Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze98.0ms (0.8%)

Memory

-34.1MiB live, 37.3MiB allocated; 111ms collecting garbage

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%	49.4%	0%	25.3%	0%	3
0%	0%	25.3%	49.4%	0%	25.3%	0%	4
0%	0%	19%	49.4%	0%	31.6%	0%	5
0%	0%	15.8%	49.4%	0%	34.8%	0%	6
0%	0%	11.1%	49.4%	0%	39.5%	0%	7
0%	0%	8.7%	49.4%	0%	41.9%	0%	8
0%	0%	5.9%	49.4%	0%	44.6%	0%	9
0%	0%	4.5%	49.4%	0%	46%	0%	10
0%	0%	3.1%	49.4%	0%	47.5%	0%	11
0%	0%	2.7%	49.4%	0%	47.9%	0%	12

Compiler

Compiled 27 to 19 computations (29.6% saved)

sample7.2s (56.9%)

Memory

-195.1MiB live, 7 710.0MiB allocated; 2.4s collecting garbage

Samples

4.2s	26 266×	0	invalid
1.1s	5 077×	1	valid
345.0ms	3 179×	0	valid

Precisions

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

const: 818.0ms (19.7% of total)

ival-sub: 707.0ms (17.1% of total)

ival-sin: 691.0ms (16.7% of total)

ival-add: 506.0ms (12.2% of total)

ival-mult: 327.0ms (7.9% of total)

ival-<: 264.0ms (6.4% of total)

ival-fabs: 241.0ms (5.8% of total)

ival-<=: 224.0ms (5.4% of total)

adjust: 196.0ms (4.7% of total)

ival-and: 111.0ms (2.7% of total)

exact: 47.0ms (1.1% of total)

ival-assert: 13.0ms (0.3% of total)

Bogosity

explain106.0ms (0.8%)

Memory

13.8MiB live, 148.4MiB allocated; 24ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
218	-	3	(8.409635607214193e-183 9.28259171940853e-185)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
1	-	1	(-22.21488810973025 0.005650194264950626)	`(sin.f64 (+.f64 x eps))`
0	-	0	-	`eps`
0	-	0	-	`(+.f64 x eps)`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	215	8

Confusion

	Predicted +	Predicted -
+	215	4
-	0	37

Precision

1.0

Recall

0.9817351598173516

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	215	4	0
-	0	5	32

Precision?

0.9776785714285714

Recall?

1.0

Freqs

test

number	freq
0	41
1	215

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

39.0ms	308×	1	valid
10.0ms	204×	0	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-sin: 11.0ms (39% of total)

adjust: 9.0ms (31.9% of total)

ival-add: 4.0ms (14.2% of total)

ival-sub: 3.0ms (10.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess47.0ms (0.4%)

Memory

-1.6MiB live, 54.1MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	43
1	22	43
2	29	43
3	37	43
4	49	43
5	71	43
6	93	43
7	147	43
8	231	43
9	385	43
10	1010	43
11	4371	43
0	6	7
0	10	7
1	11	7
0	11	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	node limit

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sin.f64 x)
cost-diff	0	(+.f64 x eps)
cost-diff	0	(sin.f64 (+.f64 x eps))
cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	11	18
0	11	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize30.0ms (0.2%)

Memory

-4.4MiB live, 43.2MiB allocated; 2ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.03807887831870883	(sin.f64 (+.f64 x eps))
accuracy	23.512286882999355	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

19.0ms	154×	1	valid
5.0ms	102×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

adjust: 5.0ms (33.5% of total)

ival-sin: 5.0ms (33.5% of total)

ival-add: 3.0ms (20.1% of total)

ival-sub: 2.0ms (13.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Counts

4 → 31

Calls

Call 1

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

Outputs
(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 (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))))))))
eps
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 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 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))))))))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Calls

6 calls:

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

simplify141.0ms (1.1%)

Memory

18.2MiB live, 106.5MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

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 (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))))))))
eps
(+ eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(- (sin (+ eps x)) (sin x))
(sin (+ eps x))
(* x (+ 1 (/ eps x)))
(sin x)
(- (sin (- eps (* -1 x))) (sin x))
(sin (- eps (* -1 x)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* 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 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))))))))
(* eps (+ 1 (/ x eps)))
(- (sin (- x (* -1 eps))) (sin x))
(sin (- x (* -1 eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Outputs
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (cos eps)))
(fma.f64 (cos.f64 eps) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps))
eps
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/5040 binary64) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64))) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(sin x)
(sin.f64 x)
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64)))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps)
(+ (sin x) (* eps (cos x)))
(fma.f64 (cos.f64 x) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps (sin.f64 x))
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64)))

rewrite234.0ms (1.9%)

Memory

-14.1MiB live, 172.9MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16

Stop Event

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

Counts

4 → 154

Calls

Call 1

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

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

eval29.0ms (0.2%)

Memory: -27.4MiB live, 28.9MiB allocated; 9ms collecting garbage
Compiler: Compiled 5 510 to 734 computations (86.7% saved)

prune23.0ms (0.2%)

Memory

20.0MiB live, 20.0MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	8	178

Accuracy

100.0%

Counts

178 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.9%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
	99.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps))
▶	98.7%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 269 to 192 computations (28.6% saved)

simplify139.0ms (1.1%)

Memory

17.9MiB live, 151.3MiB allocated; 14ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (sin.f64 eps) x)
cost-diff	0	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
cost-diff	0	(*.f64 (sin.f64 x) eps)
cost-diff	0	(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
cost-diff	0	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
cost-diff	0	(cos.f64 x)
cost-diff	0	(*.f64 (cos.f64 x) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
cost-diff	0	(sin.f64 eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
cost-diff	0	(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
cost-diff	1	(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
cost-diff	2	(+.f64 #s(literal 0 binary64) eps)

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	202
0	59	192
1	108	192
2	250	192
3	692	189
4	1702	189
5	4994	189
0	8202	189

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))
(+.f64 #s(literal 0 binary64) eps)
#s(literal 0 binary64)
eps
#s(literal 2 binary64)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(fma.f64 #s(literal 2 binary64) x eps)
x
#s(literal -2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 (sin.f64 eps) x)
(sin.f64 eps)
eps
x
#s(literal -1/2 binary64)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)
#s(literal 1 binary64)

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

localize247.0ms (2%)

Memory

-2.9MiB live, 192.5MiB allocated; 27ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
accuracy	0.11328125	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	1.2423701412875932	#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
accuracy	30.20438762370059	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0.0	(cos.f64 x)
accuracy	0.015625	(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
accuracy	0.01953125	(*.f64 (sin.f64 x) eps)
accuracy	0.7922591245969216	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
accuracy	0.0	(cos.f64 x)
accuracy	0.0078125	(*.f64 (cos.f64 x) eps)
accuracy	1.084221771332689	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0.0	(sin.f64 eps)
accuracy	1.9565912190531278	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
accuracy	0.0	(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
accuracy	0.0	(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
accuracy	0.05628720129176342	(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))

Samples

175.0ms	253×	1	valid
1.0ms	3×	0	valid

Compiler

Compiled 179 to 36 computations (79.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 148.0ms

ival-cos: 61.0ms (41.2% of total)

ival-mult: 31.0ms (21% of total)

adjust: 24.0ms (16.2% of total)

ival-add: 11.0ms (7.4% of total)

ival-sin: 11.0ms (7.4% of total)

ival-sub: 5.0ms (3.4% of total)

ival-div: 3.0ms (2% of total)

exact: 1.0ms (0.7% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series35.0ms (0.3%)

Memory

-7.5MiB live, 43.2MiB allocated; 11ms collecting garbage

Counts

20 → 103

Calls

Call 1

Inputs
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 (sin.f64 eps) x)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))

Outputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 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)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(* -1/2 (* x (sin eps)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 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)))))))))
(* 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))))
(* 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)))))))
(* -1/2 (* 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))))
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 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))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	eps	@	0	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
5.0ms	x	@	inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
4.0ms	eps	@	-inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
4.0ms	x	@	-inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))
4.0ms	eps	@	inf	((+ 0 eps) (/ (+ (* 2 x) eps) -2) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (sin (/ (+ 0 eps) 2)) 2) (- (sin (+ x eps)) (sin x)) (sin eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (- (sin (+ x eps)) (sin x)) (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) (* (sin eps) x) (cos (/ (+ (* 2 x) eps) -2)) (sin (/ (+ 0 eps) 2)) (- (cos eps) 1))

simplify144.0ms (1.1%)

Memory

31.5MiB live, 118.7MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	408	1361
1	1502	1304
2	5346	1280
0	8267	1173

Stop Event

1×	iter limit
1×	node limit

Counts

103 → 102

Calls

Call 1

Inputs
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 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)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 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)))
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(* eps x)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(- (cos eps) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(cos (* -1/2 eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(* -1 x)
(* x (- (* -1/2 (/ eps x)) 1))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* eps (sin x))
(* -1/2 (* (pow x 2) (sin eps)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(* -1/2 (* x (sin eps)))
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(cos (* -1/2 (+ eps (* 2 x))))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(- (sin (- eps (* -1 x))) (sin x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(cos (* -1/2 (- eps (* -2 x))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(* eps (+ 1 (* -1/24 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(* 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)))))))))
(* 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))))
(* 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)))))))
(* -1/2 (* 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))))
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
(cos (* -1 x))
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(* 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))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(* eps (- (* -1 (/ x eps)) 1/2))
(* 2 (sin (* 1/2 eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(sin (* 1/2 eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(cos (* -1/2 (- (* 2 x) (* -1 eps))))

Outputs
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(fma.f64 (.f64 (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64)))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) #s(literal 2 binary64) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/12 binary64) (.f64 (*.f64 eps eps) x)) x)) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(* eps x)
(*.f64 x eps)
(* x (+ eps (* -1/6 (* eps (pow x 2)))))
(.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x)
(* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) x) x (.f64 #s(literal -1/6 binary64) eps)) (.f64 x eps))
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(cos (* -1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* -1/2 eps)) (* x (sin (* -1/2 eps))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* -1/2 (* x (cos (* -1/2 eps)))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* -1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* -1/2 eps))) (* -1/6 (* x (sin (* -1/2 eps)))))) (* -1 (sin (* -1/2 eps))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* -1 x)
(neg.f64 x)
(* x (- (* -1/2 (/ eps x)) 1))
(.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x)
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(* eps (sin x))
(*.f64 (sin.f64 x) eps)
(* -1/2 (* (pow x 2) (sin eps)))
(.f64 (.f64 (*.f64 (sin.f64 eps) x) x) #s(literal -1/2 binary64))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) (.f64 x x))
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) x))) x)) (.f64 x x))
(* -1/2 (* x (sin eps)))
(.f64 (.f64 (sin.f64 eps) #s(literal -1/2 binary64)) x)
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)
(cos (* -1/2 (+ eps (* 2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* -1 (* x (+ 1 (* 1/2 (/ eps x)))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(.f64 (.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (neg.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64))) (/.f64 (sin.f64 eps) x)) (neg.f64 x))) x) x)
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(*.f64 (fma.f64 (sin.f64 eps) #s(literal -1/2 binary64) (/.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x)) x)
(cos (* -1/2 (- eps (* -2 x))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/24 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/24 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/1920 (pow eps 2)) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/1920 binary64) (.f64 eps eps)) #s(literal 1/24 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/1920 (* -1/322560 (pow eps 2)))) 1/24))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/322560 binary64) (*.f64 eps eps) #s(literal 1/1920 binary64)) eps) eps) #s(literal 1/24 binary64)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 x) #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 #s(literal 1/120 binary64) eps) eps) #s(literal 1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 eps eps) #s(literal 1/120 binary64)) eps) eps) #s(literal 1/6 binary64)) eps)
(* eps (+ 1 (* -1/2 (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (+.f64 x eps) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 x eps) #s(literal 1/24 binary64) (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 x x)) #s(literal 1/6 binary64))) eps) eps)) eps eps)
(* -1/2 (* eps x))
(.f64 (.f64 x eps) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(.f64 (.f64 eps (+.f64 x eps)) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)
(* eps (+ (* -1/2 x) (* eps (- (* eps (+ (* 1/24 eps) (* 1/12 x))) 1/2))))
(.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) eps) #s(literal 1/2 binary64)) eps (.f64 #s(literal -1/2 binary64) x)) eps)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(.f64 (.f64 (fma.f64 (*.f64 #s(literal -1/6 binary64) eps) eps #s(literal 1 binary64)) x) eps)
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(.f64 (fma.f64 (.f64 x (fma.f64 (.f64 #s(literal 1/120 binary64) eps) eps #s(literal -1/6 binary64))) (.f64 eps eps) x) eps)
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 (.f64 (.f64 x (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64))) eps) eps (.f64 #s(literal -1/6 binary64) x)) (*.f64 x eps))
(cos (* -1 x))
(cos.f64 x)
(+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* -1/8 (* eps (cos (* -1 x)))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) eps) (cos.f64 x) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos (* -1 x)) (* eps (- (* eps (+ (* -1/8 (cos (* -1 x))) (* -1/48 (* eps (sin (* -1 x)))))) (* -1/2 (sin (* -1 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/48 binary64))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(* -1/2 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal -1/2 binary64))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(.f64 (.f64 (-.f64 (.f64 (.f64 eps eps) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (-.f64 (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/40320 binary64) (.f64 eps eps)) #s(literal 1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) eps) eps) #s(literal 1/2 binary64)) (*.f64 eps eps))
(* eps (- (* -1 (/ x eps)) 1/2))
(*.f64 (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1/2 binary64)) eps)
(* 2 (sin (* 1/2 eps)))
(.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal -1/2 binary64) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 (* eps (+ 1/2 (/ x eps))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 x eps) #s(literal 1/2 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(cos (* -1/2 (- (* 2 x) (* -1 eps))))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

rewrite228.0ms (1.8%)

Memory

-30.2MiB live, 204.7MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	170
0	59	162
1	221	162
2	1875	162
0	8244	162

Stop Event

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

Counts

20 → 295

Calls

Call 1

Inputs
(+.f64 #s(literal 0 binary64) eps)
(/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(*.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(*.f64 (sin.f64 eps) x)
(cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64)))
(sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))

Outputs
(pow.f64 eps #s(literal 1 binary64))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (*.f64 eps eps)))) (neg.f64 (neg.f64 (neg.f64 eps))))
(/.f64 (neg.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (neg.f64 (neg.f64 (*.f64 eps eps))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 eps)) (pow.f64 (neg.f64 eps) #s(literal 3 binary64))) (.f64 eps eps))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 eps)) (.f64 (.f64 eps eps) (neg.f64 (neg.f64 (.f64 eps eps))))) (.f64 (*.f64 eps eps) (neg.f64 (neg.f64 eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 (.f64 eps eps)) (.f64 (.f64 eps eps) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))) (.f64 (.f64 eps eps) (neg.f64 (.f64 eps eps))))
(/.f64 (fma.f64 #s(literal 0 binary64) (neg.f64 eps) (.f64 (.f64 eps eps) (neg.f64 (*.f64 eps eps)))) (pow.f64 (neg.f64 eps) #s(literal 3 binary64)))
(/.f64 (fma.f64 #s(literal 0 binary64) (-.f64 eps #s(literal 0 binary64)) (pow.f64 eps #s(literal 4 binary64))) (.f64 (.f64 eps eps) (-.f64 eps #s(literal 0 binary64))))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 (*.f64 eps eps) (pow.f64 eps #s(literal 3 binary64)))) (pow.f64 eps #s(literal 4 binary64)))
(/.f64 (neg.f64 (neg.f64 (*.f64 eps eps))) (neg.f64 (neg.f64 eps)))
(/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 (-.f64 eps #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 eps eps)) (neg.f64 eps))
(/.f64 (*.f64 eps eps) (-.f64 eps #s(literal 0 binary64)))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (pow.f64 eps #s(literal 3 binary64)) (*.f64 eps eps))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps)) (neg.f64 eps))
(+.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps)) eps)
(+.f64 eps #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) eps)
eps
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) eps))) #s(literal -4 binary64))
(/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) #s(literal 2 binary64) (.f64 (.f64 (neg.f64 eps) #s(literal -2 binary64)) (neg.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 (neg.f64 eps) #s(literal -2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (neg.f64 (.f64 eps eps)) #s(literal -2 binary64) (.f64 (.f64 (neg.f64 eps) #s(literal -2 binary64)) (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 (neg.f64 eps) #s(literal -2 binary64)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal 2 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal -2 binary64)) (neg.f64 (.f64 x #s(literal 2 binary64))))) (.f64 (.f64 (*.f64 eps eps) #s(literal -2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -2 binary64) (.f64 (.f64 (.f64 eps eps) #s(literal -2 binary64)) (.f64 x #s(literal 2 binary64)))) (.f64 (.f64 (*.f64 eps eps) #s(literal -2 binary64)) #s(literal -2 binary64)))
(/.f64 (fma.f64 (neg.f64 eps) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (neg.f64 (.f64 x #s(literal 2 binary64))))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 eps) #s(literal -2 binary64) (.f64 #s(literal 2 binary64) (.f64 x #s(literal 2 binary64)))) #s(literal -4 binary64))
(/.f64 (fma.f64 eps #s(literal 2 binary64) (.f64 #s(literal -2 binary64) (neg.f64 (.f64 x #s(literal 2 binary64))))) #s(literal -4 binary64))
(/.f64 (fma.f64 eps #s(literal -2 binary64) (.f64 #s(literal -2 binary64) (.f64 x #s(literal 2 binary64)))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 (.f64 x #s(literal 2 binary64))) (.f64 (neg.f64 eps) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (neg.f64 (.f64 eps eps)))) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 eps) #s(literal -2 binary64))))
(/.f64 (fma.f64 (neg.f64 (.f64 x #s(literal 2 binary64))) (.f64 (.f64 eps eps) #s(literal -2 binary64)) (.f64 #s(literal 2 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 #s(literal 2 binary64) (.f64 (*.f64 eps eps) #s(literal -2 binary64))))
(/.f64 (fma.f64 (neg.f64 (.f64 x #s(literal 2 binary64))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (neg.f64 eps))) #s(literal 4 binary64))
(/.f64 (fma.f64 (neg.f64 (.f64 x #s(literal 2 binary64))) #s(literal -2 binary64) (.f64 #s(literal 2 binary64) eps)) #s(literal -4 binary64))
(/.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (.f64 (neg.f64 eps) #s(literal -2 binary64)) (.f64 #s(literal -2 binary64) (neg.f64 (.f64 eps eps)))) (.f64 #s(literal -2 binary64) (.f64 (neg.f64 eps) #s(literal -2 binary64))))
(/.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) (.f64 (.f64 eps eps) #s(literal -2 binary64)) (.f64 #s(literal -2 binary64) (pow.f64 eps #s(literal 3 binary64)))) (.f64 #s(literal -2 binary64) (.f64 (*.f64 eps eps) #s(literal -2 binary64))))
(/.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64) (.f64 #s(literal -2 binary64) (neg.f64 eps))) #s(literal -4 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64))) (/.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1 binary64) (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x #s(literal -1 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 eps #s(literal -2 binary64)) #s(literal 2 binary64)) (.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) #s(literal -2 binary64))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps))) (neg.f64 (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64))))
(/.f64 (fma.f64 (.f64 x #s(literal 2 binary64)) #s(literal -2 binary64) (.f64 #s(literal -2 binary64) eps)) #s(literal 4 binary64))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 eps) eps)) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) eps) #s(literal -2 binary64)))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 eps (-.f64 eps (.f64 x #s(literal 2 binary64))))) #s(literal -2 binary64)))
(/.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) #s(literal 2 binary64))
(/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))
(neg.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(fma.f64 x #s(literal -1 binary64) (/.f64 eps #s(literal -2 binary64)))
(fma.f64 #s(literal 2 binary64) (/.f64 x #s(literal -2 binary64)) (/.f64 eps #s(literal -2 binary64)))
(+.f64 (/.f64 eps #s(literal -2 binary64)) (*.f64 x #s(literal -1 binary64)))
(+.f64 (*.f64 x #s(literal -1 binary64)) (/.f64 eps #s(literal -2 binary64)))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #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))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))))
(.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #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 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(*.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (+.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (/.f64 eps #s(literal 2 binary64)) (/.f64 eps #s(literal 2 binary64))) #s(literal 2 binary64)))))
(*.f64 #s(literal 2 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
(+.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) (sin.f64 (/.f64 eps #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(fma.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps))) (cos.f64 eps) (.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (*.f64 eps eps))) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) #s(literal 1 binary64) (*.f64 (cos.f64 eps) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 eps) (*.f64 #s(literal 1 binary64) (sin.f64 eps)))
(sin.f64 eps)
(-.f64 (.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (cos.f64 eps)) (.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (neg.f64 eps))) (neg.f64 (sin.f64 eps))))
(+.f64 (.f64 (sin.f64 eps) #s(literal 1 binary64)) (.f64 (cos.f64 eps) #s(literal 0 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps))) (cos.f64 eps)) (.f64 (cos.f64 (/.f64 #s(literal 0 binary64) (.f64 eps eps))) (sin.f64 eps)))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 eps)) (.f64 #s(literal 1 binary64) (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (cos.f64 x) (neg.f64 (.f64 eps eps)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 eps eps)))
(/.f64 (.f64 (neg.f64 (.f64 eps eps)) (cos.f64 x)) (neg.f64 eps))
(/.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (cos.f64 x)) (.f64 eps eps))
(/.f64 (.f64 (cos.f64 x) (neg.f64 (.f64 eps eps))) (neg.f64 eps))
(/.f64 (.f64 (cos.f64 x) (pow.f64 eps #s(literal 3 binary64))) (.f64 eps eps))
(fma.f64 (cos.f64 x) eps (*.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 (cos.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) eps))
(fma.f64 eps (cos.f64 x) (*.f64 #s(literal 0 binary64) (cos.f64 x)))
(fma.f64 eps (cos.f64 x) (*.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 x) (*.f64 (cos.f64 x) eps))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 (cos.f64 x) eps))
(+.f64 (.f64 (cos.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 #s(literal 0 binary64) (cos.f64 x)))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) #s(literal 0 binary64)))
(fma.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 x) (*.f64 #s(literal 0 binary64) (sin.f64 x)))
(fma.f64 (sin.f64 x) #s(literal 0 binary64) (*.f64 (cos.f64 x) #s(literal 1 binary64)))
(sin.f64 (+.f64 (neg.f64 (neg.f64 x)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 (neg.f64 x))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (neg.f64 (sin.f64 x)) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (sin.f64 x)))
(+.f64 (.f64 (sin.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) eps)
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) eps)) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) eps)) (neg.f64 (fma.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (cos.f64 x) (-.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))))))
(/.f64 (neg.f64 (.f64 (neg.f64 (.f64 eps eps)) (fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (neg.f64 (*.f64 eps eps)))) (neg.f64 (neg.f64 eps)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps) (cos.f64 x)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (*.f64 eps eps)))
(/.f64 (neg.f64 (.f64 eps (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x))))
(/.f64 (neg.f64 (.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (fma.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (cos.f64 x) (-.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)))))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (neg.f64 (.f64 eps eps)))) (neg.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps)) (cos.f64 x)) (neg.f64 eps))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps)) (cos.f64 x)) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (neg.f64 (.f64 eps eps)))) (neg.f64 (.f64 (fma.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (cos.f64 x) (-.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 x) eps))))) (neg.f64 eps))))
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(fma.f64 (sin.f64 eps) (*.f64 #s(literal -1/2 binary64) x) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(fma.f64 x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))) (/.f64 (pow.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))))
(-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64))
(-.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (neg.f64 (.f64 (sin.f64 eps) x)) #s(literal -1/2 binary64)))
(-.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 eps) x)))
(-.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (neg.f64 (sin.f64 eps)) (.f64 #s(literal -1/2 binary64) x)))
(-.f64 (cos.f64 eps) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (sin.f64 eps) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)))))) (/.f64 (pow.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (.f64 (sin.f64 eps) x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (-.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)))))))
(+.f64 (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(+.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) (.f64 (.f64 (sin.f64 eps) x) #s(literal -1/2 binary64)))
(*.f64 (sin.f64 eps) x)
(*.f64 x (sin.f64 eps))
(fma.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (*.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))))
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(fma.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64) (*.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) (*.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)))))
(sin.f64 (+.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
(-.f64 (.f64 (cos.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (sin.f64 (/.f64 (+.f64 x eps) #s(literal 2 binary64))) (sin.f64 (/.f64 x #s(literal 2 binary64)))))
(-.f64 (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) (cos.f64 (.f64 x #s(literal -1 binary64)))) (.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))) (sin.f64 (.f64 x #s(literal -1 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (neg.f64 (.f64 x #s(literal -1 binary64)))) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(-.f64 (.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (sin.f64 (/.f64 eps #s(literal -2 binary64)))))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))
(cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 0 binary64)) (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (sin.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (+.f64 (/.f64 eps #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))) (.f64 (cos.f64 (.f64 x #s(literal -1 binary64))) (cos.f64 (/.f64 eps #s(literal -2 binary64)))))
(+.f64 (.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) (.f64 #s(literal 0 binary64) (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64)))))
(+.f64 (.f64 (sin.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal -2 binary64))) #s(literal 0 binary64)) (.f64 (cos.f64 (/.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64))) #s(literal 1 binary64)))
(neg.f64 (sin.f64 (/.f64 eps #s(literal -2 binary64))))
(fma.f64 (sin.f64 (/.f64 eps #s(literal 2 binary64))) #s(literal 1 binary64) (*.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal 0 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (/.f64 eps #s(literal -2 binary64))) (*.f64 #s(literal 1 binary64) (sin.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))) #s(literal 1 binary64)) (.f64 (cos.f64 (/.f64 eps #s(literal -2 binary64))) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (/.f64 eps #s(literal -2 binary64)))) (.f64 #s(literal 1 binary64) (sin.f64 (/.f64 eps #s(literal 2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))))))
(/.f64 (-.f64 (*.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))) (.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 1 binary64))) (pow.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal 2 binary64)))
(/.f64 (neg.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))))
(/.f64 (neg.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))
(/.f64 (-.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))))
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) (pow.f64 (+.f64 #s(literal 1 binary64) (cos.f64 eps)) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (cos.f64 eps) #s(literal 3 binary64)) (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps)))) (pow.f64 (fma.f64 (cos.f64 eps) (cos.f64 eps) (+.f64 #s(literal 1 binary64) (cos.f64 eps))) #s(literal -1 binary64)))
(-.f64 (cos.f64 eps) #s(literal 1 binary64))

eval83.0ms (0.7%)

Memory: -0.1MiB live, 103.9MiB allocated; 12ms collecting garbage
Compiler: Compiled 12 622 to 1 836 computations (85.5% saved)

prune19.0ms (0.1%)

Memory

-1.3MiB live, 44.2MiB allocated; 3ms collecting garbage

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	412	15	427
Fresh	1	1	2
Picked	3	2	5
Done	0	1	1
Total	416	19	435

Accuracy

100.0%

Counts

435 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
▶	99.8%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
	99.8%	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))
	99.4%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.3%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	98.9%	(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
▶	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
✓	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
▶	99.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 867 to 627 computations (27.7% saved)

simplify159.0ms (1.3%)

Memory

-16.2MiB live, 163.4MiB allocated; 61ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
cost-diff	1	(/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))
cost-diff	2	(+.f64 #s(literal 0 binary64) eps)
cost-diff	3	(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
cost-diff	0	(*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
cost-diff	1	(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
cost-diff	4	(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
cost-diff	0	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
cost-diff	1	(-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64))
cost-diff	0	#s(approx (cos x) #s(literal 1 binary64))
cost-diff	0	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
cost-diff	0	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
cost-diff	0	(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
cost-diff	0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	362
0	95	334
1	164	328
2	358	328
3	908	323
4	2030	323
5	4951	323
0	8184	314

Stop Event

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

Calls

Call 1

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

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

localize268.0ms (2.1%)

Memory

-0.1MiB live, 282.3MiB allocated; 19ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(PI.f64)
accuracy	0.01953125	(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
accuracy	0.0234375	(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
accuracy	0.07892912219458008	(sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64)))
accuracy	0.0078125	(*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps)
accuracy	0.03125	(+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))
accuracy	0.08220500848354913	(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
accuracy	1.084221771332689	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
accuracy	0.11328125	(.f64 (.f64 #s(literal 1/12 binary64) x) eps)
accuracy	0.3125	(*.f64 #s(literal 1/12 binary64) x)
accuracy	0.7922591245969216	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
accuracy	1.2473572419653858	#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
accuracy	0.0078125	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
accuracy	1.084221771332689	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
accuracy	1.9646642467894293	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0.0	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
accuracy	0.0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
accuracy	0.01953125	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.05628720129176342	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))

