Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	190×	body	80	valid
5.0ms	27×	body	1280	valid
3.0ms	101×	body	80	nan
2.0ms	17×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

7.0ms	(* (* 3.0 a) c)
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune261.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
11.0b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
78.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	279	732
1	1153	610
2	5001	597

prune288.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.9b

localize19.0ms

Local error

Found 4 expressions with local error:

12.0b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
24.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
91.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
94.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	351	1045
1	1300	935
2	5002	925

prune428.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.9b

localize28.0ms

Local error

Found 4 expressions with local error:

24.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
24.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
24.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
24.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite11.0ms

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:

2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
3.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
93.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	162	680
1	548	636
2	2225	628
3	5001	628

prune415.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.9b

regimes347.0ms

Accuracy

82.1% (4.0b remaining)

Error of 16.5b against oracle of 12.5b and baseline of 34.9b

bsearch122.0ms

Steps

Iters	Range		Point
10	1.9806752729915607e+21	8.491437828551758e+31	3.2720500059154253e+21
8	-6.30521239297407e+53	-2.0681333037085905e+50	-6.218858286019401e+53

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	26
1	37	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

226.0ms	1039×	body	2560	valid
216.0ms	5881×	body	80	valid
166.0ms	911×	body	1280	valid
106.0ms	2871×	body	80	nan
66.0ms	461×	body	640	valid
33.0ms	112×	body	5120	valid
27.0ms	229×	body	320	valid
7.0ms	101×	body	160	valid