Details

sample44.0ms

Algorithm

intervals

Results

19.0ms	279×	body	80	valid
5.0ms	79×	body	80	nan

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	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: 18.5b

Counts

2 → 1

localize116.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
53×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
37×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 140

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	406	2988
1	1431	1956
2	5002	1869

prune331.0ms

Filtered

152 candidates to 80 candidates (52.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	146	6	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	6	153

Merged error: 6.5b

Counts

153 → 6

localize120.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 4.0 a) c))) (cbrt (- (* b b) (* (* 4.0 a) c)))) (cbrt (- (* b b) (* (* 4.0 a) c)))))
95.0ms	(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)))

simplify187.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	362	1936
1	979	1879
2	4487	1859
3	5001	1859

prune400.0ms

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: 6.5b

Counts

115 → 6

localize122.0ms

Local error

Found 4 expressions with local error:

7.2b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 83

Calls

4 calls:

5.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
98.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	1492
1	1667	1341
2	5002	1297

prune411.0ms

Filtered

95 candidates to 79 candidates (83.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	95	6	101

Merged error: 6.5b

Counts

101 → 6

localize121.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
3.1b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.8b	(/ (* a c) b)
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
4.0ms	(/ (* a c) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
18.0ms	(/ (* a c) b)
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	454	650
1	2083	569
2	5001	564

prune290.0ms

Filtered

94 candidates to 71 candidates (75.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Merged error: 5.2b

Counts

100 → 8

regimes219.0ms

Accuracy

89.2% (1.6b remaining)

Error of 8.1b against oracle of 6.5b and baseline of 21.2b

bsearch94.0ms

Steps

Iters	Range		Point
7	3.0106008231332273e+28	3.853441604264477e+30	3.7841174599135035e+30
2	-4.193597519284562e+95	-3.5355996581575456e+95	-4.111347786643685e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	61
1	56	61

end0.0ms

sample1.0s

Algorithm

intervals

Results

578.0ms	8730×	body	80	valid
176.0ms	2863×	body	80	nan