Details

analyze1.0s (7.5%)

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)

sample10.9s (82%)

Results

4.8s	1657×	body	8192	exit
2.8s	4148×	body	1024	valid
1.2s	1698×	body	1024	invalid
902.0ms	2067×	body	512	valid
305.0ms	999×	body	256	valid
296.0ms	812×	body	512	invalid
232.0ms	165×	body	2048	valid
148.0ms	877×	body	128	valid
103.0ms	395×	body	256	invalid
61.0ms	418×	body	128	invalid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify80.0ms (0.6%)

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

59.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.5b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.7b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	3.8b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series16.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 53

Calls

3 calls:

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

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

599×	`cancel-sign-sub-inv_binary64`
541×	`fma-def_binary64`
463×	`times-frac_binary64`
381×	`div-sub_binary64`
282×	`fma-neg_binary64`

Counts

61 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1190
1	212	1105
2	477	1069
3	1265	1049
4	3482	1048
5	4641	1048
6	5116	1048

prune65.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Error

59.5b

Counts

74 → 5

Alt Table

Status	Error	Program
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (pow.f64 (cos.f64 x) 1/2)) (exp.f64 x))
	59.5b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.5b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	59.5b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

Compiler

Compiled 1327 to 389 computations (70.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
✓	1.9b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
✓	2.1b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	3.8b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series402.0ms (3%)

Counts

3 → 7

Calls

3 calls:

336.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
62.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
3.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

rewrite14.0ms (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:

4.0ms	(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))))

simplify114.0ms (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 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1836
1	215	1680
2	593	1570
3	2378	1557
4	4254	1557
5	4939	1557
6	4901	1557

prune58.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

22.3b

Counts

122 → 6

Alt Table

Status	Error	Program
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (pow.f64 (cos.f64 x) 1/2)) (exp.f64 x))
	59.5b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.5b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))))
	59.5b	(exp.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x))
▶	24.0b	(exp.f64 (neg.f64 x))

Compiler

Compiled 2542 to 569 computations (77.6% saved)

localize2.0ms (0%)

prune6.0ms (0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	0	0
Total	6	6

Error

22.3b

Counts

6 → 6

Alt Table

Status	Error	Program
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (pow.f64 (cos.f64 x) 1/2)) (exp.f64 x))
	59.5b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.5b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))))
▶	59.5b	(exp.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x))
✓	24.0b	(exp.f64 (neg.f64 x))

Compiler

Compiled 130 to 93 computations (28.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x))
✓	1.9b	(-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x)
	2.1b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	3.8b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series66.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

63.0ms	(-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x)
3.0ms	(exp.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`cbrt-prod_binary64`
102×	`prod-diff_binary64`
85×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`add-cube-cbrt_binary64`

Counts

2 → 166

Calls

2 calls:

10.0ms	(exp.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x))
7.0ms	(-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x)

simplify144.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
372×	`fma-def_binary64`
349×	`cancel-sign-sub-inv_binary64`
320×	`unswap-sqr_binary64`
242×	`distribute-rgt-in_binary64`

Counts

190 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	3839
1	248	3413
2	735	2969
3	1791	2953
4	4429	2953
5	4873	2953

prune105.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	191	6	197

Error

22.3b

Counts

197 → 6

Alt Table

Status	Error	Program
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))
	59.5b	(/.f64 (fmod.f64 (exp.f64 x) (pow.f64 (cos.f64 x) 1/2)) (exp.f64 x))
	59.5b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x)) (cbrt.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x)))) (cbrt.f64 (-.f64 (cbrt.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3)) x)))
	59.5b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.5b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))))
✓	24.0b	(exp.f64 (neg.f64 x))

Compiler

Compiled 5817 to 1820 computations (68.7% saved)

regimes67.0ms (0.5%)

Accuracy

Total 0.4b remaining (1.8%)

Threshold costs 0.4b (1.8%)

Counts

35 → 3

Compiler

Compiled 1376 to 816 computations (40.7% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	69
1	25	69
2	26	69
3	27	69
4	25	69

end100.0ms (0.7%)

Compiler: Compiled 180 to 91 computations (49.4% saved)

Details

analyze1.0s (7.5%)

sample10.9s (82%)

simplify80.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series16.0ms (0.1%)

rewrite6.0ms (0%)

simplify88.0ms (0.7%)

prune65.0ms (0.5%)

localize8.0ms (0.1%)

series402.0ms (3%)

rewrite14.0ms (0.1%)

simplify114.0ms (0.9%)

prune58.0ms (0.4%)

localize2.0ms (0%)

prune6.0ms (0%)

localize10.0ms (0.1%)

series66.0ms (0.5%)

rewrite40.0ms (0.3%)

simplify144.0ms (1.1%)

prune105.0ms (0.8%)

regimes67.0ms (0.5%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end100.0ms (0.7%)

Profiling