Samples

176.0ms	153×	1	valid
56.0ms	103×	0	valid

Compiler

Compiled 283 to 57 computations (79.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 175.0ms

ival-sin: 53.0ms (30.3% of total)

ival-mult: 33.0ms (18.9% of total)

ival-add: 32.0ms (18.3% of total)

adjust: 24.0ms (13.7% of total)

ival-div: 15.0ms (8.6% of total)

ival-cos: 7.0ms (4% of total)

ival-sub: 4.0ms (2.3% of total)

const: 4.0ms (2.3% of total)

ival-neg: 2.0ms (1.1% of total)

ival-pi: 1.0ms (0.6% of total)

exact: 1.0ms (0.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series44.0ms (0.4%)

Memory

-6.0MiB live, 45.7MiB allocated; 16ms collecting garbage

Counts

24 → 143

Calls

Call 1

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

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -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 (* 1/2 eps)))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (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)))))
(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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
-1/2
(- (* 1/12 (* eps x)) 1/2)
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin (* 1/2 (PI)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(* 1/2 (PI))
(+ (* -1 x) (* 1/2 (PI)))
(* eps (sin (* 1/2 (PI))))
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(* 1/2 (- (PI) eps))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(* 1/12 x)
(* 1/12 (* eps x))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(sin (- (* 1/2 (PI)) x))
(* -1 x)
(* x (- (* 1/2 (/ (PI) x)) 1))
(* eps (sin (- (* 1/2 (PI)) x)))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -1 x)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(sin (+ (* -1 x) (* 1/2 (PI))))
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))
(* eps (sin (+ (* -1 x) (* 1/2 (PI)))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 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 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* 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)))))
(* 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 (* 1/2 (- (PI) (* 2 x))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x)))))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))))))
(* 1/2 (- (PI) (* 2 x)))
(+ (* -1/2 eps) (* 1/2 (- (PI) (* 2 x))))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* 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))))
(- (PI) (* 2 x))
(- (+ (PI) (* -1 eps)) (* 2 x))
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 eps)
(* eps (- (* 1/2 (/ (- (PI) (* 2 x)) eps)) 1/2))
(sin (* 1/2 eps))
(* -1 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (- (PI) (* 2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))

Calls

6 calls:

Time	Variable		Point	Expression
14.0ms	x	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (sin (* 1/2 eps)) (* 1/12 x) (* (* 1/12 x) eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
9.0ms	x	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (sin (* 1/2 eps)) (* 1/12 x) (* (* 1/12 x) eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
5.0ms	eps	@	0	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (sin (* 1/2 eps)) (* 1/12 x) (* (* 1/12 x) eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
5.0ms	eps	@	-inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (sin (* 1/2 eps)) (* 1/12 x) (* (* 1/12 x) eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))
5.0ms	eps	@	inf	((* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (* (* 1/12 x) eps) 1/2) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2)) (+ 0 eps) (/ (+ (neg (+ (* x 2) eps)) (PI)) 2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (sin (* 1/2 eps)) (* 1/12 x) (* (* 1/12 x) eps) (+ (neg (+ (* x 2) eps)) (PI)) (PI))

simplify176.0ms (1.4%)

Memory

14.6MiB live, 147.7MiB allocated; 12ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	529	2109
1	1994	2034
2	7217	2026
0	8356	1865

Stop Event

1×	iter limit
1×	node limit

Counts

143 → 142

Calls

Call 1

Inputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -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 (* 1/2 eps)))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (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)))))
(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)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
-1/2
(- (* 1/12 (* eps x)) 1/2)
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(sin (* 1/2 (PI)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(* 1/2 (PI))
(+ (* -1 x) (* 1/2 (PI)))
(* eps (sin (* 1/2 (PI))))
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(sin (* 1/2 (- (PI) eps)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(* 1/2 (- (PI) eps))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(* 1/12 x)
(* 1/12 (* eps x))
(- (PI) eps)
(- (+ (PI) (* -2 x)) eps)
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (+ x (* 1/2 eps))))
(cos (+ x (* 1/2 eps)))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos x)
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(sin (- (* 1/2 (PI)) x))
(* -1 x)
(* x (- (* 1/2 (/ (PI) x)) 1))
(* eps (sin (- (* 1/2 (PI)) x)))
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(* -2 x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(cos (- (* 1/2 eps) (* -1 x)))
(- (sin (- eps (* -1 x))) (sin x))
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(sin (+ (* -1 x) (* 1/2 (PI))))
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))
(* eps (sin (+ (* -1 x) (* 1/2 (PI)))))
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(* eps (cos (* -1 x)))
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 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 (* eps (sin x))) (* 2 (cos x)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* 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)))))
(* 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 (* 1/2 (- (PI) (* 2 x))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x)))))))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))))))
(* 1/2 (- (PI) (* 2 x)))
(+ (* -1/2 eps) (* 1/2 (- (PI) (* 2 x))))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(* 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))))
(- (PI) (* 2 x))
(- (+ (PI) (* -1 eps)) (* 2 x))
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 eps)
(* eps (- (* 1/2 (/ (- (PI) (* 2 x)) eps)) 1/2))
(sin (* 1/2 eps))
(* -1 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(* 2 (cos (- x (* -1/2 eps))))
(cos (- x (* -1/2 eps)))
(- (sin (- x (* -1 eps))) (sin x))
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (- (PI) (* 2 x)) eps)))))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))

