Details

analyze83.0ms

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%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample18.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5045	25

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1_binary64` `add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-r_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

3 → 48

Calls

3 calls:

8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
5.0ms	(.f64 4 (.f64 b b))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series98.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
17.0ms	(.f64 4 (.f64 b b))
32.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify53.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5302	926

prune49.0ms

Filtered

38 candidates to 57 candidates (-50.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	3	58

Merged error: 0.0b

Counts

58 → 3

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))
0.0b	(.f64 4 (.f64 b b))
1.6b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-log-exp_binary64`
6×	`sum-log_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
2×	`associate-r_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-+l+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

3 → 61

Calls

3 calls:

14.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))
6.0ms	(.f64 4 (.f64 b b))
10.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

series107.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+.f64 (+.f64 (pow.f64 b 4) (+.f64 (pow.f64 a 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))
21.0ms	(.f64 4 (.f64 b b))
35.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5120	1197

prune57.0ms

Filtered

38 candidates to 70 candidates (-84.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	70	3	73

Merged error: 0.0b

Counts

73 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 b b) 4)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
37.2b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
11×	`pow1_binary64` `add-cbrt-cube_binary64`
9×	`times-frac_binary64`
6×	`pow-unpow_binary64` `unpow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `associate-/l_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `flip3--_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip--_binary64` `pow-exp_binary64`
1×	`unpow2_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

8.0ms	(.f64 (.f64 b b) 4)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
16.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))

series306.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(.f64 (.f64 b b) 4)
83.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
31.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
172.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))

simplify85.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4992	2745
1	4992	2745

prune114.0ms

Filtered

67 candidates to 98 candidates (-46.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	99	2	101

Merged error: 0b

Counts

101 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
26.9b	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))
37.2b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 (*.f64 b b) 4)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`unpow-prod-down_binary64` `times-frac_binary64`
8×	`add-exp-log_binary64`
7×	`cbrt-prod_binary64`
6×	`pow-unpow_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `sqr-pow_binary64` `associate-/l_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `flip3--_binary64` `pow-pow_binary64` `associate-/r/_binary64` `flip--_binary64` `pow-exp_binary64`
1×	`cbrt-undiv_binary64` `pow1/3_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 81

Calls

4 calls:

5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))
16.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 (*.f64 b b) 4)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)
79.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4)
29.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6))
170.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 4) (.f64 16 (pow.f64 b 4))) (-.f64 (cbrt.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 6)) (.f64 (*.f64 b b) 4)))

simplify84.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4939	3354
1	4939	3354

prune127.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	93	2	95

Merged error: 0b

Counts

95 → 2

regimes26.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	37
1	36	37

end0.0ms

sample504.0ms

Algorithm

intervals

Results

369.0ms	8000×	body	80	valid
0.0ms	4×	body	80	invalid

Details

analyze83.0ms

sample18.0ms

simplify73.0ms

prune3.0ms

localize9.0ms

rewrite20.0ms

series98.0ms

simplify53.0ms

prune49.0ms

localize16.0ms

rewrite32.0ms

series107.0ms

simplify68.0ms

prune57.0ms

localize16.0ms

rewrite36.0ms

series306.0ms

simplify85.0ms

prune114.0ms

localize20.0ms

rewrite33.0ms

series510.0ms

simplify84.0ms

prune127.0ms

regimes26.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample504.0ms

Profiling