Details

analyze1.2s

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

sample202.0ms

Algorithm

intervals

Results

69.0ms	122×	body	1280	valid
30.0ms	26×	body	1280	nan
21.0ms	26×	body	640	nan
19.0ms	43×	body	640	valid
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

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	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

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))
2.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 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) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series65.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
12.0ms	(pow.f64 x (/.f64 1 n))
38.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify78.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4922	1073
1	4922	1073

prune120.0ms

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: 22.5b

Counts

88 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(pow.f64 x (/.f64 1 n))
0.0b	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)))
4.4b	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n))) (pow.f64 x (/.f64 1 n)))

rewrite42.0ms

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))
4.0ms	(pow.f64 x (/.f64 1 n))
16.0ms	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)))
15.0ms	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n))) (pow.f64 x (/.f64 1 n)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
11.0ms	(pow.f64 x (/.f64 1 n))
39.0ms	(*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)))
63.0ms	(-.f64 (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n))) (pow.f64 x (/.f64 1 n)))

simplify52.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4951	2036
1	4951	2036

prune163.0ms

Filtered

87 candidates to 144 candidates (-65.5%)

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: 22.5b

Counts

149 → 5

localize10.0ms

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))
2.2b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
2.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite36.0ms

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:

6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))
12.0ms	(log.f64 (exp.f64 (-.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)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
11.0ms	(pow.f64 x (/.f64 1 n))
34.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
36.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4973	1533
1	4973	1533

prune136.0ms

Filtered

89 candidates to 119 candidates (-33.7%)

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: 22.5b

Counts

124 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

2.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
2.3b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
2.3b	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 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) (/.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))))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
35.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
133.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))
92.0ms	(log.f64 (cbrt.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4973	1980
1	4973	1980

prune174.0ms

Filtered

78 candidates to 94 candidates (-20.5%)

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: 22.3b

Counts

100 → 8

regimes312.0ms

Accuracy

84.2% (1.7b remaining)

Error of 23.9b against oracle of 22.2b and baseline of 32.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	76
1	73	76

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.2s	3774×	body	1280	valid
1.2s	1069×	body	1280	nan
672.0ms	1488×	body	640	valid
666.0ms	956×	body	640	nan
470.0ms	2654×	body	80	overflowed
235.0ms	753×	body	320	valid
183.0ms	423×	body	320	nan
181.0ms	259×	body	640	invalid
155.0ms	1635×	body	80	valid
122.0ms	95×	body	1280	invalid
73.0ms	350×	body	160	valid
65.0ms	153×	body	320	invalid
48.0ms	212×	body	160	nan
31.0ms	513×	body	80	nan
28.0ms	219×	body	80	invalid
18.0ms	74×	body	160	invalid

Details

analyze1.2s

sample202.0ms

simplify55.0ms

prune3.0ms

localize8.0ms

rewrite23.0ms

series65.0ms

simplify78.0ms

prune120.0ms

localize10.0ms

rewrite42.0ms

series117.0ms

simplify52.0ms

prune163.0ms

localize10.0ms

rewrite36.0ms

series98.0ms

simplify54.0ms

prune136.0ms

localize16.0ms

rewrite46.0ms

series294.0ms

simplify35.0ms

prune174.0ms

regimes312.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.6s

Profiling