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

sample199.0ms

Algorithm

intervals

Results

70.0ms	122×	body	1280	valid
30.0ms	26×	body	1280	nan
19.0ms	43×	body	640	valid
18.0ms	26×	body	640	nan
14.0ms	81×	body	80	overflowed
8.0ms	24×	body	320	valid
7.0ms	17×	body	320	nan
5.0ms	56×	body	80	valid
4.0ms	4×	body	1280	invalid
3.0ms	5×	body	640	invalid
2.0ms	11×	body	160	valid
2.0ms	9×	body	160	nan
1.0ms	3×	body	320	invalid
1.0ms	20×	body	80	nan
1.0ms	3×	body	160	invalid
1.0ms	6×	body	80	invalid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune3.0ms

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: 32.7b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
0.0b	(pow.f64 x (/.f64 1.0 n))
2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`pow-unpow_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
17×	`unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
8×	`sqr-pow_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
4.0ms	(pow.f64 x (/.f64 1.0 n))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

series85.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
13.0ms	(pow.f64 x (/.f64 1.0 n))
47.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5141	1177

prune122.0ms

Filtered

69 candidates to 87 candidates (-26.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 22.3b

Counts

88 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.0b	(pow.f64 x (/.f64 1.0 n))
0.0b	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)))
4.4b	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n))) (pow.f64 x (/.f64 1.0 n)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

56×	`unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
34×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64`
16×	`unswap-sqr_binary64`
15×	`swap-sqr_binary64`
14×	`sqr-pow_binary64`
13×	`pow-unpow_binary64`
11×	`associate-r_binary64` `associate-l_binary64`
9×	`prod-exp_binary64` `times-frac_binary64`
7×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`difference-of-squares_binary64`
2×	`sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 132

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 x 1.0))
4.0ms	(pow.f64 x (/.f64 1.0 n))
16.0ms	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)))
15.0ms	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n))) (pow.f64 x (/.f64 1.0 n)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sqrt.f64 (+.f64 x 1.0))
13.0ms	(pow.f64 x (/.f64 1.0 n))
77.0ms	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)))
110.0ms	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n)) (pow.f64 (sqrt.f64 (+.f64 x 1.0)) (/.f64 1.0 n))) (pow.f64 x (/.f64 1.0 n)))

simplify73.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4960	2253
1	4960	2253

prune158.0ms

Filtered

88 candidates to 144 candidates (-63.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	144	5	149

Merged error: 22.3b

Counts

149 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1.0 n))
0.0b	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
2.2b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
27×	`unpow-prod-down_binary64`
26×	`pow-unpow_binary64`
22×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64` `times-frac_binary64`
16×	`log-pow_binary64`
15×	`exp-prod_binary64`
14×	`sqr-pow_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`log-prod_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 107

Calls

4 calls:

4.0ms	(pow.f64 x (/.f64 1.0 n))
6.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
12.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow.f64 x (/.f64 1.0 n))
21.0ms	(pow.f64 (+.f64 x 1.0) (/.f64 1.0 n))
45.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))))
47.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))

simplify50.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5298	1665

prune148.0ms

Filtered

94 candidates to 119 candidates (-26.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Merged error: 22.3b

Counts

124 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
2.3b	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
2.3b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
2.3b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`unpow-prod-down_binary64`
18×	`difference-of-squares_binary64`
14×	`log-prod_binary64`
12×	`sqr-pow_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `log-pow_binary64` `add-cbrt-cube_binary64`
2×	`cbrt-div_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
46.0ms	(-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n)))
123.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))
125.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1.0) (/.f64 1.0 n)) (pow.f64 x (/.f64 1.0 n))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4958	2100
1	4958	2100

prune189.0ms

Filtered

82 candidates to 94 candidates (-14.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Merged error: 22.1b

Counts

100 → 8

regimes316.0ms

Accuracy

84.8% (1.7b remaining)

Error of 23.5b against oracle of 21.8b and baseline of 32.8b

bsearch1.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	184	80
1	184	80

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.1s	3774×	body	1280	valid
1.1s	1069×	body	1280	nan
665.0ms	956×	body	640	nan
642.0ms	1488×	body	640	valid
467.0ms	2654×	body	80	overflowed
224.0ms	753×	body	320	valid
175.0ms	259×	body	640	invalid
175.0ms	423×	body	320	nan
146.0ms	1635×	body	80	valid
119.0ms	95×	body	1280	invalid
67.0ms	350×	body	160	valid
60.0ms	153×	body	320	invalid
48.0ms	212×	body	160	nan
30.0ms	513×	body	80	nan
27.0ms	219×	body	80	invalid
18.0ms	74×	body	160	invalid

Details

analyze1.1s

sample199.0ms

simplify58.0ms

prune3.0ms

localize11.0ms

rewrite23.0ms

series85.0ms

simplify45.0ms

prune122.0ms

localize12.0ms

rewrite43.0ms

series205.0ms

simplify73.0ms

prune158.0ms

localize10.0ms

rewrite37.0ms

series126.0ms

simplify50.0ms

prune148.0ms

localize14.0ms

rewrite46.0ms

series340.0ms

simplify55.0ms

prune189.0ms

regimes316.0ms

bsearch1.0ms

simplify5.0ms

end0.0ms

sample6.4s

Profiling