Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 10 to 7 computations (30% saved)

sample148.0ms (1.2%)

Algorithm

1×

intervals

Results

52.0ms	110×	body	1024	valid
45.0ms	41×	body	2048	valid
15.0ms	50×	body	512	valid
3.0ms	19×	body	256	valid
3.0ms	36×	body	128	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

38.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	38.2b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.3b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	3.2b	(sin.f64 (+.f64 x eps))

series11.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	(sin.f64 (+.f64 x eps))

simplify101.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-neg_binary64`
483×	`fma-def_binary64`
351×	`cancel-sign-sub-inv_binary64`
291×	`sub-neg_binary64`
284×	`associate-+l-_binary64`

Counts

90 → 92

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1256
1	297	1180
2	960	1116
3	2426	1108
4	4776	1108
5	4953	1108
6	4839	1108

prune69.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Error

0.2b

Counts

93 → 3

Alt Table

Status	Error	Program
▶	23.3b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	30.4b	(-.f64 (+.f64 (.f64 1/24 (.f64 (pow.f64 eps 4) (sin.f64 x))) (.f64 eps (cos.f64 x))) (+.f64 (.f64 1/6 (.f64 (pow.f64 eps 3) (cos.f64 x))) (.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x)))))
	23.3b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

Compiler

Compiled 1683 to 521 computations (69% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
✓	0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
✓	0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
✓	3.5b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series55.0ms (0.5%)

Counts

4 → 72

Calls

4 calls:

19.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
16.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
10.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
10.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
9×	`prod-diff_binary64`

Counts

4 → 87

Calls

4 calls:

7.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
4.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
3.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))

simplify132.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

418×	`fma-neg_binary64`
276×	`distribute-rgt-in_binary64`
249×	`distribute-rgt-neg-in_binary64`
245×	`distribute-lft-in_binary64`
226×	`associate-r_binary64`

Counts

159 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	3009
1	616	2802
2	2190	2695
3	4798	2695
4	4972	2695
5	4911	2695

prune160.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	175	14	189
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	178	14	192

Error

0.1b

Counts

192 → 14

Alt Table

Status	Error	Program
	40.6b	(-.f64 (+.f64 (.f64 (.f64 (sin.f64 x) (sqrt.f64 (cos.f64 eps))) (sqrt.f64 (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	20.1b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
	30.1b	(fma.f64 eps (cos.f64 x) (.f64 (sin.f64 x) (.f64 (*.f64 eps eps) -1/2)))
	23.3b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	26.4b	(cbrt.f64 (.f64 (.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
	3.6b	(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	42.6b	(+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x))))
	24.0b	(+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))))
	5.2b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	24.4b	(/.f64 (-.f64 (.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))
	26.5b	(/.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))))
	34.9b	(.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
▶	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	24.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))

Compiler

Compiled 5193 to 1491 computations (71.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
✓	0.6b	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
✓	2.3b	(+.f64 (cos.f64 eps) -1)

series2.8s (23.5%)

Counts

4 → 84

Calls

4 calls:

1.7s	(.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
1.0s	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
33.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
2.0ms	(+.f64 (cos.f64 eps) -1)

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
16×	`pow1/3_binary64`

Counts

4 → 111

Calls

4 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
7.0ms	(.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
5.0ms	(+.f64 (cos.f64 eps) -1)
1.0ms	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))

simplify240.0ms (2%)

Algorithm

1×	egg-herbie

Rules

843×	`times-frac_binary64`
383×	`associate-r_binary64`
303×	`associate-l_binary64`
298×	`fma-def_binary64`
264×	`fma-neg_binary64`

Counts

195 → 224

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6718
1	1004	6020
2	3611	5554
3	5304	5554

prune773.0ms (6.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	379	3	382
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	381	15	396