Outputs
(* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* 2 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* x (* (cos (* -1/2 eps)) (sin (* 1/2 eps))))) (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))))))
(fma.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) x (.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
(+ (* 2 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 2 (* (sin (* -1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (cos (* -1/2 eps)) (sin (* 1/2 eps)))) (* -1/3 (* x (* (sin (* -1/2 eps)) (sin (* 1/2 eps))))))))))
(fma.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (.f64 x x) (fma.f64 (.f64 (.f64 #s(literal -1/3 binary64) x) (sin.f64 (.f64 #s(literal -1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (*.f64 #s(literal 1/2 binary64) eps))))))
(* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* -2 (* x (pow (sin (* 1/2 eps)) 2))) (* 2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))))
(.f64 #s(literal -2 binary64) (-.f64 (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) x) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) 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))))))))
(fma.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 (.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))) x))
(+ (* 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))))))))
(fma.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (.f64 #s(literal 1/3 binary64) x) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) x (.f64 (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -2 binary64))) x))
(* 2 (cos (* 1/2 eps)))
(.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* -2 (* x (sin (* 1/2 eps)))) (* 2 (cos (* 1/2 eps))))
(.f64 #s(literal -2 binary64) (-.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* -1 (* x (cos (* 1/2 eps)))))))
(fma.f64 (fma.f64 (neg.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))) x (.f64 (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(+ (* 2 (cos (* 1/2 eps))) (* x (+ (* -2 (sin (* 1/2 eps))) (* x (+ (* -1 (cos (* 1/2 eps))) (* 1/3 (* x (sin (* 1/2 eps)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal -1/2 binary64) eps (PI.f64)))) x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64))) x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(cos (* 1/2 eps))
(cos.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (cos (* 1/2 eps)) (* -1 (* x (sin (* 1/2 eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* -1/2 (* x (cos (* 1/2 eps)))) (sin (* 1/2 eps)))))
(fma.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(+ (cos (* 1/2 eps)) (* x (- (* x (+ (* -1/2 (cos (* 1/2 eps))) (* 1/6 (* x (sin (* 1/2 eps)))))) (sin (* 1/2 eps)))))
(fma.f64 (-.f64 (.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) x (cos.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/12 (* eps x)) 1/2)
(-.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64))
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps eps) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 x eps)) (.f64 (.f64 (.f64 (*.f64 eps eps) x) #s(literal 1/12 binary64)) x)) x eps)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 (*.f64 x eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 x eps)) x #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 (fma.f64 (-.f64 (.f64 (.f64 x eps) #s(literal 1/12 binary64)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))
(sin (* 1/2 (PI)))
(sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(fma.f64 (neg.f64 x) (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(fma.f64 (fma.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) x) (cos.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (PI.f64) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))))
(* 1/2 (PI))
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(+ (* -1 x) (* 1/2 (PI)))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
(* eps (sin (* 1/2 (PI))))
(.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps)
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(.f64 (neg.f64 eps) (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) x) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(fma.f64 (fma.f64 (neg.f64 eps) (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) (.f64 (.f64 (.f64 x eps) #s(literal -1/2 binary64)) (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))))) x (.f64 (sin.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64))) eps))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(fma.f64 (fma.f64 (neg.f64 eps) (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) (.f64 (fma.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) x) (cos.f64 (.f64 (PI.f64) #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) eps))) x)) x (.f64 (sin.f64 (.f64 (PI.f64) #s(literal 1/2 binary64))) eps))
(sin (* 1/2 (- (PI) eps)))
(sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
(+ (sin (* 1/2 (- (PI) eps))) (* -1 (* x (cos (* 1/2 (- (PI) eps))))))
(fma.f64 (neg.f64 x) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* -1/2 (* x (sin (* 1/2 (- (PI) eps))))))))
(fma.f64 (fma.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (.f64 #s(literal -1/2 binary64) x) (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) eps))) (* x (+ (* -1 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1/2 (sin (* 1/2 (- (PI) eps)))) (* 1/6 (* x (cos (* 1/2 (- (PI) eps))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64) (PI.f64)))) x (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(* 1/2 (- (PI) eps))
(*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(fma.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64) (neg.f64 x))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(.f64 #s(literal -2 binary64) (-.f64 (.f64 (.f64 (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(fma.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) x) (.f64 (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)))) x))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -2 binary64) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (cos.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal -1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) x)) x (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(* 1/12 x)
(*.f64 #s(literal 1/12 binary64) x)
(* 1/12 (* eps x))
(.f64 (.f64 x eps) #s(literal 1/12 binary64))
(- (PI) eps)
(-.f64 (PI.f64) eps)
(- (+ (PI) (* -2 x)) eps)
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(* 2 (* (cos (* -1/2 (+ eps (* 2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (* (cos (+ x (* 1/2 eps))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (cos (+ x (* 1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos (+ x (* 1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* x (- (* 1/12 eps) (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/12 binary64) eps (/.f64 #s(literal -1/2 binary64) x)) x)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(sin (- (* 1/2 (PI)) x))
(sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
(* -1 x)
(neg.f64 x)
(* x (- (* 1/2 (/ (PI) x)) 1))
(.f64 (-.f64 (.f64 (/.f64 (PI.f64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(* eps (sin (- (* 1/2 (PI)) x)))
(.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps)
(sin (* 1/2 (- (PI) (+ eps (* 2 x)))))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(* x (- (* 1/2 (/ (- (PI) eps) x)) 1))
(.f64 (-.f64 (.f64 (/.f64 (-.f64 (PI.f64) eps) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) x)
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) (+ eps (* 2 x)))))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* x (- (/ (PI) x) (+ 2 (/ eps x))))
(*.f64 (-.f64 (/.f64 (-.f64 (PI.f64) eps) x) #s(literal 2 binary64)) x)
(* 2 (* (cos (* -1/2 (- eps (* -2 x)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (* (cos (- (* 1/2 eps) (* -1 x))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (cos (- (* 1/2 eps) (* -1 x))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos (- (* 1/2 eps) (* -1 x)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* x (+ (* -1/12 eps) (* 1/2 (/ 1 x)))))
(*.f64 (neg.f64 x) (fma.f64 #s(literal -1/12 binary64) eps (/.f64 #s(literal 1/2 binary64) x)))
(sin (+ (* -1 x) (* 1/2 (PI))))
(sin.f64 (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
(* -1 (* x (+ 1 (* -1/2 (/ (PI) x)))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (PI.f64) x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(* eps (sin (+ (* -1 x) (* 1/2 (PI)))))
(.f64 (sin.f64 (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x)) eps)
(sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(* -1 (* x (+ 1 (* -1/2 (/ (- (PI) eps) x)))))
(*.f64 (neg.f64 x) (fma.f64 (/.f64 (-.f64 (PI.f64) eps) x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -2 x)) eps)))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* -1 (* x (+ 2 (* -1 (/ (- (PI) eps) x)))))
(*.f64 (neg.f64 x) (-.f64 #s(literal 2 binary64) (/.f64 (-.f64 (PI.f64) eps) x)))
(* eps (cos (* -1 x)))
(*.f64 (cos.f64 x) eps)
(* eps (+ (cos (* -1 x)) (* 1/2 (* eps (sin (* -1 x))))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) #s(literal 1/2 binary64) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (cos.f64 x)) (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/24 binary64))) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* 2 (cos x))
(*.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 eps #s(literal -1/4 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64))) eps (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(sin (* 1/2 (- (PI) (* 2 x))))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))
(fma.f64 (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (.f64 #s(literal -1/2 binary64) eps) (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* -1/8 (* eps (sin (* 1/2 (- (PI) (* 2 x)))))))))
(fma.f64 (fma.f64 (.f64 eps #s(literal -1/8 binary64)) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))))
(+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (- (PI) (* 2 x))))) (* 1/48 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) eps) (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1/8 binary64))) eps (.f64 (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))))
(* 1/2 (- (PI) (* 2 x)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))
(+ (* -1/2 eps) (* 1/2 (- (PI) (* 2 x))))
(*.f64 #s(literal -1/2 binary64) (-.f64 eps (fma.f64 #s(literal -2 binary64) x (PI.f64))))
(* eps (sin (* 1/2 (- (PI) (* 2 x)))))
(.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) eps)
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* -1/2 (* eps (cos (* 1/2 (- (PI) (* 2 x))))))))
(.f64 (fma.f64 (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (.f64 #s(literal -1/2 binary64) eps) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) eps)
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* 2 (* eps (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1/6 binary64)) eps (.f64 (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) eps)
(* eps (+ (sin (* 1/2 (- (PI) (* 2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (- (PI) (* 2 x))))) (* eps (+ (* 1/24 (* eps (cos (* 1/2 (- (PI) (* 2 x)))))) (* 2 (+ (* -1/16 (sin (* 1/2 (- (PI) (* 2 x))))) (* -1/48 (sin (* 1/2 (- (PI) (* 2 x)))))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) (.f64 #s(literal 1/24 binary64) eps) (.f64 (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64))) #s(literal -1/6 binary64))) eps (.f64 (cos.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal -1/2 binary64))) #s(literal -1/2 binary64))) eps (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) #s(literal 1/2 binary64)))) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(- (PI) (* 2 x))
(fma.f64 #s(literal -2 binary64) x (PI.f64))
(- (+ (PI) (* -1 eps)) (* 2 x))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(* eps (- (* 1/12 x) (* 1/2 (/ 1 eps))))
(*.f64 (fma.f64 #s(literal 1/12 binary64) x (/.f64 #s(literal -1/2 binary64) eps)) eps)
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps) eps)
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps) eps)
(* -1/2 (* eps (sin x)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps)
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps)
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(* eps (- (* 1/2 (/ (- (PI) (* 2 x)) eps)) 1/2))
(.f64 (-.f64 (.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1 eps)
(neg.f64 eps)
(* eps (- (/ (PI) eps) (+ 1 (* 2 (/ x eps)))))
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1 binary64)) eps)
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(* -1 (* eps (+ (* -1/12 x) (* 1/2 (/ 1 eps)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal -1/12 binary64) x (/.f64 #s(literal 1/2 binary64) eps)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) (neg.f64 eps))))
(sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (- (PI) (* 2 x)) eps)))))
(*.f64 (neg.f64 eps) (fma.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (- (PI) (* 2 x)) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps)))

rewrite251.0ms (2%)

Memory

-29.5MiB live, 116.1MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	272
0	95	244
1	354	244
2	2606	244
0	9104	241

Stop Event

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

Counts

24 → 398

Calls

Call 1

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

Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))
(.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
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(fma.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (*.f64 (cbrt.f64 (PI.f64)) (PI.f64))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(fma.f64 (neg.f64 x) #s(literal 2 binary64) (+.f64 (neg.f64 eps) (PI.f64)))
(fma.f64 #s(literal -2 binary64) x (+.f64 (neg.f64 eps) (PI.f64)))
(fma.f64 x #s(literal -2 binary64) (+.f64 (neg.f64 eps) (PI.f64)))
(fma.f64 #s(literal 2 binary64) (neg.f64 x) (+.f64 (neg.f64 eps) (PI.f64)))
(-.f64 (/.f64 (pow.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)) (fma.f64 #s(literal -2 binary64) x (-.f64 (neg.f64 eps) (PI.f64)))) (/.f64 (*.f64 (PI.f64) (PI.f64)) (fma.f64 #s(literal -2 binary64) x (-.f64 (neg.f64 eps) (PI.f64)))))
(-.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (neg.f64 (PI.f64)))
(+.f64 (+.f64 (PI.f64) (*.f64 #s(literal -2 binary64) x)) (neg.f64 eps))
(+.f64 (/.f64 (neg.f64 (pow.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 3 binary64))) (fma.f64 (PI.f64) (-.f64 (PI.f64) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) (pow.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))) (/.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) (fma.f64 (PI.f64) (-.f64 (PI.f64) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps))) (pow.f64 (fma.f64 x #s(literal 2 binary64) eps) #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(literal -2 binary64) x) (+.f64 (neg.f64 eps) (PI.f64)))
(+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64))
(+.f64 (PI.f64) (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))) (neg.f64 (neg.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 5 binary64))) (pow.f64 (PI.f64) #s(literal 1/6 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 4 binary64))) (cbrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (neg.f64 (PI.f64))) (sqrt.f64 (neg.f64 (PI.f64))))
(*.f64 (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (pow.f64 (PI.f64) #s(literal 1/4 binary64)))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64))) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64))) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))) (cbrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 5/2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (sqrt.f64 (PI.f64))))
(.f64 (pow.f64 (pow.f64 (.f64 (PI.f64) (cbrt.f64 (PI.f64))) #s(literal 2 binary64)) #s(literal 1/3 binary64)) (cbrt.f64 (cbrt.f64 (PI.f64))))
(*.f64 (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64)) #s(literal 1/3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (sqrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (cbrt.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(*.f64 (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)) (pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (PI.f64))) (neg.f64 (sqrt.f64 (PI.f64))))
(*.f64 (pow.f64 (PI.f64) #s(literal 1/4 binary64)) (sqrt.f64 (pow.f64 (PI.f64) #s(literal 3/2 binary64))))
(*.f64 (sqrt.f64 (PI.f64)) (log.f64 (exp.f64 (sqrt.f64 (PI.f64)))))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (PI.f64) #s(literal 1/6 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)) (cbrt.f64 (PI.f64)))
(.f64 (cbrt.f64 (PI.f64)) (sqrt.f64 (.f64 (cbrt.f64 (PI.f64)) (PI.f64))))
(*.f64 (cbrt.f64 (PI.f64)) (log.f64 (exp.f64 (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))))
(*.f64 (cbrt.f64 (PI.f64)) (pow.f64 (cbrt.f64 (PI.f64)) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (PI.f64)))
(pow.f64 (neg.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (PI.f64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)) #s(literal 1/3 binary64))
(pow.f64 (*.f64 (PI.f64) (PI.f64)) #s(literal 1/2 binary64))
(pow.f64 (cbrt.f64 (PI.f64)) #s(literal 3 binary64))
(pow.f64 (PI.f64) #s(literal 1 binary64))
(cbrt.f64 (pow.f64 (PI.f64) #s(literal 3 binary64)))
(sqrt.f64 (*.f64 (PI.f64) (PI.f64)))
(fabs.f64 (neg.f64 (PI.f64)))
(fabs.f64 (PI.f64))
(+.f64 (cosh.f64 (log.f64 (PI.f64))) (sinh.f64 (log.f64 (PI.f64))))
(exp.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (PI.f64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (PI.f64)) #s(literal 3 binary64)) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (PI.f64) #s(literal 3 binary64))) #s(literal 1/3 binary64)))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (PI.f64))) #s(literal 3 binary64)))
(exp.f64 (log.f64 (PI.f64)))
(log.f64 (exp.f64 (PI.f64)))
(PI.f64)

eval86.0ms (0.7%)

