Details

analyze1.0s (8.5%)

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)

sample297.0ms (2.4%)

Algorithm

1×

intervals

Results

155.0ms	57×	body	8192	exit
60.0ms	121×	body	1024	valid
23.0ms	56×	body	1024	nan
21.0ms	72×	body	512	valid
7.0ms	36×	body	256	valid
5.0ms	13×	body	512	nan
3.0ms	5×	body	2048	valid
2.0ms	22×	body	128	valid
2.0ms	23×	body	128	nan
2.0ms	10×	body	256	nan

Compiler

Compiled 24 to 18 computations (25% saved)

simplify85.0ms (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

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

60.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.3b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series5.0ms (0%)

Counts

2 → 4

Calls

2 calls:

3.0ms	(sqrt.f64 (cos.f64 x))
2.0ms	(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)))

simplify86.0ms (0.7%)

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

prune28.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Error

60.3b

Counts

34 → 3

Alt Table

Status	Error	Program
	60.3b	(/.f64 (cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)) (exp.f64 x))
▶	60.3b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 546 to 233 computations (57.3% saved)

localize9.0ms (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)))))
✓	2.1b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series367.0ms (3%)

Counts

2 → 12

Calls

2 calls:

365.0ms	(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)))))

rewrite4.0ms (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:

2.0ms	(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))))

simplify103.0ms (0.8%)

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

prune80.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	73	4	77

Error

60.3b

Counts

77 → 4

Alt Table

Status	Error	Program
	60.3b	(/.f64 (pow.f64 (exp.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))
	60.3b	(/.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))
▶	60.3b	(/.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1445 to 461 computations (68.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
✓	0.1b	(exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))))
	2.1b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series366.0ms (3%)

Counts

2 → 24

Calls

2 calls:

364.0ms

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

2.0ms

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

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`exp-prod_binary64`
3×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 26

Calls

2 calls:

3.0ms

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

2.0ms

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

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

592×	`unswap-sqr_binary64`
450×	`associate-*l/_binary64`
292×	`associate-/l*_binary64`
262×	`associate-/r*_binary64`
251×	`exp-prod_binary64`

Counts

50 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	1426
1	45	789
2	58	684
3	69	648
4	101	648
5	165	648
6	313	648
7	776	648
8	1729	648
9	3040	648
10	4324	648
11	4999	648
12	4783	648

prune155.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Error

60.3b

Counts

126 → 4

Alt Table

Status	Error	Program
	60.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	60.3b	(/.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.3b	(/.f64 (pow.f64 (exp.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))
	60.3b	(/.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))

Compiler

Compiled 4327 to 674 computations (84.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
✓	2.1b	(log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
	2.1b	(log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
	4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series362.0ms (3%)

Counts

2 → 24

Calls

2 calls:

359.0ms	(log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
3.0ms	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`log-prod_binary64`
9×	`log-pow_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`exp-prod_binary64`

Counts

2 → 35

Calls

2 calls:

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

simplify125.0ms (1%)

Algorithm

1×	egg-herbie

Rules

742×	`unswap-sqr_binary64`
400×	`prod-exp_binary64`
372×	`log-div_binary64`
370×	`associate-/l/_binary64`
362×	`fma-def_binary64`

Counts

59 → 57

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	53	903
1	51	822
2	64	822
3	83	822
4	120	822
5	216	822
6	455	822
7	1230	822
8	4389	822
9	4565	822
10	4682	822
11	5459	822

prune205.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	118	5	123

Error

60.3b

Counts

123 → 5

Alt Table

Status	Error	Program
	60.3b	(/.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))
	60.3b	(/.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.4b	(/.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (cbrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (log.f64 (cbrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.3b	(/.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (exp.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)))))))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
✓	60.3b	(/.f64 (exp.f64 (cbrt.f64 (.f64 (.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (log.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))

Compiler

Compiled 4516 to 858 computations (81% saved)

regimes123.0ms (1%)

Accuracy

Total 0.1b remaining (0.1%)

Threshold costs 0.1b (0.1%)

Counts

68 → 1

Compiler

Compiled 2894 to 1502 computations (48.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	17	53
2	17	53

end1.0ms (0%)

Compiler: Compiled 31 to 14 computations (54.8% saved)

sample8.5s (70.3%)

Algorithm

1×

intervals

Results

4.0s	1485×	body	8192	exit
2.0s	3996×	body	1024	valid
694.0ms	1602×	body	1024	nan
614.0ms	1964×	body	512	valid
195.0ms	983×	body	256	valid
191.0ms	737×	body	512	nan
131.0ms	185×	body	2048	valid
97.0ms	872×	body	128	valid
61.0ms	367×	body	256	nan
50.0ms	451×	body	128	nan

Compiler

Compiled 247 to 100 computations (59.5% saved)

Details

analyze1.0s (8.5%)

sample297.0ms (2.4%)

simplify85.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series5.0ms (0%)

rewrite2.0ms (0%)

simplify86.0ms (0.7%)

prune28.0ms (0.2%)

localize9.0ms (0.1%)

series367.0ms (3%)

rewrite4.0ms (0%)

simplify103.0ms (0.8%)

prune80.0ms (0.7%)

localize14.0ms (0.1%)

series366.0ms (3%)

rewrite7.0ms (0.1%)

simplify106.0ms (0.9%)

prune155.0ms (1.3%)

localize16.0ms (0.1%)

series362.0ms (3%)

rewrite5.0ms (0%)

simplify125.0ms (1%)

prune205.0ms (1.7%)

regimes123.0ms (1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample8.5s (70.3%)

Profiling