Metrics for 2sin (example 3.3)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze71.0ms (0.8%)

Memory

-21.8MiB live, 64.6MiB allocated

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)

sample6.6s (74%)

Memory

-186.4MiB live, 6 112.2MiB allocated

Samples

3.4s	26 190×	0	invalid
689.0ms	2 785×	1	valid
565.0ms	5 471×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

ival-sin: 642.0ms (18.6% of total)

const: 630.0ms (18.3% of total)

ival-<=: 551.0ms (16% of total)

ival-mult: 277.0ms (8% of total)

ival-add: 273.0ms (7.9% of total)

ival-sub: 272.0ms (7.9% of total)

ival-fabs: 263.0ms (7.6% of total)

ival-<: 222.0ms (6.4% of total)

adjust: 159.0ms (4.6% of total)

ival-and: 106.0ms (3.1% of total)

exact: 44.0ms (1.3% of total)

ival-assert: 12.0ms (0.3% of total)

Bogosity

explain115.0ms (1.3%)

Memory

0.7MiB live, 79.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
227	-	2	(-5.108445952308667e-245 5.250286183730444e-247)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	-	0	-	`(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	225	9

Confusion

	Predicted +	Predicted -
+	225	2
-	0	29

Precision

1.0

Recall

0.9911894273127754

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	225	2	0
-	0	7	22

Precision?

0.9700854700854701

Recall?

1.0

Freqs

test

number	freq
0	31
1	225

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

20.0ms	194×	1	valid
15.0ms	316×	0	valid
1.0ms	2×	3	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-sin: 10.0ms (48% of total)

adjust: 4.0ms (19.2% of total)

ival-add: 3.0ms (14.4% of total)

ival-sub: 3.0ms (14.4% of total)

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

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

preprocess53.0ms (0.6%)

Memory

-26.7MiB live, 18.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	312	35
5	383	35
6	469	35
7	509	35
8	521	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Stop Event

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

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
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	61.3%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify6.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

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	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	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)

localize22.0ms (0.3%)

Memory

24.2MiB live, 24.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 x eps)
accuracy	0.0	(sin.f64 x)
accuracy	0.01171875	(sin.f64 (+.f64 x eps))
accuracy	24.738180070786942	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

9.0ms	97×	1	valid
7.0ms	158×	0	valid
0.0ms	1×	3	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sin: 4.0ms (41.1% of total)

adjust: 2.0ms (20.6% of total)

ival-add: 2.0ms (20.6% of total)

ival-sub: 1.0ms (10.3% of total)

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

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

series4.0ms (0%)

Memory

3.4MiB live, 3.4MiB allocated

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))

simplify190.0ms (2.1%)

Memory

-22.7MiB live, 89.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	291
1	314	291
2	781	284
3	2853	284
4	6191	283
0	8157	253

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

rewrite179.0ms (2%)

Memory

13.3MiB live, 169.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	53	16
2	385	16
3	4851	16
0	8393	16

Stop Event

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

Counts

4 → 214

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

eval44.0ms (0.5%)

Memory: 17.0MiB live, 64.0MiB allocated
Compiler: Compiled 6 283 to 852 computations (86.4% saved)

prune6.0ms (0.1%)

Memory

-25.2MiB live, 12.4MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	232	3	235
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	233	3	236

Accuracy

100.0%

Counts

236 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	#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)))
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Status

Accuracy

Program

▶

99.8%

#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)))

▶

100.0%

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

▶

99.3%

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

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify125.0ms (1.4%)

Memory

21.8MiB live, 60.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
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	(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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	95
0	29	95
1	47	95
2	72	95
3	164	95
4	299	95
5	466	95
6	829	95
7	1788	95
8	2465	95
9	2647	95
10	2666	95
11	2698	95
12	2714	95
13	2757	95
14	2812	95
15	2822	95
16	2829	95
17	2831	95
0	2831	95

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize168.0ms (1.9%)

Memory

-12.1MiB live, 180.3MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 eps)
accuracy	0.10236422072784132	#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	0.11328125	(fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
accuracy	31.313177024645917	(-.f64 (cos.f64 eps) #s(literal 1 binary64))
accuracy	0.0	(cos.f64 x)
accuracy	0.0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
accuracy	0.00390625	(*.f64 (cos.f64 x) eps)
accuracy	0.0	(sin.f64 eps)
accuracy	0.44440593788206206	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Samples

