Details

analyze962.0ms (8%)

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)

sample10.0s (83.3%)

Results

4.3s	1537×	body	8192	exit
2.6s	4093×	body	1024	valid
939.0ms	1604×	body	1024	invalid
831.0ms	2054×	body	512	valid
352.0ms	801×	body	512	invalid
301.0ms	1059×	body	256	valid
252.0ms	395×	body	256	invalid
166.0ms	188×	body	2048	valid
144.0ms	862×	body	128	valid
51.0ms	381×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify81.0ms (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

prune2.0ms (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

60.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.2b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	4.5b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series11.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

7.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite7.0ms (0.1%)

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)))

simplify90.0ms (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

prune54.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Error

60.6b

Counts

74 → 4

Alt Table

Status	Error	Program
	60.6b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.6b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
▶	60.6b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

Compiler

Compiled 1303 to 373 computations (71.4% saved)

localize9.0ms (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))
✓	1.4b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
✓	1.9b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	4.5b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series298.0ms (2.5%)

Counts

3 → 7

Calls

3 calls:

247.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
47.0ms	(-.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))

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))
3.0ms	(-.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))))

simplify115.0ms (1%)

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

prune47.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	117	4	121

Error

20.9b

Counts

121 → 4

Alt Table

Status	Error	Program
	60.6b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.6b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))))
▶	21.9b	(exp.f64 (neg.f64 x))

Compiler

Compiled 2490 to 531 computations (78.7% saved)

localize2.0ms (0%)

prune3.0ms (0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

20.9b

Counts

4 → 4

Alt Table

Status	Error	Program
	60.6b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.6b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))))
✓	21.9b	(exp.f64 (neg.f64 x))

Compiler

Compiled 78 to 55 computations (29.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (sqrt.f64 (cos.f64 x)))
✓	0.1b	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
✓	0.2b	(/.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	4.5b	(fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))

series17.0ms (0.1%)

Counts

4 → 40

Calls

4 calls:

9.0ms	(/.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
3.0ms	(exp.f64 (sqrt.f64 (cos.f64 x)))
3.0ms	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
2.0ms	(fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
12×	`exp-prod_binary64`
9×	`times-frac_binary64`

Counts

4 → 74

Calls

4 calls:

3.0ms	(/.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
2.0ms	(log.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
2.0ms	(exp.f64 (sqrt.f64 (cos.f64 x)))
0.0ms	(fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

515×	`fma-neg_binary64`
463×	`times-frac_binary64`
386×	`*-commutative_binary64`
262×	`distribute-rgt-neg-in_binary64`
248×	`associate-/l*_binary64`

Counts

114 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	1784
1	280	1665
2	645	1619
3	1796	1599
4	4151	1599
5	4956	1599

prune77.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	139	4	143

Error

20.9b

Counts

143 → 4

Alt Table

Status	Error	Program
	60.6b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.6b	(/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (log.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))) (/.f64 (exp.f64 x) (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
	60.6b	(exp.f64 (log1p.f64 (expm1.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))))
✓	21.9b	(exp.f64 (neg.f64 x))

Compiler

Compiled 2556 to 664 computations (74% saved)

regimes55.0ms (0.5%)

Accuracy

Total 1.7b remaining (6.7%)

Threshold costs 0b (0%)

Counts

36 → 1

Compiler

Compiled 936 to 590 computations (37% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-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	4	5
1	8	5
2	10	5
3	11	5
4	11	5

end57.0ms (0.5%)

Compiler: Compiled 58 to 39 computations (32.8% saved)

Details

analyze962.0ms (8%)

sample10.0s (83.3%)

simplify81.0ms (0.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series11.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify90.0ms (0.7%)

prune54.0ms (0.4%)

localize9.0ms (0.1%)

series298.0ms (2.5%)

rewrite14.0ms (0.1%)

simplify115.0ms (1%)

prune47.0ms (0.4%)

localize2.0ms (0%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series17.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify90.0ms (0.7%)

prune77.0ms (0.6%)

regimes55.0ms (0.5%)

simplify2.0ms (0%)

end57.0ms (0.5%)

Profiling