Details

analyze977.0ms (7.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample10.5s (81.5%)

Results

4.7s	1624×	body	8192	exit
2.7s	4116×	body	1024	valid
994.0ms	2032×	body	512	valid
907.0ms	1567×	body	1024	invalid
312.0ms	1073×	body	256	valid
286.0ms	764×	body	512	invalid
156.0ms	168×	body	2048	valid
142.0ms	867×	body	128	valid
100.0ms	413×	body	256	invalid
53.0ms	369×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
493×	`fma-neg_binary64`
430×	`associate-/l*_binary64`
379×	`fma-def_binary64`
296×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	25	15
3	36	15
4	59	15
5	103	15
6	204	15
7	435	15
8	703	15
9	1995	15
10	2934	15
11	3478	15
12	4158	15
13	4980	15
14	4913	15

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

59.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.1b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 x)
✓	0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	4.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series18.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
3.0ms	(sqrt.f64 (cos.f64 x))
2.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1.0ms	(exp.f64 x)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 66

Calls

4 calls:

3.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(exp.f64 x)
0.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-def_binary64`
626×	`cancel-sign-sub-inv_binary64`
505×	`times-frac_binary64`
293×	`fma-neg_binary64`
252×	`associate-/l*_binary64`

Counts

78 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1297
1	245	1205
2	550	1165
3	1437	1144
4	4144	1144
5	4931	1144

prune91.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Error

46.3b

Counts

114 → 5

Alt Table

Status	Error	Program
	59.1b	(/.f64 (fmod.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3)) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	59.1b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
	59.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	47.3b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	59.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 (pow.f64 x 4) -1/96 (fma.f64 x (*.f64 x -1/4) 1))) (exp.f64 x))

Compiler

Compiled 1870 to 563 computations (69.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 x)
✓	0.0b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	0.0b	(sqrt.f64 (cos.f64 x))
✓	15.5b	(fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x)))

series11.0ms (0.1%)

Counts

2 → 4

Calls

2 calls:

9.0ms	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
2.0ms	(fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 38

Calls

2 calls:

3.0ms	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
0.0ms	(fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x)))

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

698×	`times-frac_binary64`
513×	`div-sub_binary64`
503×	`distribute-rgt-neg-in_binary64`
299×	`fma-def_binary64`
294×	`associate-l_binary64`

Counts

42 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	74	1092
1	152	1003
2	336	965
3	822	947
4	2773	946
5	4586	946
6	5245	946

prune97.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Error

46.3b

Counts

98 → 5

Alt Table

Status	Error	Program
	59.1b	(/.f64 (fmod.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3)) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
▶	59.1b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
	59.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	47.3b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	59.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 (pow.f64 x 4) -1/96 (fma.f64 x (*.f64 x -1/4) 1))) (exp.f64 x))

Compiler

Compiled 1721 to 893 computations (48.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
✓	2.2b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
✓	2.2b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
	4.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series500.0ms (3.9%)

Counts

3 → 7

Calls

3 calls:

428.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
68.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
4.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
24×	`add-cube-cbrt_binary64`
19×	`exp-sum_binary64`

Counts

3 → 89

Calls

3 calls:

8.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
4.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
1.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))

simplify122.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

937×	`fma-neg_binary64`
393×	`associate-l_binary64`
371×	`associate-r_binary64`
301×	`distribute-rgt-neg-in_binary64`
295×	`fma-def_binary64`

Counts

96 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1901
1	215	1719
2	593	1570
3	2378	1557
4	4254	1557
5	4939	1557
6	4901	1557

prune68.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	119	5	124

Error

24.7b

Counts

124 → 5

Alt Table

Status	Error	Program
	59.3b	(exp.f64 (-.f64 (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) x))
	59.1b	(/.f64 (fmod.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3)) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	59.0b	(exp.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x) 3)))
	59.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 (pow.f64 x 4) -1/96 (fma.f64 x (*.f64 x -1/4) 1))) (exp.f64 x))
▶	26.7b	(exp.f64 (neg.f64 x))

Compiler

Compiled 2580 to 567 computations (78% saved)

localize2.0ms (0%)

prune4.0ms (0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Error

24.7b

Counts

5 → 5

Alt Table

Status	Error	Program
	59.3b	(exp.f64 (-.f64 (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) x))
	59.1b	(/.f64 (fmod.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 3)) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	59.0b	(exp.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x) 3)))
	59.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 (pow.f64 x 4) -1/96 (fma.f64 x (*.f64 x -1/4) 1))) (exp.f64 x))
✓	26.7b	(exp.f64 (neg.f64 x))

Compiler

Compiled 62 to 45 computations (27.4% saved)

regimes82.0ms (0.6%)

Accuracy

Total 0.4b remaining (1.7%)

Threshold costs 0.4b (1.7%)

Counts

47 → 3

Compiler

Compiled 1214 to 838 computations (31% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	73
1	31	73
2	33	73
3	34	73
4	34	73

end90.0ms (0.7%)

Compiler: Compiled 150 to 87 computations (42% saved)

Details

analyze977.0ms (7.6%)

sample10.5s (81.5%)

simplify85.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series18.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify78.0ms (0.6%)

prune91.0ms (0.7%)

localize8.0ms (0.1%)

series11.0ms (0.1%)

rewrite5.0ms (0%)

simplify86.0ms (0.7%)

prune97.0ms (0.8%)

localize10.0ms (0.1%)

series500.0ms (3.9%)

rewrite18.0ms (0.1%)

simplify122.0ms (0.9%)

prune68.0ms (0.5%)

localize2.0ms (0%)

prune4.0ms (0%)

regimes82.0ms (0.6%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end90.0ms (0.7%)

Profiling