Details

analyze954.0ms (5.9%)

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)

sample13.0s (80.6%)

Results

5.7s	1547×	body	8192	exit
3.5s	4225×	body	1024	valid
1.3s	1697×	body	1024	invalid
1.0s	2029×	body	512	valid
355.0ms	1021×	body	256	valid
333.0ms	796×	body	512	invalid
184.0ms	142×	body	2048	valid
162.0ms	839×	body	128	valid
144.0ms	413×	body	256	invalid
73.0ms	396×	body	128	invalid
3.0ms	1×	body	2048	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify142.0ms (0.9%)

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

prune5.0ms (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

60.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.2b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 x)
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	3.9b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series43.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
11.0ms	(exp.f64 x)
9.0ms	(sqrt.f64 (cos.f64 x))
3.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite14.0ms (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:

8.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(exp.f64 x)
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify159.0ms (1%)

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 → 94

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

prune178.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Error

47.4b

Counts

116 → 5

Alt Table

Status	Error	Program
	60.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 x (*.f64 x -1/4) 1)) (exp.f64 x))
	61.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	60.2b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
▶	48.0b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 1870 to 554 computations (70.4% saved)

localize31.0ms (0.2%)

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))
✓	15.8b	(fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x)))

series20.0ms (0.1%)

Counts

2 → 4

Calls

2 calls:

17.0ms	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
3.0ms	(fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x)))

rewrite9.0ms (0.1%)

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:

5.0ms	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x)))

simplify193.0ms (1.2%)

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

prune210.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Error

47.4b

Counts

99 → 6

Alt Table

Status	Error	Program
	60.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 x (*.f64 x -1/4) 1)) (exp.f64 x))
	61.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	60.2b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
▶	59.6b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (+.f64 x 1))
✓	48.0b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 1736 to 901 computations (48.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (+.f64 x 1))
	0.0b	(sqrt.f64 (cos.f64 x))
	15.8b	(fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x)))

series27.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

27.0ms

(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (+.f64 x 1))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

1 → 35

Calls

1 calls:

6.0ms

(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (+.f64 x 1))

simplify174.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

500×	`fma-def_binary64`
497×	`div-sub_binary64`
244×	`distribute-rgt-neg-in_binary64`
232×	`associate-l_binary64`
227×	`sub-neg_binary64`

Counts

47 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	86	1450
1	186	1360
2	435	1322
3	1025	1259
4	3399	1237
5	4536	1237
6	5018	1237

prune212.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	103	6	109

Error

47.2b

Counts

109 → 6

Alt Table

Status	Error	Program
	60.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 x (*.f64 x -1/4) 1)) (exp.f64 x))
	61.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	59.7b	(/.f64 (fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1)) (+.f64 x 1))
	60.2b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
✓	48.0b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 2205 to 1355 computations (38.5% saved)

localize20.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1)) (+.f64 x 1))
✓	3.6b	(fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1))

series15.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(/.f64 (fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1)) (+.f64 x 1))
3.0ms	(fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

2 → 44

Calls

2 calls:

7.0ms	(/.f64 (fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1)) (+.f64 x 1))
1.0ms	(fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1))

simplify212.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-def_binary64`
503×	`div-sub_binary64`
262×	`associate-l_binary64`
235×	`distribute-rgt-neg-in_binary64`
233×	`sub-neg_binary64`

Counts

68 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	2054
1	194	1907
2	447	1866
3	1067	1785
4	3515	1783
5	4473	1783
6	4980	1783

prune200.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	82	6	88

Error

47.2b

Counts

88 → 6

Alt Table

Status	Error	Program
	60.2b	(/.f64 (fmod.f64 (exp.f64 x) (fma.f64 x (*.f64 x -1/4) 1)) (exp.f64 x))
	61.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
✓	59.7b	(/.f64 (fmod.f64 (+.f64 1 x) (fma.f64 x (*.f64 x -1/4) 1)) (+.f64 x 1))
	60.2b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
✓	48.0b	(/.f64 (fmod.f64 (+.f64 1 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 2213 to 1636 computations (26.1% saved)

regimes97.0ms (0.6%)

Accuracy

Total 1.0b remaining (2.2%)

Threshold costs 0b (0%)

Counts

24 → 1

Compiler

Compiled 648 to 456 computations (29.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	13	21
2	12	21

end156.0ms (1%)

Compiler: Compiled 98 to 70 computations (28.6% saved)

Details

analyze954.0ms (5.9%)

sample13.0s (80.6%)

simplify142.0ms (0.9%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series43.0ms (0.3%)

rewrite14.0ms (0.1%)

simplify159.0ms (1%)

prune178.0ms (1.1%)

localize31.0ms (0.2%)

series20.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify193.0ms (1.2%)

prune210.0ms (1.3%)

localize15.0ms (0.1%)

series27.0ms (0.2%)

rewrite10.0ms (0.1%)

simplify174.0ms (1.1%)

prune212.0ms (1.3%)

localize20.0ms (0.1%)

series15.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify212.0ms (1.3%)

prune200.0ms (1.2%)

regimes97.0ms (0.6%)

simplify5.0ms (0%)

end156.0ms (1%)

Profiling