Error

0.1b

Counts

396 → 15

Alt Table

Status	Error	Program
	40.6b	(-.f64 (+.f64 (.f64 (.f64 (sin.f64 x) (sqrt.f64 (cos.f64 eps))) (sqrt.f64 (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	20.1b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
	30.1b	(fma.f64 eps (cos.f64 x) (.f64 (sin.f64 x) (.f64 (*.f64 eps eps) -1/2)))
	23.3b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	26.4b	(cbrt.f64 (.f64 (.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
	15.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 2)))) (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))
▶	3.6b	(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	25.0b	(.f64 (pow.f64 (pow.f64 (-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x)) 2) 1/3) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	26.5b	(/.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))))
	18.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (sqrt.f64 (cos.f64 eps)) (sqrt.f64 (cos.f64 eps)) -1)))))
	34.9b	(.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	42.6b	(+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x))))
	24.0b	(+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))))
	5.2b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	24.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))

Compiler

Compiled 21523 to 10376 computations (51.8% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
✓	0.2b	(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
✓	0.2b	(log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
	2.3b	(+.f64 (cos.f64 eps) -1)

series2.0s (16.6%)

Counts

3 → 72

Calls

3 calls:

1.9s

(log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))

19.0ms

(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

17.0ms

(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`expm1-log1p-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms

(log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))

0.0ms

(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

697×	`times-frac_binary64`
429×	`fma-neg_binary64`
358×	`cancel-sign-sub-inv_binary64`
173×	`fma-def_binary64`
158×	`sub-neg_binary64`

Counts

104 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	3036
1	536	2763
2	2009	2655
3	4719	2653
4	5008	2653

prune149.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Error

0.0b

Counts

133 → 13

Alt Table

Status	Error	Program
	3.6b	(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log.f64 (exp.f64 (+.f64 (cos.f64 eps) -1)))))))
	23.3b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	26.4b	(cbrt.f64 (.f64 (.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)) (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
	3.4b	(expm1.f64 (log1p.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1))))))
	24.0b	(+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (neg.f64 (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))))
	18.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (sqrt.f64 (cos.f64 eps)) (sqrt.f64 (cos.f64 eps)) -1)))))
	34.9b	(.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	20.1b	(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
	15.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x))) 2)))) (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))
	42.6b	(+.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x))))
	5.2b	(/.f64 (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))
	26.5b	(/.f64 (-.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (cos.f64 eps) (sin.f64 x))) (fma.f64 (cos.f64 eps) (sin.f64 x) (fma.f64 (sin.f64 eps) (cos.f64 x) (sin.f64 x))))))
	24.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))) (cbrt.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))

Compiler

Compiled 3470 to 1799 computations (48.2% saved)

regimes1.0s (8.6%)

Accuracy

Total 0.3b remaining (82.1%)

Threshold costs 0.3b (82.1%)

Counts

269 → 1

Compiler

Compiled 22935 to 13460 computations (41.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	13	19
2	13	19

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample4.0s (33.7%)

Algorithm

1×

intervals

Results

1.7s	3511×	body	1024	valid
1.3s	1212×	body	2048	valid
371.0ms	1352×	body	512	valid
109.0ms	1340×	body	128	valid
97.0ms	581×	body	256	valid
11.0ms	4×	body	4096	valid

Compiler

Compiled 456 to 227 computations (50.2% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Details

analyze2.0ms (0%)

sample148.0ms (1.2%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series11.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify101.0ms (0.8%)

prune69.0ms (0.6%)

localize11.0ms (0.1%)

series55.0ms (0.5%)

rewrite24.0ms (0.2%)

simplify132.0ms (1.1%)

prune160.0ms (1.3%)

localize13.0ms (0.1%)

series2.8s (23.5%)

rewrite43.0ms (0.4%)

simplify240.0ms (2%)

prune773.0ms (6.5%)

localize31.0ms (0.3%)

series2.0s (16.6%)

rewrite2.0ms (0%)

simplify99.0ms (0.8%)

prune149.0ms (1.2%)

regimes1.0s (8.6%)

simplify4.0ms (0%)

end1.0ms (0%)

sample4.0s (33.7%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11