Details

analyze921.0ms (7.1%)

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)

sample353.0ms (2.7%)

Algorithm

1×

intervals

Results

128.0ms	49×	body	8192	exit
54.0ms	110×	body	1024	valid
23.0ms	59×	body	1024	nan
19.0ms	68×	body	512	valid
7.0ms	40×	body	256	valid
7.0ms	12×	body	2048	valid
7.0ms	29×	body	512	nan
3.0ms	17×	body	256	nan
3.0ms	26×	body	128	valid
1.0ms	8×	body	128	nan

Compiler

Compiled 24 to 18 computations (25% saved)

simplify83.0ms (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

59.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.4b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series13.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

9.0ms	(/.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)))

rewrite9.0ms (0.1%)

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)))

simplify93.0ms (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

prune52.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Error

59.4b

Counts

74 → 3

Alt Table

Status	Error	Program
▶	59.4b	(/.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))
	59.4b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.4b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 1289 to 353 computations (72.6% saved)

localize14.0ms (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)))))

series361.0ms (2.8%)

Counts

4 → 48

Calls

4 calls:

184.0ms	(*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
171.0ms	(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:

8.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))
7.0ms	(*.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)))))

simplify130.0ms (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

prune256.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	244	3	247

Error

59.4b

Counts

247 → 3

Alt Table

Status	Error	Program
	59.4b	(/.f64 (log.f64 (exp.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))
	60.4b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	59.4b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 5975 to 1613 computations (73% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (pow.f64 (cos.f64 x) 1/6))
✓	0.1b	(cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))
✓	0.2b	(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)
✓	5.1b	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

series634.0ms (4.9%)

Counts

4 → 48

Calls

4 calls:

229.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))
225.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)
178.0ms	(cbrt.f64 (pow.f64 (cos.f64 x) 1/6))
2.0ms	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))
3.0ms	(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)
1.0ms	(cbrt.f64 (pow.f64 (cos.f64 x) 1/6))
0.0ms	(fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))

simplify116.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-def_binary64`
596×	`cancel-sign-sub-inv_binary64`
339×	`fma-neg_binary64`
314×	`log-prod_binary64`
214×	`unswap-sqr_binary64`

Counts

112 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1926
1	285	1793
2	608	1768
3	1702	1757
4	4253	1751
5	4890	1751
6	4940	1751

prune145.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Error

59.4b

Counts

112 → 4

Alt Table

Status	Error	Program
▶	59.4b	(/.f64 (cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)))) 3)) (exp.f64 x))
	59.4b	(/.f64 (log.f64 (exp.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))
	60.4b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
✓	59.4b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 4090 to 1625 computations (60.3% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(cbrt.f64 (pow.f64 (cos.f64 x) 1/6))
	0.1b	(cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x)))))
	0.2b	(pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)
✓	5.1b	(fmod.f64 (exp.f64 x) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4))))

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fmod.f64 (exp.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 9

Calls

1 calls:

0.0ms

(fmod.f64 (exp.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4))))

simplify176.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1057×	`sqr-pow_binary64`
666×	`unswap-sqr_binary64`
584×	`cube-prod_binary64`
549×	`fabs-mul_binary64`
540×	`*-commutative_binary64`

Counts

21 → 11

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	684
1	39	593
2	64	593
3	111	593
4	232	593
5	755	593
6	965	593
7	1547	593
8	1678	593
9	1865	593
10	2068	593
11	2321	593
12	2610	593
13	2935	593
14	3480	593
15	3749	593
16	3983	593
17	4170	593
18	4247	593
19	4304	593
20	4840	593

prune405.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	103	4	107

Error

59.4b

Counts

107 → 4

Alt Table

Status	Error	Program
	59.4b	(/.f64 (cbrt.f64 (pow.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)))))) 3)) (exp.f64 x))
	59.4b	(/.f64 (log.f64 (exp.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))
	60.4b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
✓	59.4b	(/.f64 (fmod.f64 (exp.f64 x) (.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cos.f64 x))) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (pow.f64 (cbrt.f64 (pow.f64 (cos.f64 x) 1/6)) 4)) (cbrt.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 4070 to 1807 computations (55.6% saved)

regimes422.0ms (3.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

162 → 1

Compiler

Compiled 7032 to 3818 computations (45.7% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	50
1	19	50
2	19	50

end1.0ms (0%)

Compiler: Compiled 30 to 16 computations (46.7% saved)

sample8.7s (67.1%)

Algorithm

1×

intervals

Results

4.2s	1568×	body	8192	exit
1.9s	3960×	body	1024	valid
699.0ms	1590×	body	1024	nan
626.0ms	1972×	body	512	valid
244.0ms	1074×	body	256	valid
199.0ms	818×	body	512	nan
117.0ms	175×	body	2048	valid
84.0ms	819×	body	128	valid
71.0ms	433×	body	256	nan
43.0ms	421×	body	128	nan
2.0ms	2×	body	2048	nan

Compiler

Compiled 138 to 79 computations (42.8% saved)

Details

analyze921.0ms (7.1%)

sample353.0ms (2.7%)

simplify83.0ms (0.6%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series13.0ms (0.1%)

rewrite9.0ms (0.1%)

simplify93.0ms (0.7%)

prune52.0ms (0.4%)

localize14.0ms (0.1%)

series361.0ms (2.8%)

rewrite27.0ms (0.2%)

simplify130.0ms (1%)

prune256.0ms (2%)

localize16.0ms (0.1%)

series634.0ms (4.9%)

rewrite11.0ms (0.1%)

simplify116.0ms (0.9%)

prune145.0ms (1.1%)

localize19.0ms (0.1%)

series2.0ms (0%)

rewrite1.0ms (0%)

simplify176.0ms (1.4%)

prune405.0ms (3.1%)

regimes422.0ms (3.2%)

simplify6.0ms (0%)

end1.0ms (0%)

sample8.7s (67.1%)

Profiling