Memory: 45.3MiB live, 91.0MiB allocated; 2ms collecting garbage
Compiler: Compiled 18 817 to 2 933 computations (84.4% saved)

prune65.0ms (0.5%)

Memory

-27.1MiB live, 31.6MiB allocated; 15ms collecting garbage

Pruning

20 alts after pruning (14 fresh and 6 done)

	Pruned	Kept	Total
New	560	7	567
Fresh	4	7	11
Picked	2	3	5
Done	0	3	3
Total	566	20	586

Accuracy

100.0%

Counts

586 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
▶	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
✓	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
▶	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
▶	99.8%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
	99.8%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
✓	99.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
	99.4%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
▶	99.3%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
	98.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 976 to 697 computations (28.6% saved)

simplify123.0ms (1%)

Memory

9.3MiB live, 55.9MiB allocated; 3ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
cost-diff	0	(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
cost-diff	0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
cost-diff	0	#s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
cost-diff	0	(sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
cost-diff	0	(.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
cost-diff	0	#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
cost-diff	1	(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
cost-diff	0	(.f64 (.f64 #s(literal -1/2 binary64) x) x)
cost-diff	0	(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
cost-diff	0	#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps))
cost-diff	0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
cost-diff	0	(.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
cost-diff	0	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
cost-diff	1	(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
cost-diff	1	(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	431
0	108	427
1	196	424
2	521	424
3	1567	411
4	3456	409
5	6199	409
0	8187	402

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
#s(literal 2 binary64)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
#s(literal -2 binary64)
x
(-.f64 (PI.f64) eps)
(PI.f64)
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
(.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps)
(sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(PI.f64)
#s(literal 1/2 binary64)
x
eps
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)

Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps) x))) #s(literal 2 binary64)))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (.f64 (sin.f64 (*.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps) x))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
(*.f64 (sin.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps) x))) #s(literal 2 binary64))
#s(literal 2 binary64)
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(sin.f64 (neg.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps) x)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
(neg.f64 (fma.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps) x))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
#s(literal -2 binary64)
x
(-.f64 (PI.f64) eps)
(PI.f64)
eps
#s(literal 1/2 binary64)
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(*.f64 #s(literal 1/2 binary64) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(*.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
(.f64 #s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
(*.f64 x x)
x
#s(literal 1/2 binary64)
#s(literal 1 binary64)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x)))) eps))
(.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps)
(*.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x)))) eps)
(sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
(sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))))
#s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
#s(approx (+ (neg x) (/ (PI) 2)) (fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x)))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/2 binary64) (PI.f64) (neg.f64 x))
(*.f64 (PI.f64) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
(PI.f64)
#s(literal 1/2 binary64)
x
eps
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64)))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(.f64 (.f64 #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal 2 binary64))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(fma.f64 #s(literal 1/2 binary64) eps x)
#s(literal 1/2 binary64)
eps
x
#s(literal 2 binary64)
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64))
#s(literal -1/48 binary64)
(*.f64 eps eps)

localize311.0ms (2.5%)

Memory

6.4MiB live, 243.4MiB allocated; 13ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
accuracy	0.01953125	(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
accuracy	0.05628720129176342	(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
accuracy	0.40646090350606906	#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
accuracy	0.0078125	(.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps)
accuracy	0.03125	(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
accuracy	0.08220500848354913	(sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
accuracy	1.084221771332689	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
accuracy	0.0078125	(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
accuracy	0.20703125	(.f64 #s(literal 1/24 binary64) (.f64 x x))
accuracy	1.084221771332689	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
accuracy	1.1622167349347945	#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.0	(*.f64 #s(literal -1/2 binary64) x)
accuracy	0.00390625	(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
accuracy	1.084221771332689	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
accuracy	1.2423909212346724	#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps))
accuracy	0.00390625	(-.f64 (PI.f64) eps)
accuracy	0.01953125	(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
accuracy	0.03125	(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
accuracy	0.07892912219458008	(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))

Samples

209.0ms	153×	1	valid
56.0ms	103×	0	valid

Compiler

Compiled 288 to 68 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 225.0ms

ival-sin: 73.0ms (32.5% of total)

ival-mult: 39.0ms (17.4% of total)

const: 34.0ms (15.1% of total)

adjust: 30.0ms (13.4% of total)

ival-add: 15.0ms (6.7% of total)

ival-sub: 14.0ms (6.2% of total)

ival-div: 8.0ms (3.6% of total)

ival-cos: 5.0ms (2.2% of total)

ival-pi: 2.0ms (0.9% of total)

ival-neg: 2.0ms (0.9% of total)

exact: 1.0ms (0.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series41.0ms (0.3%)

Memory

-8.1MiB live, 37.7MiB allocated; 4ms collecting garbage

Counts

28 → 157

Calls

Call 1

Inputs
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
(.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps)
(sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(-.f64 (PI.f64) eps)
(*.f64 #s(literal -1/2 binary64) x)
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)

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

Calls

6 calls:

Time	Variable		Point	Expression
16.0ms	x	@	inf	((* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (- (* 1/24 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (+ (* -2 x) (- (PI) eps)) (- (PI) eps) (* -1/2 x) (* 1/24 (* x x)) (- (* (PI) 1/2) x) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps))
5.0ms	eps	@	-inf	((* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (- (* 1/24 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (+ (* -2 x) (- (PI) eps)) (- (PI) eps) (* -1/2 x) (* 1/24 (* x x)) (- (* (PI) 1/2) x) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps))
5.0ms	eps	@	inf	((* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (- (* 1/24 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (+ (* -2 x) (- (PI) eps)) (- (PI) eps) (* -1/2 x) (* 1/24 (* x x)) (- (* (PI) 1/2) x) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps))
5.0ms	eps	@	0	((* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (- (* 1/24 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (+ (* -2 x) (- (PI) eps)) (- (PI) eps) (* -1/2 x) (* 1/24 (* x x)) (- (* (PI) 1/2) x) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps))
4.0ms	x	@	-inf	((* (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (sin (* 1/2 eps))) (* (+ (* -2 x) (- (PI) eps)) 1/2) (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (* 2 (sin (* (+ (* -2 x) (- (PI) eps)) 1/2))) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* -1/2 x) x) eps) eps) (* (* -1/2 x) x) (- (* 1/24 (* x x)) 1/2) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (sin (+ (neg x) (/ (PI) 2))) eps) (sin (+ (neg x) (/ (PI) 2))) (+ (neg x) (/ (PI) 2)) (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (* (* (cos (+ (* 1/2 eps) x)) 2) (sin (* 1/2 eps))) (* (cos (+ (* 1/2 eps) x)) 2) (cos (+ (* 1/2 eps) x)) (sin (* (+ (* -2 x) (- (PI) eps)) 1/2)) (+ (* -2 x) (- (PI) eps)) (- (PI) eps) (* -1/2 x) (* 1/24 (* x x)) (- (* (PI) 1/2) x) (sin (* 1/2 eps)) (* (+ (* -1/48 (* eps eps)) 1/2) eps))

simplify171.0ms (1.4%)

Memory

-9.8MiB live, 129.8MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	566	2407
1	2167	2239
2	7469	2236
0	8031	2085

