Details

sample54.0ms

Algorithm

intervals

Results

13.0ms	191×	body	80	valid
7.0ms	24×	body	2560	valid
6.0ms	27×	body	1280	valid
5.0ms	106×	body	80	nan
3.0ms	15×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

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: 30.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b	(- (* b b) (* (* 4.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune154.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 4.6b

Counts

83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b	(- (* b b) (* (* 4.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (* 4.0 a) c)
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 4.0 a) c)
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	302	468
1	1299	428
2	5002	417

prune111.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	72	9	81

Merged error: 4.6b

Counts

81 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (* b b) (* (* 4.0 a) c))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

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` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(- (* b b) (* (* 4.0 a) c))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	147	474
1	570	446
2	2550	444
3	5001	442

prune145.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 4.6b

Counts

75 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* (* 4.0 a) c))
20.7b	(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)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	147	505
1	570	483
2	2550	480
3	5001	477

prune170.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	69	9	78

Merged error: 4.6b

Counts

78 → 9

regimes279.0ms

Accuracy

86.4% (3.9b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 33.8b

bsearch110.0ms

Steps

Iters	Range	Point
9	1.4207218227508602e+125	1.7687561556963888e+130	3.1899052552331176e+125
9	1.4140249174076056e-267	1.6486910309601152e-261	4.1502694039604683e-262
10	-3.692428373978256e+65	-2.9514001404867553e+50	-6.741241628846222e+60

Iters

Range

Point

1.4207218227508602e+125

1.7687561556963888e+130

3.1899052552331176e+125

1.4140249174076056e-267

1.6486910309601152e-261

4.1502694039604683e-262

-3.692428373978256e+65

-2.9514001404867553e+50

-6.741241628846222e+60

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	29
1	52	29
2	52	29

end0.0ms

sample1.5s

Algorithm

intervals

Results

313.0ms	1063×	body	2560	valid
296.0ms	5894×	body	80	valid
211.0ms	887×	body	1280	valid
138.0ms	2829×	body	80	nan
85.0ms	443×	body	640	valid
35.0ms	100×	body	5120	valid
33.0ms	213×	body	320	valid
11.0ms	117×	body	160	valid

Details

sample54.0ms

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite27.0ms

series65.0ms

simplify43.0ms

prune154.0ms

localize13.0ms

rewrite23.0ms

series41.0ms

simplify41.0ms

prune111.0ms

localize16.0ms

rewrite15.0ms

series45.0ms

simplify77.0ms

prune145.0ms

localize17.0ms

rewrite17.0ms

series51.0ms

simplify79.0ms

prune170.0ms

regimes279.0ms

bsearch110.0ms

simplify2.0ms

end0.0ms

sample1.5s

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