146.0ms

256×

valid

Compiler

Compiled 77 to 20 computations (74% saved)

Precisions

Click to see histograms. Total time spent on operations: 125.0ms

ival-cos: 74.0ms (59.2% of total)

ival-mult: 14.0ms (11.2% of total)

adjust: 12.0ms (9.6% of total)

ival-sin: 10.0ms (8% of total)

ival-sub: 9.0ms (7.2% of total)

ival-add: 6.0ms (4.8% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

19.0MiB live, 19.0MiB allocated

Counts

11 → 53

Calls

Call 1

Inputs
#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)) (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)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)

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)))
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)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos 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)))
(- (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)))))
(* 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 (* -1/6 (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)
(* 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)))))))
(* -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))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(- (sin (- x (* -1 eps))) (sin x))

Calls

6 calls:

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

simplify157.0ms (1.8%)

Memory

-4.0MiB live, 112.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	215	669
1	644	655
2	1762	640
3	4595	628
0	8211	559

Stop Event

1×	iter limit
1×	node limit

Counts

53 → 52

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)))
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)))
(- (cos eps) 1)
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(* x (sin eps))
(- (sin (+ eps x)) (sin x))
(* eps (cos x))
(cos 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)))
(- (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)))))
(* 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 (* -1/6 (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)
(* 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)))))))
(* -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))
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(- (sin (- x (* -1 eps))) (sin x))

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 #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) (* 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 (.f64 (.f64 x x) eps) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 eps (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64))) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) 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 (fma.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 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(- (cos eps) 1)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* x (sin eps))
(*.f64 (sin.f64 eps) x)
(- (sin (+ eps x)) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* eps (cos x))
(*.f64 (cos.f64 x) eps)
(cos x)
(cos.f64 x)
(* -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 (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x)
(* (pow x 2) (- (+ (* -1/2 (sin eps)) (+ (/ (cos eps) x) (/ (sin eps) (pow x 2)))) (/ 1 x)))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 eps) (-.f64 (/.f64 (sin.f64 eps) x) (-.f64 #s(literal 1 binary64) (cos.f64 eps)))) x)
(* -1/2 (* x (sin eps)))
(.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) x)
(* x (- (+ (* -1/2 (sin eps)) (/ (cos eps) x)) (/ 1 x)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(- (sin (- eps (* -1 x))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (- (cos eps) 1)) (* -1 (/ (sin eps) x))) x)) (* -1/2 (sin eps))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) x) (sin.f64 eps) (-.f64 (/.f64 (sin.f64 eps) x) (-.f64 #s(literal 1 binary64) (cos.f64 eps)))) x)
(* -1 (* x (+ (* -1 (/ (- (cos eps) 1) x)) (* 1/2 (sin eps)))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (sin.f64 eps)) x (-.f64 (cos.f64 eps) #s(literal 1 binary64)))
(* 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)
(* 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 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 (.f64 (cos.f64 x) #s(literal -1/6 binary64)) eps)) 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)) (fma.f64 #s(literal 1/120 binary64) (*.f64 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)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 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 (+.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (* 1/12 (pow x 2)) 1/6)))))))
(.f64 (fma.f64 (.f64 (+.f64 eps x) x) #s(literal -1/2 binary64) (fma.f64 (.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 x x) #s(literal -1/6 binary64)) eps) eps #s(literal 1 binary64))) eps)
(* eps (+ 1 (+ (* -1/2 (pow x 2)) (* eps (+ (* -1/2 x) (* eps (- (+ (* 1/24 (* eps x)) (* 1/12 (pow x 2))) 1/6)))))))
(.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 #s(literal 1/12 binary64) x (.f64 #s(literal 1/24 binary64) eps)) #s(literal -1/6 binary64)) eps) eps (fma.f64 (.f64 (+.f64 eps x) x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
(* -1/2 (* eps x))
(.f64 (.f64 #s(literal -1/2 binary64) x) eps)
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64))
(* eps (+ (* -1/2 x) (* eps (- (* 1/12 (* eps x)) 1/2))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 eps x) #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 (fma.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)
(*.f64 eps x)
(* eps (+ x (* -1/6 (* (pow eps 2) x))))
(*.f64 x (fma.f64 (pow.f64 eps #s(literal 3 binary64)) #s(literal -1/6 binary64) eps))
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* 1/120 (* (pow eps 2) x))))))
(.f64 (.f64 x (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 eps eps) #s(literal -1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64))) eps)
(* eps (+ x (* (pow eps 2) (+ (* -1/6 x) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) x)) (* 1/120 x)))))))
(.f64 (fma.f64 (.f64 x (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps) #s(literal -1/6 binary64))) (*.f64 eps eps) x) 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 (fma.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 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(.f64 (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/40320 binary64) (.f64 eps eps) #s(literal -1/720 binary64)) (.f64 eps eps) #s(literal 1/24 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64)) eps) eps)
(+ 1 (* -1/2 (pow eps 2)))
(fma.f64 (*.f64 eps eps) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/24 binary64) #s(literal -1/2 binary64)) (.f64 eps eps) #s(literal 1 binary64))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 eps eps) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) (.f64 eps eps) #s(literal -1/2 binary64)) (*.f64 eps eps) #s(literal 1 binary64))
(cos eps)
(cos.f64 eps)
(- (sin (- x (* -1 eps))) (sin x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))

