Details

analyze504.0ms

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample35.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	13×	body	80	invalid

simplify258.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (256.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

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: 21.7b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
1.2b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `sqrt-div_binary64`
3×	`diff-log_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`associate--l-_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))
18.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4901	985
1	4901	985

prune124.0ms

Filtered

55 candidates to 70 candidates (-27.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	64	6	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	6	71

Merged error: 9.6b

Counts

71 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

5.9b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
31.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5107	1108

prune141.0ms

Filtered

58 candidates to 64 candidates (-10.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	62	8	70

Merged error: 9.6b

Counts

70 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`

Counts

4 → 60

Calls

4 calls:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5056	932

prune156.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 9.6b

Counts

80 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

14.2b	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
25.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

9.0ms	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(-.f64 (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4.0 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c))))) b)
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
27.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))
28.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4928	1108
1	4928	1108

prune120.0ms

Filtered

57 candidates to 64 candidates (-12.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	64	8	72

Merged error: 9.6b

Counts

72 → 8

regimes229.0ms

Accuracy

90.2% (1.2b remaining)

Error of 8.9b against oracle of 7.7b and baseline of 19.7b

bsearch50.0ms

Steps

Iters	Range		Point
8	6.093467662767075e+66	1.6571798933176391e+69	1.6435099743363113e+69
6	-1.7832963248470996e+80	-3.612699187479539e+79	-1.7621272729921349e+80

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	149	129
1	149	129

end0.0ms

sample972.0ms

Algorithm

intervals

Results

684.0ms	8000×	body	80	valid
53.0ms	657×	body	80	nan
30.0ms	367×	body	80	invalid

Details

analyze504.0ms

sample35.0ms

simplify258.0ms

prune10.0ms

localize20.0ms

rewrite24.0ms

series66.0ms

simplify57.0ms

prune124.0ms

localize25.0ms

rewrite24.0ms

series114.0ms

simplify52.0ms

prune141.0ms

localize25.0ms

rewrite19.0ms

series71.0ms

simplify49.0ms

prune156.0ms

localize29.0ms

rewrite24.0ms

series109.0ms

simplify39.0ms

prune120.0ms

regimes229.0ms

bsearch50.0ms

simplify3.0ms

end0.0ms

sample972.0ms

Profiling