Stop Event

1×	iter limit
1×	node limit

Counts

157 → 156

Calls

Call 1

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

Outputs
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))))
(+ (* -2 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))) (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))))
(.f64 #s(literal -2 binary64) (-.f64 (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) x) (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps)))) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* -1 (* x (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps)))))))))
(fma.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) x) (.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))))) x (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))))
(+ (* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* x (+ (* -2 (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps)))) (* x (+ (* -1 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (PI) eps))))) (* 1/3 (* x (* (cos (* 1/2 (- (PI) eps))) (sin (* 1/2 eps))))))))))
(fma.f64 (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -2 binary64)) (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))) (.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) eps)) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/3 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))))) x)) x (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))))
(* 1/2 (- (PI) eps))
(*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))
(+ (* -1 x) (* 1/2 (- (PI) eps)))
(-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)
(* 2 (sin (* 1/2 (- (PI) eps))))
(.f64 (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* -2 (* x (cos (* 1/2 (- (PI) eps))))) (* 2 (sin (* 1/2 (- (PI) eps)))))
(.f64 #s(literal -2 binary64) (-.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))) x) (sin.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))))
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* -1 (* x (sin (* 1/2 (- (PI) eps))))))))
(fma.f64 (fma.f64 (sin.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))) x (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))) #s(literal -2 binary64))) x (.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(+ (* 2 (sin (* 1/2 (- (PI) eps)))) (* x (+ (* -2 (cos (* 1/2 (- (PI) eps)))) (* x (+ (* -1 (sin (* 1/2 (- (PI) eps)))) (* 1/3 (* x (cos (* 1/2 (- (PI) eps))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) x) (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))) (sin.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps)))) x (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (PI.f64) eps))) #s(literal -2 binary64))) x (.f64 (sin.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) x) x (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps)
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/24 (pow x 2)) 1/2)
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(* eps (sin (* 1/2 (PI))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) eps)
(+ (* -1 (* eps (* x (cos (* 1/2 (PI)))))) (* eps (sin (* 1/2 (PI)))))
(.f64 (neg.f64 eps) (-.f64 (.f64 (cos.f64 (.f64 #s(literal -1/2 binary64) (PI.f64))) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)))))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* -1/2 (* eps (* x (sin (* 1/2 (PI)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 (neg.f64 eps) (cos.f64 (.f64 #s(literal -1/2 binary64) (PI.f64))))) x (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))) eps))
(+ (* eps (sin (* 1/2 (PI)))) (* x (+ (* -1 (* eps (cos (* 1/2 (PI))))) (* x (+ (* -1/2 (* eps (sin (* 1/2 (PI))))) (* 1/6 (* eps (* x (cos (* 1/2 (PI)))))))))))
(fma.f64 (fma.f64 (neg.f64 eps) (cos.f64 (.f64 #s(literal -1/2 binary64) (PI.f64))) (.f64 (fma.f64 (.f64 (.f64 #s(literal 1/6 binary64) eps) x) (cos.f64 (.f64 #s(literal -1/2 binary64) (PI.f64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) (.f64 #s(literal -1/2 binary64) eps))) x)) x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) eps))
(sin (* 1/2 (PI)))
(sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)))
(+ (sin (* 1/2 (PI))) (* -1 (* x (cos (* 1/2 (PI))))))
(fma.f64 (neg.f64 x) (cos.f64 (.f64 #s(literal -1/2 binary64) (PI.f64))) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* -1/2 (* x (sin (* 1/2 (PI))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) (PI.f64)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(+ (sin (* 1/2 (PI))) (* x (+ (* -1 (cos (* 1/2 (PI)))) (* x (+ (* -1/2 (sin (* 1/2 (PI)))) (* 1/6 (* x (cos (* 1/2 (PI))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/6 binary64) x) (cos.f64 (.f64 #s(literal -1/2 binary64) (PI.f64))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (PI.f64))) #s(literal -1/2 binary64))) x (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) (PI.f64)))) x (sin.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64))))
(* 1/2 (PI))
(*.f64 #s(literal 1/2 binary64) (PI.f64))
(+ (* -1 x) (* 1/2 (PI)))
(-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)
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(.f64 (fma.f64 (neg.f64 (sin.f64 x)) (.f64 #s(literal 1/2 binary64) eps) (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* 2 (* eps (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos (* -1 x)) (* eps (+ (* 1/2 (sin (* -1 x))) (* eps (+ (* -1/24 (* eps (sin (* -1 x)))) (* 2 (+ (* -1/16 (cos (* -1 x))) (* -1/48 (cos (* -1 x)))))))))))
(.f64 (fma.f64 (fma.f64 (neg.f64 (sin.f64 x)) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal -1/24 binary64) (neg.f64 (sin.f64 x))) eps (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps)) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* 2 (* eps (+ (* -1/16 (cos x)) (* -1/48 (cos x)))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* 1/24 (* eps (sin x))) (* 2 (+ (* -1/16 (cos x)) (* -1/48 (cos x))))))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps)
(* 2 (cos x))
(*.f64 (cos.f64 x) #s(literal 2 binary64))
(+ (* -1 (* eps (sin x))) (* 2 (cos x)))
(fma.f64 (neg.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* -1/4 (* eps (cos x))))))
(fma.f64 (fma.f64 (.f64 eps #s(literal -1/4 binary64)) (cos.f64 x) (neg.f64 (sin.f64 x))) eps (.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (* 2 (cos x)) (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/4 (cos x)) (* 1/24 (* eps (sin x))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/4 binary64) (cos.f64 x))) eps (neg.f64 (sin.f64 x))) eps (*.f64 (cos.f64 x) #s(literal 2 binary64)))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) eps (cos.f64 x))
(+ (cos x) (* eps (- (* -1/8 (* eps (cos x))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (cos.f64 x) eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(+ (cos x) (* eps (- (* eps (+ (* -1/8 (cos x)) (* 1/48 (* eps (sin x))))) (* 1/2 (sin x)))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (cos.f64 x) (.f64 #s(literal 1/48 binary64) (.f64 (sin.f64 x) eps))) eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x))
(sin (* 1/2 (+ (PI) (* -2 x))))
(sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* -1/2 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))
(fma.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) (.f64 #s(literal -1/2 binary64) eps) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* -1/8 (* eps (sin (* 1/2 (+ (PI) (* -2 x)))))))))
(fma.f64 (fma.f64 (.f64 eps #s(literal -1/8 binary64)) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)) (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64))) eps (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(+ (sin (* 1/2 (+ (PI) (* -2 x)))) (* eps (+ (* -1/2 (cos (* 1/2 (+ (PI) (* -2 x))))) (* eps (+ (* -1/8 (sin (* 1/2 (+ (PI) (* -2 x))))) (* 1/48 (* eps (cos (* 1/2 (+ (PI) (* -2 x)))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/48 binary64) eps) (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) (.f64 #s(literal -1/8 binary64) (sin.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x)))) eps (.f64 (cos.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x)) #s(literal -1/2 binary64))) eps (sin.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) (PI.f64)) x)))
(+ (PI) (* -2 x))
(fma.f64 #s(literal -2 binary64) x (PI.f64))
(+ (PI) (+ (* -2 x) (* -1 eps)))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(PI)
(PI.f64)
(+ (PI) (* -1 eps))
(-.f64 (PI.f64) eps)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal -1/48 binary64) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(fma.f64 (pow.f64 eps #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 eps eps) #s(literal 1/3840 binary64)) eps) eps) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) eps))
(* -1/2 eps)
(*.f64 #s(literal -1/2 binary64) eps)
(* eps (- (* 1/2 (/ (+ (PI) (* -2 x)) eps)) 1/2))
(.f64 (-.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (PI.f64)) x) eps) #s(literal 1/2 binary64)) eps)
(* -1 eps)
(neg.f64 eps)
(* eps (- (+ (* -2 (/ x eps)) (/ (PI) eps)) 1))
(*.f64 (-.f64 (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps) #s(literal 1 binary64)) eps)
(* eps (- (/ (PI) eps) 1))
(*.f64 (-.f64 (/.f64 (PI.f64) eps) #s(literal 1 binary64)) eps)
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1/48 (pow eps 3))
(*.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/48 binary64))
(* (pow eps 3) (- (* 1/2 (/ 1 (pow eps 2))) 1/48))
(.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (pow.f64 eps #s(literal 3 binary64)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (-.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))
(* -1 (* eps (+ 1/2 (* -1/2 (/ (+ (PI) (* -2 x)) eps)))))
(*.f64 (neg.f64 eps) (+.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (PI.f64) x) eps) #s(literal 1/2 binary64)))
(* 2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (+ (PI) (* -1 eps)) (* 2 x))))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (-.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)))
(* 2 (sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps))))))
(.f64 (sin.f64 (-.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x)) #s(literal 2 binary64))
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(.f64 (neg.f64 eps) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(* 2 (* (cos (* -1/2 (- (* 2 x) (* -1 eps)))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (* (cos (- x (* -1/2 eps))) (sin (* 1/2 eps))))
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
(* 2 (cos (- x (* -1/2 eps))))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos (- x (* -1/2 eps)))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ (PI) (+ (* -2 x) (* -1 eps)))))
(sin.f64 (-.f64 (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))
(* -1 (* eps (+ 1 (* -1 (/ (+ (PI) (* -2 x)) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal -2 binary64) x (PI.f64)) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (PI) eps)))))
(*.f64 (neg.f64 eps) (-.f64 #s(literal 1 binary64) (/.f64 (PI.f64) eps)))
(* -1 (* (pow eps 3) (- 1/48 (* 1/2 (/ 1 (pow eps 2))))))
(.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (-.f64 #s(literal 1/48 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))

rewrite216.0ms (1.7%)

Memory

6.8MiB live, 150.6MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	370
0	108	363
1	404	363
2	3124	363
0	8265	361

Stop Event

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

Counts

28 → 290

Calls

Call 1

Inputs
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps))
(fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)
(.f64 (.f64 #s(literal -1/2 binary64) x) x)
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
(.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps)
(sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)))
#s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)))
(*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64))
(cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin.f64 (*.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps))
(-.f64 (PI.f64) eps)
(*.f64 #s(literal -1/2 binary64) x)
(.f64 #s(literal 1/24 binary64) (.f64 x x))
(-.f64 (*.f64 (PI.f64) #s(literal 1/2 binary64)) x)
#s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))
(.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)