rewrite172.0ms (1.9%)

Memory

9.6MiB live, 251.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	86
0	29	86
1	120	86
2	913	86
0	8271	86

Stop Event

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

Counts

11 → 176

Calls

Call 1

Inputs
#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)) (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)
(-.f64 (cos.f64 eps) #s(literal 1 binary64))
(cos.f64 eps)

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

eval35.0ms (0.4%)

Memory: -19.2MiB live, 55.5MiB allocated
Compiler: Compiled 9 354 to 1 092 computations (88.3% saved)

prune3.0ms (0%)

Memory

12.5MiB live, 12.5MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	227	3	230
Fresh	0	0	0
Picked	3	0	3
Done	0	0	0
Total	230	3	233

Accuracy

100.0%

Counts

233 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

99.8%

#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))

▶

99.3%

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

▶

100.0%

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

Compiler

Compiled 59 to 41 computations (30.5% saved)

simplify23.0ms (0.3%)

Memory

-13.0MiB live, 24.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	153
0	34	153
1	63	153
2	137	153
3	298	153
4	402	153
5	434	153
6	466	153
7	616	153
8	663	153
9	681	153
10	690	153
0	690	153

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize66.0ms (0.7%)

Memory

4.0MiB live, 83.9MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	#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))
accuracy	0.00390625	(.f64 #s(approx (cos x) (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))) eps)
accuracy	0.10691291177505044	#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.0	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps))
accuracy	0.00390625	(*.f64 #s(approx (cos x) #s(literal 1 binary64)) eps)
accuracy	0.4590650281035783	#s(approx (cos x) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.0	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps)))
accuracy	0.0	#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)) eps))
accuracy	0.09375	(.f64 (.f64 x x) eps)

Samples

29.0ms	160×	0	valid
22.0ms	96×	1	valid

Compiler

Compiled 89 to 21 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-sin: 11.0ms (30.4% of total)

ival-mult: 9.0ms (24.9% of total)

ival-add: 5.0ms (13.8% of total)

adjust: 4.0ms (11.1% of total)

const: 3.0ms (8.3% of total)

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

ival-sub: 1.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

series13.0ms (0.1%)

Memory

21.2MiB live, 21.2MiB allocated

Counts

12 → 29

Calls

Call 1

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

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) (+ (* 1/24 (* x x)) -1/2)) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x))
2.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) (+ (* 1/24 (* x x)) -1/2)) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x))
2.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) (+ (* 1/24 (* x x)) -1/2)) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x))
2.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) (+ (* 1/24 (* x x)) -1/2)) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x))
1.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) (+ (* 1/24 (* x x)) -1/2)) eps) (* (* x x) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (* x x) -1/2) 1) (* x x))

simplify180.0ms (2%)

Memory

-12.3MiB live, 239.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	322
1	315	322
2	829	309
3	3385	307
0	8086	275

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

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

rewrite146.0ms (1.6%)

Memory

-22.4MiB live, 139.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	134
0	34	134
1	137	134
2	965	134
0	8230	134

