Details

analyze986.0ms (7.6%)

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)

sample10.1s (78.2%)

Results

4.6s	1520×	body	8192	exit
2.7s	4171×	body	1024	valid
862.0ms	2045×	body	512	valid
851.0ms	1551×	body	1024	invalid
302.0ms	840×	body	512	invalid
290.0ms	1001×	body	256	valid
155.0ms	891×	body	128	valid
132.0ms	148×	body	2048	valid
108.0ms	440×	body	256	invalid
54.0ms	389×	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

58.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	58.5b	(/.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	(sqrt.f64 (cos.f64 x))
✓	0.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	4.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series12.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

8.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(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)))

simplify87.0ms (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

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	6	74

Error

58.5b

Counts

74 → 6

Alt Table

Status	Error	Program
	58.5b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	58.6b	(.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))))) (sqrt.f64 (exp.f64 x))) (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (exp.f64 x))))
▶	58.5b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	58.5b	(/.f64 (exp.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	58.8b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1383 to 405 computations (70.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (cos.f64 x))
	0.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	2.6b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	4.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series9.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

8.0ms

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

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-pow_binary64`
13×	`exp-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

1 → 27

Calls

1 calls:

3.0ms

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

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

530×	`distribute-rgt-neg-in_binary64`
427×	`distribute-lft-neg-in_binary64`
303×	`associate-l_binary64`
293×	`cancel-sign-sub-inv_binary64`
275×	`fma-def_binary64`

Counts

39 → 54

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	846
1	138	797
2	287	761
3	676	743
4	2216	732
5	4567	732
6	5045	732

prune162.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	127	6	133

Error

58.5b

Counts

133 → 6

Alt Table

Status	Error	Program
	58.5b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	58.5b	(exp.f64 (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))
	58.7b	(*.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 1))))
	58.7b	(.f64 (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.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))))) 1))))
	58.5b	(.f64 (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 x))) (log.f64 (exp.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)))))))

Compiler

Compiled 2723 to 719 computations (73.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(exp.f64 (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))
	0.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	2.6b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	4.3b	(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 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`exp-sum_binary64`
17×	`log-prod_binary64`
17×	`exp-prod_binary64`
15×	`log-pow_binary64`
10×	`*-un-lft-identity_binary64`

Counts

1 → 31

Calls

1 calls:

4.0ms

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

simplify126.0ms (1%)

Algorithm

1×	egg-herbie

Rules

516×	`distribute-rgt-neg-in_binary64`
316×	`fma-def_binary64`
309×	`associate-l_binary64`
309×	`cancel-sign-sub-inv_binary64`
263×	`associate-r_binary64`

Counts

43 → 58

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	1109
1	205	1034
2	407	972
3	951	939
4	2936	918
5	4253	918
6	4923	918
7	4990	918
8	4924	918

prune231.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	161	7	168

Error

58.5b

Counts

168 → 7

Alt Table

Status	Error	Program
	58.5b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	58.5b	(pow.f64 (E.f64) (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))
	58.5b	(.f64 (exp.f64 (log.f64 (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))) (exp.f64 (log.f64 (log.f64 (exp.f64 (.f64 (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))) (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)))))))))
	58.7b	(*.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 1))))
	58.7b	(.f64 (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.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))))) 1))))
	58.7b	(exp.f64 (log.f64 (.f64 (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.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))))) 1))))))

Compiler

Compiled 3920 to 965 computations (75.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (E.f64) (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))
	0.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	2.6b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	4.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series339.0ms (2.6%)

Counts

1 → 12

Calls

1 calls:

339.0ms

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

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`unpow-prod-up_binary64`
17×	`log-prod_binary64`
15×	`log-pow_binary64`
13×	`exp-prod_binary64`
11×	`*-un-lft-identity_binary64`

Counts

1 → 38

Calls

1 calls:

5.0ms

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

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-l_binary64`
608×	`fma-neg_binary64`
313×	`fma-def_binary64`
302×	`cancel-sign-sub-inv_binary64`
228×	`sqr-pow_binary64`

Counts

50 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	166	1573
1	305	1452
2	655	1380
3	1678	1354
4	4269	1352
5	4996	1352
6	4934	1352

prune299.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	171	3	174
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	174	7	181

Error

58.5b

Counts

181 → 7

Alt Table

Status	Error	Program
	58.5b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.0b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	58.5b	(pow.f64 (E.f64) (log.f64 (.f64 (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))) (log.f64 (exp.f64 (.f64 (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))) (cbrt.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)))))))))
	58.7b	(pow.f64 (E.f64) (log.f64 (.f64 (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.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))))) 1))))))
	58.7b	(*.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) 1))))
	58.7b	(.f64 (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (exp.f64 x)) (log.f64 (exp.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))))) 1))))
	58.5b	(cbrt.f64 (.f64 (.f64 (pow.f64 (E.f64) (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x)))))) (pow.f64 (E.f64) (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))) (pow.f64 (E.f64) (log.f64 (log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))))))

Compiler

Compiled 4328 to 956 computations (77.9% saved)

regimes64.0ms (0.5%)

Accuracy

Total 0.1b remaining (0.2%)

Threshold costs 0.1b (0.2%)

Counts

38 → 1

Compiler

Compiled 1594 to 786 computations (50.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	16	25
2	15	25

end114.0ms (0.9%)

Compiler: Compiled 227 to 106 computations (53.3% saved)

Details

analyze986.0ms (7.6%)

sample10.1s (78.2%)

simplify81.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series12.0ms (0.1%)

rewrite6.0ms (0%)

simplify87.0ms (0.7%)

prune77.0ms (0.6%)

localize8.0ms (0.1%)

series9.0ms (0.1%)

rewrite5.0ms (0%)

simplify73.0ms (0.6%)

prune162.0ms (1.2%)

localize10.0ms (0.1%)

series8.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify126.0ms (1%)

prune231.0ms (1.8%)

localize10.0ms (0.1%)

series339.0ms (2.6%)

rewrite14.0ms (0.1%)

simplify95.0ms (0.7%)

prune299.0ms (2.3%)

regimes64.0ms (0.5%)

simplify2.0ms (0%)

end114.0ms (0.9%)

Profiling