Details

analyze1.3s

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

sample212.0ms

Algorithm

intervals

Results

47.0ms	88×	body	1024	valid
44.0ms	63×	body	2048	valid
42.0ms	52×	body	1024	nan
13.0ms	68×	body	128	overflowed
12.0ms	34×	body	512	valid
12.0ms	22×	body	512	nan
6.0ms	6×	body	1024	invalid
5.0ms	51×	body	128	valid
4.0ms	16×	body	256	nan
4.0ms	20×	body	256	valid
3.0ms	7×	body	512	invalid
3.0ms	2×	body	2048	nan
2.0ms	25×	body	128	nan
1.0ms	5×	body	128	invalid
0.0ms	1×	body	256	invalid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5193	19

prune1.0ms

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: 33.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
3.2b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite28.0ms

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) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series444.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
86.0ms	(pow.f64 x (/.f64 1 n))
258.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify67.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4937	1617
1	4937	1617

prune93.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

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: 22.0b

Counts

88 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1/2 n))
0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(*.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))
4.9b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (*.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
26×	`pow-unpow_binary64` `unpow-prod-down_binary64`
18×	`add-exp-log_binary64` `times-frac_binary64`
13×	`sqr-pow_binary64`
9×	`unswap-sqr_binary64` `prod-exp_binary64`
8×	`pow-to-exp_binary64` `pow-exp_binary64`
7×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`difference-of-squares_binary64`
2×	`pow-pow_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 121

Calls

4 calls:

4.0ms	(pow.f64 x (/.f64 1/2 n))
6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
8.0ms	(*.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (*.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))

series637.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow.f64 x (/.f64 1/2 n))
101.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
109.0ms	(*.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n)))
341.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (*.f64 (pow.f64 x (/.f64 1/2 n)) (pow.f64 x (/.f64 1/2 n))))

simplify81.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4970	2163
1	4970	2163

prune119.0ms

Filtered

88 candidates to 133 candidates (-51.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	133	5	138

Merged error: 22.0b

Counts

138 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
3.2b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
3.2b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))

rewrite48.0ms

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:

9.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
13.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))

series849.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
70.0ms	(pow.f64 x (/.f64 1 n))
242.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
439.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5122	2308

prune124.0ms

Filtered

89 candidates to 119 candidates (-33.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Merged error: 22.0b

Counts

124 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
3.2b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
3.2b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
3.2b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

rewrite60.0ms

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:

15.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
11.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

series1.8s

Counts

4 → 12

Calls

4 calls:

237.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
244.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
653.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
654.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4922	3034
1	4922	3034

prune187.0ms

Filtered

78 candidates to 94 candidates (-20.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	94	7	101

Merged error: 21.9b

Counts

101 → 7

regimes134.0ms

Accuracy

82.1% (1.9b remaining)

Error of 24.3b against oracle of 22.4b and baseline of 32.9b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	96
1	71	96

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.4s	2714×	body	1024	valid
1.3s	1479×	body	1024	nan
1.2s	1730×	body	2048	valid
528.0ms	2746×	body	128	overflowed
421.0ms	1181×	body	512	valid
359.0ms	686×	body	512	nan
190.0ms	195×	body	1024	invalid
178.0ms	1808×	body	128	valid
145.0ms	270×	body	512	invalid
122.0ms	567×	body	256	valid
98.0ms	375×	body	256	nan
63.0ms	840×	body	128	nan
41.0ms	143×	body	256	invalid
36.0ms	239×	body	128	invalid
9.0ms	8×	body	2048	nan

Details

analyze1.3s

sample212.0ms

simplify66.0ms

prune1.0ms

localize8.0ms

rewrite28.0ms

series444.0ms

simplify67.0ms

prune93.0ms

localize11.0ms

rewrite40.0ms

series637.0ms

simplify81.0ms

prune119.0ms

localize11.0ms

rewrite48.0ms

series849.0ms

simplify60.0ms

prune124.0ms

localize16.0ms

rewrite60.0ms

series1.8s

simplify106.0ms

prune187.0ms

regimes134.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample6.4s

Profiling