Details

analyze430.0ms

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

sample45.0ms

Algorithm

intervals

Results

11.0ms	43×	body	2560	valid
9.0ms	154×	body	80	valid
7.0ms	29×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	9×	body	160	valid
1.0ms	16×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	5×	body	80	invalid

simplify473.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune18.0ms

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: 36.0b

Counts

2 → 1

localize25.0ms

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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.5b	(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)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
25.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5743	1403

prune124.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	82	12	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 6.9b

Counts

95 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.8b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite43.0ms

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:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(/.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)))

series137.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
47.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
65.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5864	5186

prune189.0ms

Filtered

173 candidates to 228 candidates (-31.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	231	9	240

Merged error: 6.8b

Counts

240 → 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)))))
0.5b	(+.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))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite24.0ms

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))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/.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))))
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
17.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5326	1109

prune82.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	83	9	92

Merged error: 6.8b

Counts

92 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
0.5b	(+.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))
23.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`distribute-lft-out_binary64` `prod-exp_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

15.0ms	(.f64 c (/.f64 1 (+.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)))

series96.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(.f64 c (/.f64 1 (+.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))))
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
16.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4906	1078
1	4906	1078

prune65.0ms

Filtered

66 candidates to 91 candidates (-37.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Merged error: 6.8b

Counts

100 → 9

regimes234.0ms

Accuracy

96.7% (0.8b remaining)

Error of 6.4b against oracle of 5.6b and baseline of 29.7b

bsearch90.0ms

Steps

Iters	Range	Point
10	6.4851974710934e+151	6.7846503122979244e+162	8.828154833930211e+151
7	-3.588378087479768e-211	-3.8670254222860854e-213	-9.281927902223943e-213
10	-1.9898668609638904e+139	-6.411886552711472e+128	-9.444009031655424e+133

Iters

Range

Point

6.4851974710934e+151

6.7846503122979244e+162

8.828154833930211e+151

-3.588378087479768e-211

-3.8670254222860854e-213

-9.281927902223943e-213

-1.9898668609638904e+139

-6.411886552711472e+128

-9.444009031655424e+133

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

272.0ms	1057×	body	2560	valid
224.0ms	5073×	body	80	valid
188.0ms	907×	body	1280	valid
80.0ms	484×	body	640	valid
42.0ms	130×	body	5120	valid
30.0ms	731×	body	80	nan
30.0ms	224×	body	320	valid
12.0ms	268×	body	80	invalid
10.0ms	125×	body	160	valid

Details

analyze430.0ms

sample45.0ms

simplify473.0ms

prune18.0ms

localize25.0ms

rewrite34.0ms

series81.0ms

simplify56.0ms

prune124.0ms

localize10.0ms

rewrite43.0ms

series137.0ms

simplify72.0ms

prune189.0ms

localize9.0ms

rewrite24.0ms

series97.0ms

simplify50.0ms

prune82.0ms

localize10.0ms

rewrite32.0ms

series96.0ms

simplify51.0ms

prune65.0ms

regimes234.0ms

bsearch90.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling