Details

analyze799.0ms (5.8%)

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)

sample9.2s (66.9%)

Infinites

0% of outputs are infinite.

Results

4.5s	1590×	body	8192	exit
2.3s	4128×	body	1024	valid
791.0ms	1580×	body	1024	invalid
665.0ms	1959×	body	512	valid
250.0ms	818×	body	512	invalid
245.0ms	1040×	body	256	valid
137.0ms	184×	body	2048	valid
131.0ms	945×	body	128	valid
93.0ms	429×	body	256	invalid
55.0ms	421×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify79.0ms (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

59.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.0b	(/.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%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	4.2b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series4.0ms (0%)

Counts

2 → 4

Calls

2 calls:

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64`
3×	`sqrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 24

Calls

2 calls:

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

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

487×	`distribute-rgt-out--_binary64`
408×	`distribute-rgt-neg-in_binary64`
373×	`distribute-rgt-out_binary64`
350×	`distribute-lft-neg-in_binary64`
334×	`*-commutative_binary64`

Counts

28 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	306
1	89	283
2	170	281
3	455	279
4	1563	279
5	3297	279
6	4584	279
7	4993	279

prune23.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	32	2	34

Error

59.0b

Counts

34 → 2

Alt Table

Status	Error	Program
▶	59.0b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Status

Error

Program

▶

59.0b

(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

59.1b

(/.f64 (*.f64 (*.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 550 to 217 computations (60.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.1b	(exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
✓	3.1b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	4.2b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series347.0ms (2.5%)

Counts

2 → 12

Calls

2 calls:

345.0ms	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
2.0ms	(exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

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

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1041×	`fma-def_binary64`
620×	`unswap-sqr_binary64`
349×	`associate-/l*_binary64`
287×	`associate-/r*_binary64`
266×	`sqr-pow_binary64`

Counts

43 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	648
1	45	577
2	58	577
3	76	569
4	115	569
5	187	569
6	357	569
7	891	569
8	1953	569
9	3238	569
10	4536	569
11	4988	569
12	4832	569

prune86.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	72	4	76

Error

59.0b

Counts

76 → 4

Alt Table

Status	Error	Program
	59.1b	(/.f64 (exp.f64 (+.f64 (*.f64 (log.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) 2) (log.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
✓	59.0b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.0b	(/.f64 (exp.f64 (.f64 (.f64 (cbrt.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (cbrt.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
▶	59.0b	(/.f64 (pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1387 to 451 computations (67.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.2b	(pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	3.1b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	4.2b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series540.0ms (3.9%)

Counts

1 → 12

Calls

1 calls:

540.0ms

(pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow-unpow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

1 → 24

Calls

1 calls:

3.0ms

(pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary64`
496×	`unswap-sqr_binary64`
437×	`associate-/l*_binary64`
418×	`associate-/r/_binary64`
266×	`*-commutative_binary64`

Counts

36 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	653
1	87	624
2	172	624
3	407	624
4	1012	624
5	2458	624
6	4494	624
7	4841	624
8	4819	624

prune96.0ms (0.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	75	5	80

Error

59.0b

Counts

80 → 5

Alt Table

Status	Error	Program
✓	59.0b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.0b	(/.f64 (pow.f64 (E.f64) (.f64 (.f64 (cbrt.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (cbrt.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
▶	59.0b	(/.f64 (*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	59.1b	(/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (E.f64)) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (exp.f64 x))
✓	59.0b	(/.f64 (pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1593 to 499 computations (68.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))))
✓	0.1b	(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
✓	3.1b	(log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	4.2b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series1.5s (10.5%)

Counts

3 → 24

Calls

3 calls:

543.0ms

(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))))

541.0ms

(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))

372.0ms

(log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
60×	`log-prod_binary64`
54×	`unpow-prod-up_binary64`
30×	`sqrt-prod_binary64`
25×	`unswap-sqr_binary64`

Counts

3 → 145

Calls

3 calls:

9.0ms

(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))))

3.0ms

(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))

1.0ms

(log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

simplify333.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

460×	`fma-def_binary64`
396×	`associate-+l+_binary64`
336×	`associate-/l*_binary64`
324×	`associate-/l/_binary64`
319×	`*-commutative_binary64`

Counts

169 → 163

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	135	4445
1	211	4037
2	726	3518
3	997	3514
4	1755	3270
5	4173	3254
6	4965	3254
7	4996	3254
8	4766	3254

prune303.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	238	3	241
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	241	5	246

Error

59.0b

Counts

246 → 5

Alt Table

Status	Error	Program
✓	59.0b	(/.f64 (pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.3b	(/.f64 (*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))) (exp.f64 x))
✓	59.0b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.2b	(/.f64 (*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (log.f64 (exp.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	59.2b	(/.f64 (*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (pow.f64 (E.f64) (log1p.f64 (expm1.f64 (log.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))) (exp.f64 x))

Compiler

Compiled 7872 to 1094 computations (86.1% saved)

regimes68.0ms (0.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

27 → 1

Compiler

Compiled 1162 to 570 computations (50.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	9	19

end89.0ms (0.6%)

Compiler: Compiled 127 to 76 computations (40.2% saved)

Details

analyze799.0ms (5.8%)

sample9.2s (66.9%)

simplify79.0ms (0.6%)

prune3.0ms (0%)

localize6.0ms (0%)

series4.0ms (0%)

rewrite2.0ms (0%)

simplify82.0ms (0.6%)

prune23.0ms (0.2%)

localize8.0ms (0.1%)

series347.0ms (2.5%)

rewrite3.0ms (0%)

simplify93.0ms (0.7%)

prune86.0ms (0.6%)

localize14.0ms (0.1%)

series540.0ms (3.9%)

rewrite4.0ms (0%)

simplify82.0ms (0.6%)

prune96.0ms (0.7%)

localize14.0ms (0.1%)

series1.5s (10.5%)

rewrite31.0ms (0.2%)

simplify333.0ms (2.4%)

prune303.0ms (2.2%)

regimes68.0ms (0.5%)

simplify2.0ms (0%)

end89.0ms (0.6%)

Profiling