Outputs
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) #s(literal 2 binary64))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(+.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))
(*.f64 (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (-.f64 (.f64 x #s(literal -2 binary64)) (-.f64 (PI.f64) eps)))
(/.f64 (.f64 (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (.f64 x #s(literal -2 binary64))))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 2 binary64)))) (-.f64 (.f64 x #s(literal -2 binary64)) (-.f64 (PI.f64) eps)))
(/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal -8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (PI.f64) eps) #s(literal 3 binary64)))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (-.f64 (PI.f64) eps) (-.f64 (-.f64 (PI.f64) eps) (.f64 x #s(literal -2 binary64))))))
(fma.f64 (.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64) (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)))
(fma.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps) (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -2 binary64))))
(fma.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 (.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) (*.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) (.f64 (*.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -2 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)))
(+.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (PI.f64) eps)) (.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (sin.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)) (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps))) (*.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))) #s(literal 2 binary64)))))
(.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 x #s(literal -2 binary64) (-.f64 (PI.f64) eps)))))
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eval96.0ms (0.8%)

Memory: -12.1MiB live, 80.3MiB allocated; 4ms collecting garbage
Compiler: Compiled 17 828 to 2 249 computations (87.4% saved)

prune71.0ms (0.6%)

Memory

-4.0MiB live, 53.4MiB allocated; 10ms collecting garbage

Pruning

23 alts after pruning (14 fresh and 9 done)

	Pruned	Kept	Total
New	418	6	424
Fresh	1	8	9
Picked	2	3	5
Done	0	6	6
Total	421	23	444

Accuracy

100.0%

Counts

444 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.2%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps))
	98.4%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
✓	98.3%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
✓	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
✓	97.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
✓	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
✓	96.9%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
	98.1%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
	98.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
	5.0%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
	99.8%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (-.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
	99.3%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
	99.3%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
✓	99.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
	99.4%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
✓	99.3%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
	98.9%	#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))

Compiler

Compiled 1 601 to 717 computations (55.2% saved)

regimes27.0ms (0.2%)

Memory

33.0MiB live, 33.0MiB allocated; 0ms collecting garbage

Counts

36 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (sin.f64 (-.f64 (.f64 (-.f64 (PI.f64) eps) #s(literal 1/2 binary64)) x))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (sin (/ (+ (neg (+ (* x 2) eps)) (PI)) 2))) (.f64 (.f64 #s(literal 2 binary64) (sin.f64 (.f64 (fma.f64 #s(literal -2 binary64) x (-.f64 (PI.f64) eps)) #s(literal 1/2 binary64)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (sin.f64 (/.f64 (+.f64 (neg.f64 (fma.f64 x #s(literal 2 binary64) eps)) (PI.f64)) #s(literal 2 binary64))))
(.f64 (.f64 (sin.f64 (/.f64 (+.f64 #s(literal 0 binary64) eps) #s(literal 2 binary64))) #s(literal 2 binary64)) (cos.f64 #s(approx (/ (+ (* 2 x) eps) -2) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) x))))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 (sin.f64 x) #s(literal -1/2 binary64))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64))) eps (cos.f64 x)) eps))

Outputs

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes79.0ms (0.6%)

Memory

-21.2MiB live, 26.2MiB allocated; 2ms collecting garbage

Counts

26 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (sin.f64 (+.f64 (neg.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (/.f64 (PI.f64) #s(literal 2 binary64)))) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))

Outputs

#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/3840 binary64) (*.f64 eps eps)) #s(literal 1/48 binary64)) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))

Calls

3 calls:

65.0ms	eps
6.0ms	x
6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
99.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.4%	1	`x`
99.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes16.0ms (0.1%)

Memory

22.8MiB live, 22.8MiB allocated; 0ms collecting garbage

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))
(.f64 (.f64 #s(approx (sin (/ (+ 0 eps) 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps)) #s(literal 2 binary64)) (cos.f64 (/.f64 (fma.f64 #s(literal 2 binary64) x eps) #s(literal -2 binary64))))

Outputs

#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (*.f64 (*.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)) eps))))

Calls

3 calls:

5.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	x
5.0ms	eps

Results

Accuracy	Segments	Branch
99.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.3%	1	`eps`
99.3%	1	`x`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes39.0ms (0.3%)

Memory

-28.4MiB live, 18.8MiB allocated; 1ms collecting garbage

Counts

17 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64)))) eps))

Outputs

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

Calls

3 calls:

29.0ms	eps
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes13.0ms (0.1%)

Memory

23.5MiB live, 23.5MiB allocated; 0ms collecting garbage

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))

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

Calls

3 calls:

4.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.4%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes15.0ms (0.1%)

Memory

-9.4MiB live, 32.5MiB allocated; 3ms collecting garbage

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))

Calls

3 calls:

6.0ms	eps
4.0ms	x
4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Results

Accuracy	Segments	Branch
98.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.3%	1	`x`
98.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes20.0ms (0.2%)

Memory

-14.6MiB live, 29.6MiB allocated; 11ms collecting garbage

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

Calls

3 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
98.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.3%	1	`x`
98.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes11.0ms (0.1%)

Memory

20.5MiB live, 20.5MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) #s(approx (+ (* (* (* -1/2 x) x) eps) eps) (.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) x)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 #s(literal -1/2 binary64) x) x) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 #s(literal 1/12 binary64) x) eps) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (+ (* (+ (* (* (sin eps) x) -1/2) (- (cos eps) 1)) x) (sin eps)) (fma.f64 (fma.f64 (.f64 x (+.f64 x eps)) #s(literal -1/2 binary64) (.f64 (.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (*.f64 x x)) #s(literal 1/6 binary64)) eps) eps)) eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Outputs

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

Calls

3 calls:

4.0ms	eps
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
98.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.1%	1	`x`
98.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes25.0ms (0.2%)

Memory

-4.0MiB live, 31.2MiB allocated; 17ms collecting garbage

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	eps
3.0ms	x

Results

Accuracy	Segments	Branch
98.1%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.1%	1	`x`
98.1%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes7.0ms (0.1%)

Memory

27.7MiB live, 27.7MiB allocated; 0ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x
2.0ms	eps

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
98.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes12.0ms (0.1%)

Memory

-27.4MiB live, 17.4MiB allocated; 8ms collecting garbage

Accuracy

Total -58.9b remaining (-2938.8%)

Threshold costs -58.9b (-2938.8%)

Counts

2 → 1

Calls

Call 1

Inputs

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

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

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

Calls

3 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	x
1.0ms	eps

Results

Accuracy	Segments	Branch
96.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
96.9%	1	`x`
96.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify67.0ms (0.5%)

Memory

41.5MiB live, 85.1MiB allocated; 9ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	98	292
1	138	292
2	257	292
3	675	292
4	1678	292
5	2850	292
6	4062	291
7	6757	291

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

Outputs
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 eps eps)) #s(literal 1/48 binary64)) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 eps eps) #s(literal 1/2 binary64)) eps))))
#s(approx (* (* (sin (/ (+ 0 eps) 2)) 2) (cos (/ (+ (* 2 x) eps) -2))) (.f64 (.f64 (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal 2 binary64)) #s(approx (sin (* 1/2 eps)) (*.f64 #s(literal 1/2 binary64) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(approx ( (sin x) eps) (*.f64 x eps)) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (sin.f64 #s(approx (+ (neg x) (/ (PI) 2)) (-.f64 (.f64 (PI.f64) #s(literal 1/2 binary64)) x))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 eps (+.f64 x eps)) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))

derivations1.2s (9.6%)

Memory

11.7MiB live, 1 070.1MiB allocated; 238ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	51	16
2	365	16
3	4452	16
0	8177	16
0	35	170
0	59	162
1	221	162
2	1875	162
0	8244	162
0	529	2109
1	1994	2034
2	7217	2026
0	8356	1865
0	408	1361
1	1502	1304
2	5346	1280
0	8267	1173
0	107	303
1	366	303
2	1224	296
3	4149	296
4	7986	296
0	8046	267
0	75	370
0	108	363
1	404	363
2	3124	363
0	8265	361

Stop Event

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

Compiler

Compiled 300 to 101 computations (66.3% saved)

preprocess202.0ms (1.6%)

Memory: 28.4MiB live, 170.1MiB allocated; 137ms collecting garbage
Compiler: Compiled 644 to 240 computations (62.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze98.0ms (0.8%)

sample7.2s (56.9%)

explain106.0ms (0.8%)

preprocess47.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize30.0ms (0.2%)

series4.0ms (0%)

simplify141.0ms (1.1%)

rewrite234.0ms (1.9%)

eval29.0ms (0.2%)

prune23.0ms (0.2%)

simplify139.0ms (1.1%)

localize247.0ms (2%)

series35.0ms (0.3%)

simplify144.0ms (1.1%)

rewrite228.0ms (1.8%)

eval83.0ms (0.7%)

prune19.0ms (0.1%)

simplify159.0ms (1.3%)

localize268.0ms (2.1%)

series44.0ms (0.4%)

simplify176.0ms (1.4%)

rewrite251.0ms (2%)

eval86.0ms (0.7%)

prune65.0ms (0.5%)

simplify123.0ms (1%)

localize311.0ms (2.5%)

series41.0ms (0.3%)

simplify171.0ms (1.4%)

rewrite216.0ms (1.7%)

eval96.0ms (0.8%)

prune71.0ms (0.6%)

regimes27.0ms (0.2%)

regimes79.0ms (0.6%)

regimes16.0ms (0.1%)

regimes39.0ms (0.3%)

regimes13.0ms (0.1%)

regimes15.0ms (0.1%)

regimes20.0ms (0.2%)

regimes11.0ms (0.1%)

regimes25.0ms (0.2%)

regimes7.0ms (0.1%)

regimes12.0ms (0.1%)

simplify67.0ms (0.5%)

derivations1.2s (9.6%)

preprocess202.0ms (1.6%)

end0.0ms (0%)

Profiling