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)

sample10.7s (75.8%)

Results

4.9s	1581×	body	8192	exit
2.8s	4154×	body	1024	valid
940.0ms	1687×	body	1024	invalid
853.0ms	1981×	body	512	valid
328.0ms	855×	body	512	invalid
320.0ms	1063×	body	256	valid
162.0ms	891×	body	128	valid
146.0ms	167×	body	2048	valid
98.0ms	391×	body	256	invalid
71.0ms	448×	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

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

59.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	59.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	59.3b	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Compiler

Compiled 62 to 37 computations (40.3% saved)

localize8.0ms (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))
✓	4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series14.0ms (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)))

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)))

simplify90.0ms (0.6%)

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

prune83.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	68	7	75

Error

59.3b

Counts

75 → 7

Alt Table

Status	Error	Program
	59.3b	(/.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 x))) (sqrt.f64 (exp.f64 x)))
▶	59.3b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	59.4b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	59.3b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.6b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.3b	(/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))
	60.8b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 1375 to 417 computations (69.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 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))
✓	0.2b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	4.0b	(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))))

rewrite5.0ms (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

prune155.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	122	5	127
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	127	7	134

Error

59.3b

Counts

134 → 7

Alt Table

Status	Error	Program
▶	59.3b	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	59.6b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.3b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))
	59.3b	(/.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 x))) (sqrt.f64 (exp.f64 x)))
	60.8b	(exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	59.4b	(exp.f64 (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))
	59.3b	(exp.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))))

Compiler

Compiled 2648 to 750 computations (71.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 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))
✓	0.2b	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	4.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series465.0ms (3.3%)

Counts

1 → 12

Calls

1 calls:

465.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-up_binary64`
13×	`log-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 35

Calls

1 calls:

4.0ms

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

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

647×	`associate-l_binary64`
613×	`fma-neg_binary64`
330×	`fma-def_binary64`
313×	`cancel-sign-sub-inv_binary64`
218×	`sqr-pow_binary64`

Counts

47 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1375
1	290	1338
2	659	1260
3	1710	1240
4	4480	1240
5	4998	1240
6	4932	1240

prune171.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	139	6	145

Error

59.3b

Counts

145 → 6

Alt Table

Status	Error	Program
	59.3b	(/.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 x))) (sqrt.f64 (exp.f64 x)))
	59.3b	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))))
	59.6b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.8b	(pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	59.4b	(exp.f64 (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))
▶	59.3b	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))

Compiler

Compiled 3058 to 805 computations (73.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))
✓	0.1b	(pow.f64 (sqrt.f64 (cos.f64 x)) 3)
✓	0.2b	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))
✓	4.0b	(fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3)))

series444.0ms (3.2%)

Counts

4 → 48

Calls

4 calls:

432.0ms	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))
7.0ms	(pow.f64 (sqrt.f64 (cos.f64 x)) 3)
3.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))
2.0ms	(fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3)))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

4.0ms	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x))))
2.0ms	(pow.f64 (sqrt.f64 (cos.f64 x)) 3)
2.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))
0.0ms	(fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3)))

simplify137.0ms (1%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-l_binary64`
447×	`associate-r_binary64`
432×	`fma-neg_binary64`
335×	`log-prod_binary64`
262×	`unswap-sqr_binary64`

Counts

155 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	218	2421
1	466	2356
2	1155	2222
3	3491	2208
4	4788	2208
5	5000	2208
6	4906	2208

prune243.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	163	7	170

Error

59.2b

Counts

170 → 7

Alt Table

Status	Error	Program
	60.8b	(pow.f64 (E.f64) (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	59.3b	(pow.f64 (pow.f64 (E.f64) (*.f64 (cbrt.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x)))) (cbrt.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x)))))) (cbrt.f64 (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x)))))
	59.3b	(/.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (exp.f64 x))) (sqrt.f64 (exp.f64 x)))
	59.3b	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))))
	59.3b	(pow.f64 (E.f64) (log.f64 (/.f64 (fmod.f64 (exp.f64 x) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3)) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3)))) (cbrt.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))))) (exp.f64 x))))
	59.3b	(pow.f64 (pow.f64 (E.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) (cbrt.f64 (pow.f64 (sqrt.f64 (cos.f64 x)) 3))) (exp.f64 x)))))
	59.4b	(exp.f64 (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))

Compiler

Compiled 3808 to 1743 computations (54.2% saved)

regimes100.0ms (0.7%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

55 → 1

Compiler

Compiled 1891 to 1221 computations (35.4% saved)

simplify3.0ms (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	20	66
1	24	66
2	30	66
3	32	66
4	33	66
5	32	66

end148.0ms (1.1%)

Compiler: Compiled 250 to 145 computations (42% saved)

Details

analyze1.0s (7.2%)

sample10.7s (75.8%)

simplify81.0ms (0.6%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series14.0ms (0.1%)

rewrite6.0ms (0%)

simplify90.0ms (0.6%)

prune83.0ms (0.6%)

localize10.0ms (0.1%)

series8.0ms (0.1%)

rewrite5.0ms (0%)

simplify84.0ms (0.6%)

prune155.0ms (1.1%)

localize9.0ms (0.1%)

series465.0ms (3.3%)

rewrite8.0ms (0.1%)

simplify94.0ms (0.7%)

prune171.0ms (1.2%)

localize11.0ms (0.1%)

series444.0ms (3.2%)

rewrite14.0ms (0.1%)

simplify137.0ms (1%)

prune243.0ms (1.7%)

regimes100.0ms (0.7%)

simplify3.0ms (0%)

end148.0ms (1.1%)

Profiling