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)

sample186.0ms (1.6%)

Algorithm

1×

intervals

Results

89.0ms	39×	body	2048	valid
48.0ms	100×	body	1024	valid
13.0ms	55×	body	512	valid
4.0ms	47×	body	128	valid
3.0ms	15×	body	256	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify13.0ms (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

37.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	37.0b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
✓	2.9b	(sin.f64 (+.f64 x eps))

series13.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

rewrite11.0ms (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))

simplify100.0ms (0.9%)

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

prune79.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	4	93

Error

0.2b

Counts

93 → 4

Alt Table

Status	Error	Program
	19.8b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
▶	19.7b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	38.5b	(-.f64 (fma.f64 (cos.f64 eps) x (sin.f64 eps)) (fma.f64 1/2 (.f64 (sin.f64 eps) (.f64 x x)) x))
	31.5b	(+.f64 (.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6))) (.f64 (sin.f64 x) (-.f64 (.f64 1/24 (pow.f64 eps 4)) (.f64 1/2 (.f64 eps eps)))))

Compiler

Compiled 1707 to 535 computations (68.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
✓	2.3b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series57.0ms (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))
17.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
11.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
9.0ms	(*.f64 (sin.f64 x) (cos.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:

8.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
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))
3.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

simplify133.0ms (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

prune177.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	176	13	189
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	179	14	193

Error

0.1b

Counts

193 → 14

Alt Table

Status	Error	Program
	20.5b	(+.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))))
	29.5b	(log.f64 (exp.f64 (-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
	21.5b	(/.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)))
▶	1.8b	(.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)))))
	41.2b	(fma.f64 (sqrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
	29.6b	(log.f64 (/.f64 (exp.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (exp.f64 (sin.f64 x))))
	43.4b	(+.f64 (fma.f64 1 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sin.f64 x))) (sqrt.f64 (sin.f64 x)) (.f64 (sqrt.f64 (sin.f64 x)) (sqrt.f64 (sin.f64 x)))))
	23.1b	(/.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))))))
	31.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)))) (sin.f64 x))
	19.7b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	32.8b	(.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)))))
	31.5b	(+.f64 (.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6))) (.f64 (sin.f64 x) (-.f64 (.f64 1/24 (pow.f64 eps 4)) (.f64 1/2 (.f64 eps eps)))))
	5.5b	(/.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))))
	20.7b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))))) (cbrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (.f64 (cbrt.f64 (sin.f64 x)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (.f64 (cbrt.f64 (sin.f64 x)) (.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))

Compiler

Compiled 5287 to 1534 computations (71% saved)

localize15.0ms (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)))))
✓	0.7b	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
✓	2.8b	(+.f64 (cos.f64 eps) -1)

series2.2s (18.4%)

Counts

4 → 84

Calls

4 calls:

1.2s	(.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)))))
939.0ms	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
23.0ms	(.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)

rewrite27.0ms (0.2%)

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:

7.0ms	(.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)))))
6.0ms	(.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)))))
3.0ms	(+.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))))

simplify138.0ms (1.2%)

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

prune443.0ms (3.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	378	4	382
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	383	13	396

Error

0.1b

Counts

396 → 13

Alt Table

Status	Error	Program
	33.2b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (sqrt.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)))))
	23.1b	(/.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))))))
	31.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)))) (sin.f64 x))
	29.5b	(log.f64 (exp.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x)))))
	15.7b	(.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))))))
	21.5b	(/.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)))
	41.2b	(fma.f64 (sqrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
▶	2.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))) (cbrt.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)))))
	19.7b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	32.8b	(.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)))))
	31.5b	(+.f64 (.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6))) (.f64 (sin.f64 x) (-.f64 (.f64 1/24 (pow.f64 eps 4)) (.f64 1/2 (.f64 eps eps)))))
	5.5b	(/.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))))
	29.6b	(log.f64 (/.f64 (exp.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (exp.f64 (sin.f64 x))))

Compiler

Compiled 21553 to 10410 computations (51.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
	0.7b	(cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
	2.8b	(+.f64 (cos.f64 eps) -1)

series2.0s (17.3%)

Counts

2 → 48

Calls

2 calls:

1.1s

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

973.0ms

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

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`

Counts

2 → 72

Calls

2 calls:

7.0ms

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

1.0ms

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

simplify159.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

843×	`times-frac_binary64`
350×	`associate-r_binary64`
253×	`associate-l_binary64`
252×	`fma-def_binary64`
226×	`fma-neg_binary64`

Counts

120 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	6557
1	839	6157
2	3129	5491
3	4965	5491
4	4949	5491

prune937.0ms (8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	633	0	633
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	633	13	646

Error

0.1b

Counts

646 → 13

Alt Table

Status	Error	Program
	33.2b	(.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (sqrt.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)))))
	23.1b	(/.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))))))
	31.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (sqrt.f64 (cos.f64 x)) (*.f64 (sqrt.f64 (cos.f64 x)) (sin.f64 eps)))) (sin.f64 x))
	29.5b	(log.f64 (exp.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x)))))
	15.7b	(.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))))))
	21.5b	(/.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)))
	41.2b	(fma.f64 (sqrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (sin.f64 x)))
✓	2.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))) (cbrt.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)))))
	19.7b	(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
	32.8b	(.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)))))
	31.5b	(+.f64 (.f64 (cos.f64 x) (+.f64 eps (.f64 (pow.f64 eps 3) -1/6))) (.f64 (sin.f64 x) (-.f64 (.f64 1/24 (pow.f64 eps 4)) (.f64 1/2 (.f64 eps eps)))))
	5.5b	(/.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))))
	29.6b	(log.f64 (/.f64 (exp.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (exp.f64 (sin.f64 x))))

Compiler

Compiled 58212 to 28368 computations (51.3% saved)

regimes876.0ms (7.5%)

Accuracy

Total 0.3b remaining (71.6%)

Threshold costs 0.3b (71.6%)

Counts

226 → 1

Compiler

Compiled 20178 to 11558 computations (42.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	18	19
2	17	19

end1.0ms (0%)

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

sample4.1s (34.8%)

Algorithm

1×

intervals

Results

1.7s	3484×	body	1024	valid
1.2s	1187×	body	2048	valid
383.0ms	1417×	body	512	valid
125.0ms	1341×	body	128	valid
95.0ms	570×	body	256	valid
3.0ms	1×	body	4096	valid

Compiler

Compiled 516 to 267 computations (48.3% 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%)

sample186.0ms (1.6%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series13.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify100.0ms (0.9%)

prune79.0ms (0.7%)

localize16.0ms (0.1%)

series57.0ms (0.5%)

rewrite24.0ms (0.2%)

simplify133.0ms (1.1%)

prune177.0ms (1.5%)

localize15.0ms (0.1%)

series2.2s (18.4%)

rewrite27.0ms (0.2%)

simplify138.0ms (1.2%)

prune443.0ms (3.8%)

localize18.0ms (0.2%)

series2.0s (17.3%)

rewrite17.0ms (0.1%)

simplify159.0ms (1.4%)

prune937.0ms (8%)

regimes876.0ms (7.5%)

simplify2.0ms (0%)

end1.0ms (0%)

sample4.1s (34.8%)

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