Stop Event

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

Counts

12 → 152

Calls

Call 1

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

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 (*.f64 x x) eps) eps)))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 (*.f64 x x) eps) eps))
(.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)) eps)
(.f64 (-.f64 (.f64 eps eps) (.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 eps (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) (*.f64 eps x)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 eps) eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) (*.f64 eps x) (neg.f64 eps)))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) (.f64 eps x))) (.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) (.f64 (neg.f64 eps) eps)) (pow.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) (*.f64 eps x) (neg.f64 eps)) #s(literal -1 binary64)))
(.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 eps eps (.f64 (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) (.f64 eps x)) (fma.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) (*.f64 eps x) (neg.f64 eps))))))
(.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 eps #s(literal 3 binary64))) (pow.f64 (fma.f64 eps (-.f64 eps (.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) x) (.f64 eps x))) (.f64 (pow.f64 (.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) eps) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 (.f64 x x) eps) eps))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 (*.f64 x x) eps) eps)) #s(literal -1 binary64))
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(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)) (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))))))
(fma.f64 (*.f64 #s(literal -1/2 binary64) x) x #s(literal 1 binary64))
(fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 x (*.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal -1 binary64))) (neg.f64 (pow.f64 (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal -1 binary64)) #s(literal -1 binary64))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval43.0ms (0.5%)

Memory: -2.5MiB live, 44.3MiB allocated
Compiler: Compiled 7 100 to 933 computations (86.9% saved)

prune5.0ms (0.1%)

Memory

12.2MiB live, 12.2MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	192	3	195

Accuracy

100.0%

Counts

195 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

✓

99.8%

#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))

✓

99.3%

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

✓

100.0%

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

Compiler

Compiled 169 to 80 computations (52.7% saved)

regimes7.0ms (0.1%)

Memory

11.3MiB live, 11.3MiB allocated

Counts

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

-31.1MiB live, 7.6MiB allocated

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

Calls

3 calls:

3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	eps
1.0ms	x

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0%)

Memory

6.9MiB live, 6.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify64.0ms (0.7%)

Memory

-3.7MiB live, 34.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	59
1	30	59
2	34	59
3	40	59
4	51	59
5	68	59
6	125	59
7	384	59
8	3280	59
9	7304	59

Stop Event

1×	node limit

Calls

Call 1

Inputs

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

Outputs

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

soundness380.0ms (4.2%)

Memory

2.7MiB live, 194.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	215	669
1	644	655
2	1762	640
3	4595	628
0	8211	559
0	107	291
1	314	291
2	781	284
3	2853	284
4	6191	283
0	8157	253

Stop Event

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

Compiler

Compiled 82 to 49 computations (40.2% saved)

preprocess30.0ms (0.3%)

Memory: 31.6MiB live, 31.6MiB allocated
Compiler: Compiled 162 to 86 computations (46.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	312	35
5	383	35
6	469	35
7	509	35
8	521	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Iter	Nodes	Cost
0	24	153
0	34	153
1	63	153
2	137	153
3	298	153
4	402	153
5	434	153
6	466	153
7	616	153
8	663	153
9	681	153
10	690	153
0	690	153

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	312	35
5	383	35
6	469	35
7	509	35
8	521	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Iter	Nodes	Cost
0	24	153
0	34	153
1	63	153
2	137	153
3	298	153
4	402	153
5	434	153
6	466	153
7	616	153
8	663	153
9	681	153
10	690	153
0	690	153

start0.0ms (0%)

analyze71.0ms (0.8%)

sample6.6s (74%)

explain115.0ms (1.3%)

preprocess53.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify6.0ms (0.1%)

localize22.0ms (0.3%)

series4.0ms (0%)

simplify190.0ms (2.1%)

rewrite179.0ms (2%)

eval44.0ms (0.5%)

prune6.0ms (0.1%)

simplify125.0ms (1.4%)

localize168.0ms (1.9%)

series13.0ms (0.1%)

simplify157.0ms (1.8%)

rewrite172.0ms (1.9%)

eval35.0ms (0.4%)

prune3.0ms (0%)

simplify23.0ms (0.3%)

localize66.0ms (0.7%)

series13.0ms (0.1%)

simplify180.0ms (2%)

rewrite146.0ms (1.6%)

eval43.0ms (0.5%)

prune5.0ms (0.1%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes3.0ms (0%)

simplify64.0ms (0.7%)

soundness380.0ms (4.2%)

preprocess30.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	312	35
5	383	35
6	469	35
7	509	35
8	521	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	110	7
8	159	7
9	175	7
10	183	7
0	183	7

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
2	18	18
3	24	18
4	32	18
5	47	18
6	80	18
7	110	18
8	159	18
9	175	18
10	183	18
0	183	18

Iter	Nodes	Cost
0	24	153
0	34	153
1	63	153
2	137	153
3	298	153
4	402	153
5	434	153
6	466	153
7	616	153
8	663	153
9	681	153
10	690	153
0	690	153