Details

analyze444.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample44.0ms

Algorithm

intervals

Results

11.0ms	168×	body	80	valid
9.0ms	32×	body	2560	valid
5.0ms	23×	body	1280	valid
4.0ms	22×	body	640	valid
2.0ms	36×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	17×	body	80	invalid
0.0ms	5×	body	160	valid

simplify218.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune6.0ms

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: 34.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
11.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5261	1302

prune97.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 4.5b

Counts

83 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
7.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify78.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4947	1460
1	4947	1460

prune67.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 4.5b

Counts

99 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4931	869
1	4931	869

prune80.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Merged error: 4.5b

Counts

77 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
10.7b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
24.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
24.3b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64`

Counts

4 → 48

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
9.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
6.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
33.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
23.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4988	1074
1	4988	1074

prune53.0ms

Filtered

53 candidates to 60 candidates (-13.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	60	9	69

Merged error: 4.5b

Counts

69 → 9

regimes220.0ms

Accuracy

80.7% (5.4b remaining)

Error of 11.2b against oracle of 5.8b and baseline of 33.8b

bsearch53.0ms

Steps

Iters	Range		Point
9	2.392514258149656e-126	6.579720982939558e-118	6.471134733128259e-118
9	-112243332068.72598	-89552.36570462812	-110883243782.23416

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	91	35
1	91	35

end0.0ms

sample1.3s

Algorithm

intervals

Results

339.0ms	1096×	body	2560	valid
286.0ms	5154×	body	80	valid
242.0ms	917×	body	1280	valid
88.0ms	423×	body	640	valid
39.0ms	710×	body	80	nan
35.0ms	88×	body	5120	valid
33.0ms	217×	body	320	valid
19.0ms	357×	body	80	invalid
10.0ms	105×	body	160	valid

Details

analyze444.0ms

sample44.0ms

simplify218.0ms

prune6.0ms

localize10.0ms

rewrite30.0ms

series73.0ms

simplify47.0ms

prune97.0ms

localize11.0ms

rewrite37.0ms

series72.0ms

simplify78.0ms

prune67.0ms

localize16.0ms

rewrite21.0ms

series56.0ms

simplify38.0ms

prune80.0ms

localize14.0ms

rewrite25.0ms

series91.0ms

simplify50.0ms

prune53.0ms

regimes220.0ms

bsearch53.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling