64))))
(+ (* 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))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (-.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(+ (* 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))))))))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x (+.f64 (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))) (.f64 x (-.f64 (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal 1/3 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 2 (* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.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)))))))
(* 1/2 (* eps (cos x)))
(.f64 eps (.f64 (cos.f64 x) #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 eps (.f64 (sin.f64 x) #s(literal -1/4 binary64)))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/12 binary64))) (.f64 (sin.f64 x) #s(literal -1/4 binary64))))))
(* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/4 (sin x)) (* eps (+ (* -1/16 (cos x)) (+ (* -1/48 (cos x)) (* 1/48 (* eps (sin x))))))))))
(.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal 1/2 binary64)) (.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal -1/4 binary64)) (.f64 eps (+.f64 (.f64 (cos.f64 x) #s(literal -1/12 binary64)) (.f64 (sin.f64 x) (.f64 eps #s(literal 1/48 binary64)))))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.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))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.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))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.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))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.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))))))
(* (sin (* 1/2 eps)) (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))))
(.f64 (sin.f64 (.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))))))
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(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (cos x) (cos (* 1/2 eps)))
(.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))
(* 1/2 (* eps (sin x)))
(.f64 eps (.f64 (sin.f64 x) #s(literal 1/2 binary64)))
(* eps (+ (* -1/48 (* (pow eps 2) (sin x))) (* 1/2 (sin x))))
(.f64 eps (.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* 1/3840 (* (pow eps 2) (sin x)))))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (+.f64 #s(literal -1/48 binary64) (.f64 (*.f64 eps eps) #s(literal 1/3840 binary64)))))))
(* eps (+ (* 1/2 (sin x)) (* (pow eps 2) (+ (* -1/48 (sin x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (sin x))) (* 1/3840 (sin x))))))))
(.f64 eps (+.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (.f64 (.f64 (sin.f64 x) (+.f64 #s(literal 1/3840 binary64) (.f64 (.f64 eps eps) #s(literal -1/645120 binary64)))) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* x (sin (* 1/2 eps)))
(.f64 x (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* x (+ (sin (* 1/2 eps)) (* -1/6 (* (pow x 2) (sin (* 1/2 eps))))))
(.f64 x (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* 1/120 (* (pow x 2) (sin (* 1/2 eps))))))))
(.f64 x (+.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 x x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64)))))))
(* x (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/6 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/120 (sin (* 1/2 eps)))))))))
(.f64 x (+.f64 (.f64 (+.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (+.f64 (.f64 (.f64 x x) #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) (.f64 (.f64 x x) (*.f64 x x)))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* (sin x) (sin (* 1/2 eps)))
(.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* 1/12 x)
(*.f64 x #s(literal 1/12 binary64))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* (pow eps 2) (- (* 1/12 (pow x 2)) 1/6))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* -1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/6 binary64))
(+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(+ (* -1/6 (pow eps 2)) (* 1/12 (* (pow eps 2) (pow x 2))))
(.f64 eps (.f64 eps (+.f64 (.f64 (.f64 x x) #s(literal 1/12 binary64)) #s(literal -1/6 binary64))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/6 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x)))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/6 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x)))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/6 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x)))))
(* 1/12 (* (pow eps 2) (pow x 2)))
(.f64 x (.f64 x (.f64 (.f64 eps eps) #s(literal 1/12 binary64))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/6 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x)))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/6 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x)))))
(* (pow x 2) (+ (* -1/6 (/ (pow eps 2) (pow x 2))) (* 1/12 (pow eps 2))))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 eps eps) #s(literal 1/12 binary64)) (.f64 #s(literal -1/6 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x)))))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* 1/12 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/12 binary64))
(* eps x)
(*.f64 eps x)
(* x (+ eps x))
(*.f64 x (+.f64 eps x))
(* x (+ eps x))
(*.f64 x (+.f64 eps x))
(* x (+ eps x))
(*.f64 x (+.f64 eps x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ eps x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ eps x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(* (pow x 2) (+ 1 (/ eps x)))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 eps x)))
(pow x 2)
(*.f64 x x)
(+ (* eps x) (pow x 2))
(*.f64 x (+.f64 eps x))
(+ (* eps x) (pow x 2))
(*.f64 x (+.f64 eps x))
(+ (* eps x) (pow x 2))
(*.f64 x (+.f64 eps x))
(* eps x)
(*.f64 eps x)
(* eps (+ x (/ (pow x 2) eps)))
(.f64 eps (+.f64 x (/.f64 (.f64 x x) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(.f64 eps (+.f64 x (/.f64 (.f64 x x) eps)))
(* eps (+ x (/ (pow x 2) eps)))
(.f64 eps (+.f64 x (/.f64 (.f64 x x) eps)))
(* eps x)
(*.f64 eps x)
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(.f64 eps (+.f64 x (/.f64 (.f64 x x) eps)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(.f64 eps (+.f64 x (/.f64 (.f64 x x) eps)))
(* -1 (* eps (+ (* -1 x) (* -1 (/ (pow x 2) eps)))))
(.f64 eps (+.f64 x (/.f64 (.f64 x x) eps)))
(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 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (.f64 (cos.f64 x) #s(literal -1/8 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 (sin.f64 x) (.f64 eps #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 (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 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))))

eval150.0ms (1%)

Compiler: Compiled 35610 to 2565 computations (92.8% saved)

prune150.0ms (1%)

Pruning

25 alts after pruning (20 fresh and 5 done)

	Pruned	Kept	Total
New	997	10	1007
Fresh	8	10	18
Picked	4	1	5
Done	0	4	4
Total	1009	25	1034

Accuracy

100.0%

Counts

1034 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	7.1%	(/.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)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))))
	35.1%	(/.f64 (+.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (*.f64 eps eps))
	35.1%	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))) (.f64 eps eps))
	62.3%	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
✓	62.1%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.2%	(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	54.1%	(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 x)))) #s(literal 2 binary64))
✓	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
	99.6%	(.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
	35.3%	(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
✓	99.6%	(.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 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	49.3%	(.f64 eps (+.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
	97.6%	(.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
	99.2%	(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
	98.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
	97.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))))
	98.1%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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))))))))
	98.0%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
	97.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
	97.9%	(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
✓	98.6%	(*.f64 eps (cos.f64 x))
	8.1%	(neg.f64 x)
✓	97.6%	eps

Compiler

Compiled 1616 to 603 computations (62.7% saved)

regimes52.0ms (0.3%)

Counts

54 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 eps x))) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 eps eps) (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) x)) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x x))))))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 (.f64 (.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 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 #s(literal -1/6 binary64) (*.f64 x x)))))
(.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (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 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 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)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 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))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))) (.f64 eps eps))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.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 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(/.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
(/.f64 (+.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (.f64 eps eps))
(.f64 eps (+.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 x)))) #s(literal 2 binary64))
(.f64 eps (.f64 (-.f64 (.f64 (sin.f64 x) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (/.f64 (cos.f64 x) eps)) eps)) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps)))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (+.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)))))))) #s(literal 2 binary64))
(/.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)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))))
(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64))) (+.f64 (cos.f64 x) (.f64 eps (+.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps (+.f64 (.f64 (.f64 eps (sin.f64 x)) #s(literal 1/48 binary64)) (.f64 (cos.f64 x) #s(literal -1/8 binary64)))))))) #s(literal 2 binary64))

Outputs

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

Calls

3 calls:

16.0ms	x
15.0ms	eps
14.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 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)

regimes46.0ms (0.3%)

Counts

52 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 eps x))) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 eps eps) (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) x)) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x x))))))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 (.f64 (.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 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 #s(literal -1/6 binary64) (*.f64 x x)))))
(.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (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 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 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)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 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))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (+.f64 x (*.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))))) (.f64 eps eps))
(.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) eps)) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps (*.f64 x #s(literal 2 binary64))) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.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 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 #s(literal -1/24 binary64) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) (/.f64 (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))) (*.f64 eps eps))))
(/.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (*.f64 eps eps)) eps)
(/.f64 (+.f64 (.f64 (.f64 (cos.f64 x) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (*.f64 eps eps))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal -1/6 binary64)))) (cos.f64 x)) (.f64 eps eps)) eps) (.f64 eps (.f64 (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))) (.f64 eps eps))
(.f64 eps (+.f64 (.f64 (.f64 eps eps) (+.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (/.f64 (cos.f64 x) eps) eps))) (.f64 (.f64 eps (sin.f64 x)) (+.f64 (.f64 eps (.f64 eps #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (+.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (*.f64 eps eps)))) (sin.f64 x)))) #s(literal 2 binary64))
(.f64 eps (.f64 (-.f64 (.f64 (sin.f64 x) #s(literal -1/24 binary64)) (/.f64 (-.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 x) #s(literal 1/2 binary64)) (/.f64 (cos.f64 x) eps)) eps)) eps)) (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps)))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (+.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)))))))) #s(literal 2 binary64))
(/.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)))))) #s(literal 2 binary64)) (.f64 (sin.f64 (/.f64 (+.f64 eps (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 2 binary64)))))
(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`eps`
99.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes32.0ms (0.2%)

Counts

35 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 eps x))) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 eps eps) (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) x)) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x x))))))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 (.f64 (.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 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 #s(literal -1/6 binary64) (*.f64 x x)))))
(.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/48 binary64) (.f64 eps eps)))) (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 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64))))))))
(.f64 (.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 eps eps) (+.f64 #s(literal -1/48 binary64) (.f64 (.f64 eps eps) #s(literal 1/3840 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)) (sin.f64 x))
(.f64 eps (+.f64 (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))

Outputs
(.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))

Calls

3 calls:

10.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
9.0ms	eps
9.0ms	x

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.2%)

Counts

29 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 eps x))) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 eps eps) (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) x)) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x x))))))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)
(.f64 (.f64 (.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 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 #s(literal -1/6 binary64) (*.f64 x x)))))

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

Calls

2 calls:

8.0ms	eps
7.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes20.0ms (0.1%)

Counts

26 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 eps x))) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 eps eps) (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) x)) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x x))))))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))))))))
(sin.f64 eps)
(*.f64 eps (cos.f64 x))
(-.f64 (sin.f64 (+.f64 x eps)) x)

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

Calls

2 calls:

10.0ms	x
7.0ms	eps

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes14.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64)))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 eps x))) (.f64 x (.f64 x (.f64 (*.f64 eps eps) #s(literal 1/12 binary64)))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 eps x))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (*.f64 x #s(literal 1/12 binary64))) #s(literal -1/6 binary64))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))))))
(+.f64 eps (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))))))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 eps eps) (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))) x)) (.f64 eps (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/12 binary64)))) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x x))))))
(+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (.f64 (.f64 eps x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 eps eps))))))))
(.f64 eps (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (.f64 x (+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64))) (.f64 (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))) (*.f64 eps #s(literal -1/6 binary64)))))))))
(+.f64 (.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps eps) #s(literal -1/6 binary64)))) (.f64 x (+.f64 (.f64 eps (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps))))) (.f64 x (+.f64 (.f64 eps (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) #s(literal 1/12 binary64)))) (.f64 (.f64 eps eps) (.f64 #s(literal -1/6 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (.f64 eps eps)))))))))))
(sin.f64 eps)

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

6.0ms	x
6.0ms	eps

Results

Accuracy	Segments	Branch
98.1%	1	`eps`
98.1%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes10.0ms (0.1%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes6.0ms (0%)

Counts

7 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x))))

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

Calls

2 calls:

3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Counts

5 → 1

Calls

Call 1

Inputs
eps
(neg.f64 x)
(-.f64 #s(literal 0 binary64) x)
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (*.f64 eps eps) #s(literal -1/6 binary64))))

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

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Accuracy

Total -57.3b remaining (-3671.5%)

Threshold costs -57.3b (-3671.5%)

Counts

3 → 1

Calls

Call 1

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

Outputs
eps

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

62×	`*-commutative_binary64`
28×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	126
1	100	126
2	111	126
3	117	126
4	121	126
5	122	126

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(.f64 (.f64 eps (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 eps #s(literal -1/48 binary64)))) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64)))))) #s(literal 2 binary64))
(.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (cos.f64 (+.f64 x (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64))
(*.f64 eps (cos.f64 x))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 (.f64 x 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 x x) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/24 binary64) (*.f64 x x))))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x (+.f64 eps x)))))
(.f64 eps (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/2 binary64)))))
eps

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

soundness2.0s (13%)

Rules

6318×	`-lowering-.f32`
6318×	`-lowering-.f64`
5916×	`-lowering-.f32`
5916×	`-lowering-.f64`
4194×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	564	6051
1	2038	5176
2	7782	5173
0	8298	5173
0	6	16
1	49	16
2	406	16
3	5276	16
0	8497	16
0	57	272
1	338	244
2	2900	244
0	8609	244
0	427	5330
1	1453	4786
2	5031	4647
0	8632	4647
0	107	488
1	327	459
2	964	455
3	3564	455
0	8263	455
0	471	4357
1	1619	3738
2	5918	3722
0	8088	3722

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 325 to 188 computations (42.2% saved)

preprocess59.0ms (0.4%)

Compiler: Compiled 304 to 138 computations (54.6% 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

analyze64.0ms (0.4%)

sample7.4s (48.2%)

preprocess50.0ms (0.3%)

explain125.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.1%)

localize45.0ms (0.3%)

series4.0ms (0%)

rewrite298.0ms (2%)

simplify224.0ms (1.5%)

eval46.0ms (0.3%)

prune34.0ms (0.2%)

simplify146.0ms (1%)

localize334.0ms (2.2%)

series33.0ms (0.2%)

rewrite375.0ms (2.5%)

simplify265.0ms (1.7%)

eval138.0ms (0.9%)

prune105.0ms (0.7%)

simplify180.0ms (1.2%)

localize334.0ms (2.2%)

series43.0ms (0.3%)

rewrite438.0ms (2.9%)

simplify377.0ms (2.5%)

eval141.0ms (0.9%)

prune366.0ms (2.4%)

simplify212.0ms (1.4%)

localize239.0ms (1.6%)

series29.0ms (0.2%)

rewrite385.0ms (2.5%)

simplify300.0ms (2%)

eval150.0ms (1%)

prune150.0ms (1%)

regimes52.0ms (0.3%)

regimes46.0ms (0.3%)

regimes32.0ms (0.2%)

regimes25.0ms (0.2%)

regimes20.0ms (0.1%)

regimes14.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

simplify13.0ms (0.1%)

soundness2.0s (13%)

preprocess59.0ms (0.4%)

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