Details

analyze779.0ms (8.8%)

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)

sample197.0ms (2.2%)

Algorithm

1×

intervals

Results

84.0ms	51×	body	8192	exit
46.0ms	120×	body	1024	valid
16.0ms	70×	body	512	valid
14.0ms	56×	body	1024	nan
8.0ms	26×	body	512	nan
4.0ms	28×	body	256	valid
4.0ms	8×	body	2048	valid
2.0ms	30×	body	128	valid
2.0ms	16×	body	256	nan
1.0ms	9×	body	128	nan

Compiler

Compiled 24 to 18 computations (25% saved)

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
430×	`associate-/l*_binary64`
308×	`rec-exp_binary64`
296×	`*-commutative_binary64`
293×	`exp-prod_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	25	15
3	36	15
4	57	15
5	101	15
6	202	15
7	431	15
8	694	15
9	1973	15
10	2876	15
11	3314	15
12	3808	15
13	4103	15
14	4799	15
15	4981	15

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

61.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	61.1b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 30 to 18 computations (40% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (cos.f64 x))
0.5b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

61.1b

Rules

13×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow1_binary64` `add-exp-log_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 773 to 159 computations (79.4% saved)

series30.0ms (0.3%)

Error

61.1b

Counts

3 → 12

Calls

3 calls:

12.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
7.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
6.0ms	(sqrt.f64 (cos.f64 x))

Compiler

Compiled 363 to 174 computations (52.1% saved)

simplify104.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

513×	`div-sub_binary64`
494×	`distribute-rgt-neg-in_binary64`
407×	`distribute-lft-neg-in_binary64`
325×	`cancel-sign-sub-inv_binary64`
297×	`associate-l_binary64`

Counts

59 → 16

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	82	1143
1	159	1021
2	341	1006
3	804	995
4	2622	992
5	4631	992
6	5294	992

prune16.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	15	2	17

Error

61.1b

Counts

17 → 2

Alt Table

Status	Error	Program
	61.4b	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (-.f64 1 x))
▶	61.1b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))

Compiler

Compiled 251 to 100 computations (60.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (cos.f64 x))
0.0b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
0.5b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite109.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

61.1b

Rules

32×	`cbrt-prod_binary64`
29×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
27×	`times-frac_binary64`
13×	`unpow-prod-down_binary64` `cube-prod_binary64`

Counts

4 → 89

Calls

4 calls:

5.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
4.0ms	(/.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)))

Compiler

Compiled 1647 to 507 computations (69.2% saved)

series46.0ms (0.5%)

Error

61.1b

Counts

4 → 18

Calls

4 calls:

13.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
11.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
6.0ms	(sqrt.f64 (cos.f64 x))
6.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 674 to 340 computations (49.6% saved)

simplify160.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

718×	`times-frac_binary64`
504×	`associate-/l*_binary64`
452×	`associate-*l/_binary64`
373×	`associate-*r/_binary64`
283×	`associate-/r*_binary64`

Counts

107 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	2495
1	330	2270
2	927	2182
3	4197	2182
4	4608	2148
5	4917	2148
6	4946	2148

prune47.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	3	66

Error

61.1b

Counts

66 → 3

Alt Table

Status	Error	Program
	61.4b	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (-.f64 1 x))
	61.1b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 2) (sqrt.f64 (exp.f64 x))) (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (exp.f64 x))))
▶	61.1b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)) 3))

Compiler

Compiled 800 to 278 computations (65.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
0.0b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)) 3))
0.5b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite193.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

61.1b

Rules

172×	`cbrt-prod_binary64`
74×	`unpow-prod-down_binary64` `cube-prod_binary64`
63×	`times-frac_binary64`
60×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
7×	`div-inv_binary64`

Counts

4 → 162

Calls

4 calls:

12.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)) 3))
5.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
4.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 2841 to 1108 computations (61% saved)

series59.0ms (0.7%)

Error

61.1b

Counts

4 → 21

Calls

4 calls:

