Details

analyze1.0s (7.2%)

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)

sample10.6s (75.8%)

Results

4.6s	1563×	body	8192	exit
2.7s	4102×	body	1024	valid
1.1s	1662×	body	1024	invalid
921.0ms	2023×	body	512	valid
316.0ms	856×	body	512	invalid
301.0ms	1029×	body	256	valid
166.0ms	184×	body	2048	valid
160.0ms	918×	body	128	valid
114.0ms	443×	body	256	invalid
56.0ms	391×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify81.0ms (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

59.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.2b	(/.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%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.5b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	5.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series14.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

10.0ms	(/.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)))

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

prune123.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	7	74

Error

59.2b

Counts

74 → 7

Alt Table

Status	Error	Program
	59.2b	(/.f64 (cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)) (exp.f64 x))
	59.5b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.0b	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (-.f64 1 x))
	60.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	59.2b	(/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))
	59.2b	(.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))))) (*.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 x)))) (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 x))))
▶	59.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))

Compiler

Compiled 1417 to 427 computations (69.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	0.5b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	5.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series8.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

8.0ms

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`exp-sum_binary64`
13×	`log-prod_binary64`
9×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

1 → 28

Calls

1 calls:

3.0ms

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

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

519×	`distribute-rgt-neg-in_binary64`
333×	`fma-def_binary64`
320×	`cancel-sign-sub-inv_binary64`
310×	`associate-l_binary64`
297×	`neg-mul-1_binary64`

Counts

40 → 54

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	995
1	188	940
2	399	877
3	932	849
4	3073	828
5	4244	828
6	4928	828

prune165.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	126	8	134

Error

59.2b

Counts

134 → 8

Alt Table

Status	Error	Program
	59.2b	(/.f64 (cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)) (exp.f64 x))
	60.3b	(exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	59.5b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.5b	(exp.f64 (log.f64 (/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))))
	60.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	59.2b	(*.f64 (exp.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 x))))) (exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 x))))))
	59.2b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)) (cbrt.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)))) (cbrt.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)))))
	59.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))

Compiler

Compiled 2716 to 780 computations (71.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 x)))
✓	2.5b	(log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 x))))
	5.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
✓	5.3b	(log.f64 (/.f64 1 (sqrt.f64 (exp.f64 x))))

series661.0ms (4.7%)

Counts

3 → 36

Calls

3 calls:

425.0ms

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

225.0ms

(log.f64 (/.f64 1 (sqrt.f64 (exp.f64 x))))

10.0ms

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

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
44×	`log-prod_binary64`

Counts

3 → 121

Calls

3 calls:

4.0ms

(log.f64 (/.f64 1 (sqrt.f64 (exp.f64 x))))

3.0ms

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

3.0ms

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

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

642×	`fma-neg_binary64`
480×	`fma-def_binary64`
357×	`cancel-sign-sub-inv_binary64`
342×	`distribute-rgt-in_binary64`
316×	`associate-/l*_binary64`

Counts

157 → 175

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	162	3629
1	291	3474
2	604	3323
3	1478	3192
4	4368	3189
5	5082	3189

prune285.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	185	8	193

Error

59.2b

Counts

193 → 8

Alt Table

Status	Error	Program
▶	59.2b	(/.f64 (cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)) (exp.f64 x))
	60.3b	(exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	59.5b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.4b	(*.f64 (exp.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 x))))) (exp.f64 (log1p.f64 (expm1.f64 (fma.f64 -1/2 x (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))))))
	59.5b	(exp.f64 (log.f64 (/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))))
	60.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	59.2b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)) (cbrt.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)))) (cbrt.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)))))
	59.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))

Compiler

Compiled 5459 to 1901 computations (65.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3))
✓	0.0b	(pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)
✓	0.5b	(/.f64 (cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)) (exp.f64 x))
	5.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series21.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

11.0ms

(pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)

9.0ms

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

2.0ms

(cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-prod_binary64`
45×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
41×	`add-cube-cbrt_binary64`

Counts

3 → 125

Calls

3 calls:

5.0ms

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

1.0ms

(pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3)

1.0ms

(cbrt.f64 (pow.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) 3))

simplify133.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
582×	`fma-neg_binary64`
499×	`associate-l_binary64`
452×	`associate-r_binary64`
346×	`associate-/l*_binary64`

Counts

149 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	3617
1	228	3273
2	774	3223
3	3434	3216
4	4968	3216
5	4963	3216

prune262.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	171	7	178

Error

59.2b

Counts

178 → 7

Alt Table

Status	Error	Program
	59.5b	(/.f64 (cbrt.f64 (pow.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) 3)) (exp.f64 x))
	59.4b	(*.f64 (exp.f64 (log.f64 (/.f64 1 (sqrt.f64 (exp.f64 x))))) (exp.f64 (log1p.f64 (expm1.f64 (fma.f64 -1/2 x (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))))))
	60.3b	(exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	59.5b	(exp.f64 (log.f64 (/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))))
	60.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	59.2b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)) (cbrt.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x)))) (cbrt.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)))))
	59.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))

Compiler

Compiled 3813 to 1247 computations (67.3% saved)

regimes110.0ms (0.8%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

63 → 1

Compiler

Compiled 2222 to 1346 computations (39.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	11	17
2	16	17
3	18	17
4	19	17
5	19	17

end119.0ms (0.9%)

Compiler: Compiled 139 to 91 computations (34.5% saved)

Details

analyze1.0s (7.2%)

sample10.6s (75.8%)

simplify81.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0%)

series14.0ms (0.1%)

rewrite6.0ms (0%)

simplify93.0ms (0.7%)

prune123.0ms (0.9%)

localize8.0ms (0.1%)

series8.0ms (0.1%)

rewrite6.0ms (0%)

simplify84.0ms (0.6%)

prune165.0ms (1.2%)

localize15.0ms (0.1%)

series661.0ms (4.7%)

rewrite20.0ms (0.1%)

simplify125.0ms (0.9%)

prune285.0ms (2%)

localize9.0ms (0.1%)

series21.0ms (0.2%)

rewrite19.0ms (0.1%)

simplify133.0ms (0.9%)

prune262.0ms (1.9%)

regimes110.0ms (0.8%)

simplify2.0ms (0%)

end119.0ms (0.9%)

Profiling