Details

sample47.0ms

Algorithm

intervals

Results

23.0ms	283×	body	80	valid
8.0ms	96×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	18
1	67	18
2	123	18
3	160	18
4	175	18
5	177	18
6	177	18

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 22.2b

Counts

2 → 1

localize113.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	170	540
1	665	506
2	2968	498
3	5001	488

prune282.0ms

Filtered

78 candidates to 62 candidates (79.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Merged error: 8.8b

Counts

79 → 6

localize118.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 97

Calls

4 calls:

17.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
101.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify195.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	362	1930
1	970	1879
2	4477	1859
3	5001	1859

prune412.0ms

Filtered

109 candidates to 76 candidates (69.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	109	6	115

Merged error: 8.8b

Counts

115 → 6

localize128.0ms

Local error

Found 4 expressions with local error:

25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 62

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
99.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	215	657
1	688	619
2	2689	612
3	5001	611

prune374.0ms

Filtered

74 candidates to 68 candidates (91.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	8	80

Merged error: 8.8b

Counts

80 → 8

localize124.0ms

Local error

Found 4 expressions with local error:

26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))
26.2b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	161	680
1	548	636
2	2229	628
3	5001	628

prune412.0ms

Filtered

72 candidates to 68 candidates (94.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	72	8	80

Merged error: 8.8b

Counts

80 → 8

regimes206.0ms

Accuracy

87.1% (1.6b remaining)

Error of 9.1b against oracle of 7.5b and baseline of 19.8b

bsearch159.0ms

Steps

Iters	Range		Point
7	0.008549975533169097	1.4731263457460937	1.4443031837246074
7	-1.573165836586651e+155	-6.856469880078083e+152	-1.35463732932136e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	65
1	52	65

end0.0ms

sample1.1s

Algorithm

intervals

Results

640.0ms	8727×	body	80	valid
204.0ms	2883×	body	80	nan