Details

analyze626.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample47.0ms

Algorithm

intervals

Results

12.0ms	44×	body	2560	valid
10.0ms	157×	body	80	valid
7.0ms	32×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	22×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	6×	body	80	invalid

simplify479.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 35.9b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5743	1403

prune118.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 6.8b

Counts

95 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.3b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
11.4b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
31×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 216

Calls

4 calls:

7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
48.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
57.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5864	5186

prune191.0ms

Filtered

173 candidates to 228 candidates (-31.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	224	4	228
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	228	9	237

Merged error: 6.7b

Counts

237 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.9b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
16.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5326	1109

prune85.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Merged error: 6.7b

Counts

92 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.6b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
15.3b	(+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`log-prod_binary64` `exp-sum_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `log-pow_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `exp-diff_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
9.0ms	(+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
13.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
15.0ms	(+.f64 b_2 (exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4925	789
1	4925	789

prune59.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	71	10	81

Merged error: 6.7b

Counts

81 → 10

regimes249.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.7b

bsearch79.0ms

Steps

Iters	Range	Point
8	2.4494090990456073e+89	8.358794736598994e+93	7.245534320204247e+93
7	-8.137348282676893e-302	-2.5614861063430777e-303	-3.1746359072212486e-302
8	-4.039848956748369e+114	-2.2961699941186647e+110	-6.274887904862192e+110

Iters

Range

Point

2.4494090990456073e+89

8.358794736598994e+93

7.245534320204247e+93

-8.137348282676893e-302

-2.5614861063430777e-303

-3.1746359072212486e-302

-4.039848956748369e+114

-2.2961699941186647e+110

-6.274887904862192e+110

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	55
1	100	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

279.0ms	1046×	body	2560	valid
248.0ms	5188×	body	80	valid
191.0ms	893×	body	1280	valid
83.0ms	440×	body	640	valid
33.0ms	754×	body	80	nan
33.0ms	103×	body	5120	valid
29.0ms	223×	body	320	valid
13.0ms	231×	body	80	invalid
9.0ms	107×	body	160	valid

Details

analyze626.0ms

sample47.0ms

simplify479.0ms

prune10.0ms

localize10.0ms

rewrite34.0ms

series75.0ms

simplify55.0ms

prune118.0ms

localize10.0ms

rewrite44.0ms

series126.0ms

simplify70.0ms

prune191.0ms

localize9.0ms

rewrite25.0ms

series88.0ms

simplify48.0ms

prune85.0ms

localize13.0ms

rewrite26.0ms

series52.0ms

simplify44.0ms

prune59.0ms

regimes249.0ms

bsearch79.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling