Details

analyze907.0ms (6.8%)

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)

sample351.0ms (2.6%)

Algorithm

1×

intervals

Results

126.0ms	45×	body	8192	exit
63.0ms	139×	body	1024	valid
21.0ms	55×	body	1024	nan
16.0ms	48×	body	512	valid
9.0ms	38×	body	256	valid
5.0ms	23×	body	512	nan
3.0ms	5×	body	2048	valid
2.0ms	26×	body	128	valid
1.0ms	13×	body	128	nan
1.0ms	7×	body	256	nan

Compiler

Compiled 24 to 18 computations (25% saved)

simplify89.0ms (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

59.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.9b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	5.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series15.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

11.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
3.0ms	(sqrt.f64 (cos.f64 x))
2.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite6.0ms (0%)

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)))

simplify91.0ms (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

prune77.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Error

59.8b

Counts

74 → 5

Alt Table

Status	Error	Program
	59.9b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	59.9b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.9b	(.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x)))) (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 x))))
	60.9b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	59.9b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1369 to 391 computations (71.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
✓	0.1b	(*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
✓	0.1b	(cbrt.f64 (sqrt.f64 (cos.f64 x)))
✓	5.1b	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

series348.0ms (2.6%)

Counts

4 → 48

Calls

4 calls:

172.0ms	(cbrt.f64 (sqrt.f64 (cos.f64 x)))
171.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
3.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
2.0ms	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`cbrt-prod_binary64`
46×	`add-sqr-sqrt_binary64`
30×	`pow1_binary64`
27×	`sqrt-prod_binary64`
21×	`*-un-lft-identity_binary64`

Counts

4 → 125

Calls

4 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
6.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
1.0ms	(cbrt.f64 (sqrt.f64 (cos.f64 x)))
0.0ms	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

simplify134.0ms (1%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-def_binary64`
580×	`cancel-sign-sub-inv_binary64`
468×	`log-prod_binary64`
355×	`associate-l_binary64`
339×	`fma-neg_binary64`

Counts

173 → 180

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	2423
1	259	2256
2	652	1923
3	1720	1844
4	4277	1816
5	4861	1816
6	5054	1816

prune289.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	244	5	249

Error

59.8b

Counts

249 → 5

Alt Table

Status	Error	Program
	59.9b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	59.9b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.9b	(.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x)))) (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 x))))
	60.9b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	59.9b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))

Compiler

Compiled 6019 to 1635 computations (72.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
✓	0.1b	(expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))
	0.1b	(cbrt.f64 (sqrt.f64 (cos.f64 x)))
✓	47.0b	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))))

series186.0ms (1.4%)

Counts

2 → 24

Calls

2 calls:

184.0ms

(expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

2.0ms

(fmod.f64 (exp.f64 x) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms

(fmod.f64 (exp.f64 x) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))))

0.0ms

(expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

simplify121.0ms (0.9%)

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`
344×	`*-commutative_binary64`

Counts

44 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	723
1	90	442
2	176	440
3	471	438
4	1598	438
5	3352	438
6	4437	438
7	4973	438
8	4879	438

prune254.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	214	5	219

Error

59.8b

Counts

219 → 5

Alt Table

Status	Error	Program
	59.9b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	59.9b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.9b	(.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x)))) (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 x))))
	60.9b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	59.8b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))

Compiler

Compiled 5898 to 1573 computations (73.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x)))))
✓	0.2b	(cbrt.f64 (cos.f64 x))
✓	0.2b	(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)
✓	47.0b	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))))

series936.0ms (7%)

Counts

4 → 48

Calls

4 calls:

518.0ms	(cbrt.f64 (cos.f64 x))
244.0ms	(cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x)))))
171.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)
2.0ms	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-prod_binary64`
13×	`unpow-prod-down_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 63

Calls

4 calls:

9.0ms	(cbrt.f64 (cos.f64 x))
4.0ms	(cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x)))))
3.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)
0.0ms	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x)))))))

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-def_binary64`
629×	`log-prod_binary64`
596×	`cancel-sign-sub-inv_binary64`
473×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`

Counts

111 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	1657
1	295	1499
2	639	1472
3	1977	1219
4	4915	1219
5	5592	1219

prune292.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	141	5	146

Error

59.8b

Counts

146 → 5

Alt Table

Status	Error	Program
	59.9b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	59.9b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.9b	(.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x)))) (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 x))))
	60.9b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
✓	59.8b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (expm1.f64 (log1p.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))

Compiler

Compiled 5036 to 1976 computations (60.8% saved)

regimes71.0ms (0.5%)

Accuracy

Total 0.1b remaining (0.1%)

Threshold costs 0.1b (0.1%)

Counts

34 → 1

Compiler

Compiled 1314 to 790 computations (39.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	47
1	23	47
2	23	47

end2.0ms (0%)

Compiler: Compiled 28 to 20 computations (28.6% saved)

sample9.0s (67.4%)

Algorithm

1×

intervals

Results

4.3s	1569×	body	8192	exit
2.1s	3979×	body	1024	valid
671.0ms	1562×	body	1024	nan
664.0ms	1984×	body	512	valid
214.0ms	835×	body	512	nan
183.0ms	997×	body	256	valid
110.0ms	166×	body	2048	valid
89.0ms	874×	body	128	valid
79.0ms	419×	body	256	nan
34.0ms	394×	body	128	nan

Compiler

Compiled 131 to 82 computations (37.4% saved)

Details

analyze907.0ms (6.8%)

sample351.0ms (2.6%)

simplify89.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series15.0ms (0.1%)

rewrite6.0ms (0%)

simplify91.0ms (0.7%)

prune77.0ms (0.6%)

localize11.0ms (0.1%)

series348.0ms (2.6%)

rewrite27.0ms (0.2%)

simplify134.0ms (1%)

prune289.0ms (2.2%)

localize15.0ms (0.1%)

series186.0ms (1.4%)

rewrite2.0ms (0%)

simplify121.0ms (0.9%)

prune254.0ms (1.9%)

localize21.0ms (0.2%)

series936.0ms (7%)

rewrite19.0ms (0.1%)

simplify91.0ms (0.7%)

prune292.0ms (2.2%)

regimes71.0ms (0.5%)

simplify3.0ms (0%)

end2.0ms (0%)

sample9.0s (67.4%)

Profiling