15.0ms	(cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3))
13.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
11.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)) 3))
6.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 913 to 461 computations (49.5% saved)

simplify260.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

718×	`times-frac_binary64`
504×	`associate-/l*_binary64`
452×	`associate-*l/_binary64`
373×	`associate-*r/_binary64`
283×	`associate-/r*_binary64`

Counts

183 → 145

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	200	5399
1	365	4863
2	957	4692
3	4254	4692
4	4590	4602
5	4900	4602
6	4954	4602

prune58.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	145	3	148

Error

61.1b

Counts

148 → 3

Alt Table

Status	Error	Program
	61.1b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 2) (sqrt.f64 (exp.f64 x))) (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (exp.f64 x))))
✓	61.1b	(cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)) 3)) 3))
▶	61.1b	(cbrt.f64 (pow.f64 (exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)) 3))

Compiler

Compiled 1126 to 392 computations (65.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
1.1b	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
3.2b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite90.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

61.1b

Rules

16×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`log-prod_binary64`
7×	`pow1_binary64` `add-log-exp_binary64` `exp-sum_binary64`

Counts

4 → 62

Calls

4 calls:

6.0ms	(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))))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 1189 to 364 computations (69.4% saved)

series66.0ms (0.7%)

Error

22.7b

Counts

4 → 18

Calls

4 calls:

23.0ms	(-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)
16.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
11.0ms	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
6.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 605 to 382 computations (36.9% saved)

simplify119.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

418×	`cancel-sign-sub-inv_binary64`
407×	`times-frac_binary64`
401×	`unsub-neg_binary64`
328×	`*-commutative_binary64`
252×	`distribute-rgt-in_binary64`

Counts

80 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1474
1	185	1327
2	396	1301
3	1236	1279
4	3348	1279
5	4941	1279
6	4958	1279

prune25.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	37	3	40

Error

22.7b

Counts

40 → 3

Alt Table

Status	Error	Program
	61.1b	(cbrt.f64 (pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x) 3))) 3))
	23.7b	(cbrt.f64 (pow.f64 (exp.f64 (neg.f64 x)) 3))
	63.2b	(cbrt.f64 (pow.f64 (exp.f64 (/.f64 (-.f64 (pow.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 3) (pow.f64 x 3)) (+.f64 (.f64 x x) (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (+.f64 x (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))) 3))

Compiler

Compiled 545 to 221 computations (59.4% saved)

regimes191.0ms (2.1%)

Accuracy

Total 1.8b remaining (7.1%)

Threshold costs 0b (0%)

Compiler

Compiled 2479 to 1663 computations (32.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	10	10
2	12	10
3	13	10
4	14	10
5	14	10

end1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

sample6.1s (68.9%)

Algorithm

1×

intervals

Results

2.6s	1524×	body	8192	exit
1.5s	3955×	body	1024	valid
457.0ms	2001×	body	512	valid
449.0ms	1611×	body	1024	nan
152.0ms	765×	body	512	nan
147.0ms	967×	body	256	valid
102.0ms	166×	body	2048	valid
77.0ms	911×	body	128	valid
53.0ms	417×	body	256	nan
28.0ms	392×	body	128	nan
1.0ms	1×	body	2048	nan

Compiler

Compiled 84 to 56 computations (33.3% saved)

Details

analyze779.0ms (8.8%)

sample197.0ms (2.2%)

simplify115.0ms (1.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite51.0ms (0.6%)

series30.0ms (0.3%)

simplify104.0ms (1.2%)

prune16.0ms (0.2%)

localize9.0ms (0.1%)

rewrite109.0ms (1.2%)

series46.0ms (0.5%)

simplify160.0ms (1.8%)

prune47.0ms (0.5%)

localize11.0ms (0.1%)

rewrite193.0ms (2.2%)

series59.0ms (0.7%)

simplify260.0ms (2.9%)

prune58.0ms (0.6%)

localize11.0ms (0.1%)

rewrite90.0ms (1%)

series66.0ms (0.7%)

simplify119.0ms (1.3%)

prune25.0ms (0.3%)

regimes191.0ms (2.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample6.1s (68.9%)

Profiling