Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample228.0ms

Algorithm

intervals

Results

73.0ms	128×	body	1280	valid
40.0ms	36×	body	1280	nan
26.0ms	49×	body	640	valid
23.0ms	32×	body	640	nan
12.0ms	67×	body	80	overflowed
7.0ms	24×	body	320	valid
6.0ms	14×	body	320	nan
6.0ms	4×	body	1280	invalid
4.0ms	47×	body	80	valid
4.0ms	5×	body	640	invalid
3.0ms	7×	body	320	invalid
2.0ms	9×	body	160	nan
2.0ms	8×	body	160	valid
1.0ms	8×	body	80	invalid
1.0ms	17×	body	80	nan
0.0ms	1×	body	160	invalid

simplify257.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4805	19
1	4805	19

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 34.5b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_559`
19×	`*-un-lft-identity_binary64_574`
14×	`unpow-prod-down_binary64_509`
13×	`pow-unpow_binary64_507`
10×	`add-cube-cbrt_binary64_545`
9×	`difference-of-squares_binary64_603` `times-frac_binary64_569`
7×	`sqr-pow_binary64_606`
4×	`add-log-exp_binary64_539`
3×	`pow1_binary64_520` `distribute-lft-out--_binary64_619` `add-exp-log_binary64_538`
2×	`add-cbrt-cube_binary64_546` `distribute-lft-out_binary64_618`
1×	`flip3--_binary64_573` `pow-to-exp_binary64_499` `div-inv_binary64_575` `pow-exp_binary64_498` `pow-pow_binary64_502` `diff-log_binary64_490` `sub-neg_binary64_578` `flip--_binary64_600`

Counts

2 → 51

Calls

2 calls:

6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series185.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
132.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify93.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5046	1272

prune182.0ms

Filtered

46 candidates to 57 candidates (-23.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 22.9b

Counts

58 → 4

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
1.9b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_559`
29×	`*-un-lft-identity_binary64_574`
24×	`unpow-prod-down_binary64_509`
18×	`difference-of-squares_binary64_603`
16×	`log-pow_binary64_495`
15×	`exp-prod_binary64_528`
13×	`add-cube-cbrt_binary64_545` `sqr-pow_binary64_606` `pow-unpow_binary64_507`
9×	`times-frac_binary64_569`
6×	`distribute-lft-out--_binary64_619`
5×	`pow1_binary64_520` `add-log-exp_binary64_539`
4×	`log-prod_binary64_492` `add-exp-log_binary64_538`
3×	`add-cbrt-cube_binary64_546` `distribute-lft-out_binary64_618`
2×	`sub-neg_binary64_578`
1×	`exp-diff_binary64_535` `flip3--_binary64_573` `pow-to-exp_binary64_499` `log-div_binary64_493` `exp-sum_binary64_533` `div-inv_binary64_575` `pow-exp_binary64_498` `pow-pow_binary64_502` `diff-log_binary64_490` `rem-log-exp_binary64_537` `flip--_binary64_600`

Counts

3 → 80

Calls

3 calls:

10.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
12.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series309.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
132.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
124.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify84.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5025	1981

prune265.0ms

Filtered

71 candidates to 89 candidates (-25.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	87	6	93

Merged error: 22.9b

Counts

93 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.0b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
2.0b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_559`
22×	`*-un-lft-identity_binary64_574`
20×	`unpow-prod-down_binary64_509`
18×	`difference-of-squares_binary64_603`
14×	`log-prod_binary64_492`
12×	`sqr-pow_binary64_606`
8×	`add-cube-cbrt_binary64_545` `cbrt-prod_binary64_541` `add-log-exp_binary64_539`
6×	`pow1_binary64_520` `distribute-lft-out--_binary64_619` `add-exp-log_binary64_538`
4×	`add-cbrt-cube_binary64_546` `sub-neg_binary64_578` `log-pow_binary64_495`
2×	`exp-diff_binary64_535` `pow1/3_binary64_512` `flip3--_binary64_573` `cbrt-div_binary64_542` `log-div_binary64_493` `exp-sum_binary64_533` `diff-log_binary64_490` `rem-log-exp_binary64_537` `distribute-lft-out_binary64_618` `flip--_binary64_600`

Counts

4 → 82

Calls

4 calls:

10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
12.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
15.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

127.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
131.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
372.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
369.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5407	3090

prune437.0ms

Filtered

82 candidates to 94 candidates (-14.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	93	7	100

Merged error: 22.8b

Counts

100 → 7

localize30.0ms

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.0b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
2.2b	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
2.2b	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod_binary64_492`
26×	`cbrt-prod_binary64_541`
24×	`add-sqr-sqrt_binary64_559`
19×	`*-un-lft-identity_binary64_574`
12×	`add-cube-cbrt_binary64_545`
10×	`unpow-prod-down_binary64_509`
9×	`difference-of-squares_binary64_603`
7×	`pow1_binary64_520` `add-exp-log_binary64_538`
6×	`sqr-pow_binary64_606` `log-pow_binary64_495` `add-log-exp_binary64_539`
5×	`cbrt-div_binary64_542`
4×	`add-cbrt-cube_binary64_546` `sub-neg_binary64_578`
3×	`exp-diff_binary64_535` `pow1/3_binary64_512` `log-div_binary64_493` `exp-sum_binary64_533` `distribute-lft-out--_binary64_619` `rem-log-exp_binary64_537`
1×	`flip3--_binary64_573` `diff-log_binary64_490` `distribute-lft-out_binary64_618` `flip--_binary64_600`

Counts

4 → 83

Calls

4 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
13.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
12.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
12.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
373.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
379.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))
374.0ms	(log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4943	3363
1	4943	3363

prune523.0ms

Filtered

83 candidates to 95 candidates (-14.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	95	7	102

Merged error: 22.7b

Counts

102 → 7

regimes496.0ms

Accuracy

85.1% (1.7b remaining)

Error of 23.9b against oracle of 22.1b and baseline of 33.7b

bsearch2.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	190
1	96	190

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.1s	3734×	body	1280	valid
1.4s	1141×	body	1280	nan
740.0ms	1645×	body	640	valid
657.0ms	911×	body	640	nan
522.0ms	2841×	body	80	overflowed
241.0ms	757×	body	320	valid
198.0ms	450×	body	320	nan
163.0ms	226×	body	640	invalid
146.0ms	1536×	body	80	valid
122.0ms	89×	body	1280	invalid
80.0ms	180×	body	320	invalid
65.0ms	328×	body	160	valid
54.0ms	237×	body	160	nan
33.0ms	534×	body	80	nan
32.0ms	221×	body	80	invalid
25.0ms	102×	body	160	invalid

Details

analyze1.1s

sample228.0ms

simplify257.0ms

prune5.0ms

localize12.0ms

rewrite18.0ms

series185.0ms

simplify93.0ms

prune182.0ms

localize16.0ms

rewrite35.0ms

series309.0ms

simplify84.0ms

prune265.0ms

localize22.0ms

rewrite50.0ms

series1.0s

simplify86.0ms

prune437.0ms

localize30.0ms

rewrite51.0ms

series1.3s

simplify90.0ms

prune523.0ms

regimes496.0ms

bsearch2.0ms

simplify4.0ms

end0.0ms

sample7.0s

Profiling