Details

sample284.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	198×	body	80	valid
4.0ms	92×	body	80	nan
4.0ms	24×	body	1280	valid
2.0ms	15×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

41.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune243.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (* b_2 b_2) (* a c))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite14.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series189.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	140	390
1	455	366
2	1490	364
3	5002	360

prune223.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite15.0ms

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:

2.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	140	423
1	455	403
2	1490	400
3	5002	394

prune248.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.8b

localize23.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (- (* b_2 b_2) (* a c)))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))
23.9b	(cbrt (- (* b_2 b_2) (* a c)))
23.9b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))
2.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))
86.0ms	(cbrt (- (* b_2 b_2) (* a c)))
89.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	192	496
1	567	470
2	1742	464
3	5002	460

prune342.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.8b

regimes267.0ms

Accuracy

85% (4.4b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 34.5b

bsearch93.0ms

Steps

Iters	Range		Point
9	3.6106127752583374e-71	6.7695755698382385e-65	9.390367471089922e-69
9	-8.652530131639494e+154	-2.4576771469086066e+149	-2.9358923729233266e+149

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample1.0s

Algorithm

intervals

Results

224.0ms	1117×	body	2560	valid
195.0ms	5732×	body	80	valid
148.0ms	930×	body	1280	valid
88.0ms	2852×	body	80	nan
58.0ms	473×	body	640	valid
24.0ms	101×	body	5120	valid
22.0ms	240×	body	320	valid
7.0ms	109×	body	160	valid