Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	197×	body	80	valid
5.0ms	28×	body	1280	valid
3.0ms	90×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	2×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b	(- (* b b) (* (* 3.0 a) c))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

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:

6.0ms	(* (* 3.0 a) c)
12.0ms	(+ (- 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)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
49.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (42.0ms)

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

prune266.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 3.0 a) c))
10.0b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

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))
6.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (34.0ms)

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

prune313.0ms

Filtered

87 candidates to 74 candidates (85.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt b)
1.2b	(- (* b b) (* (* 3.0 a) c))
22.0b	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 56

Calls

4 calls:

0.0ms	(cbrt b)
3.0ms	(- (* b b) (* (* 3.0 a) c))
0.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt b)
51.0ms	(- (* b b) (* (* 3.0 a) c))
139.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	244	479
1	840	434
2	3607	420
3	5001	419

prune246.0ms

Filtered

68 candidates to 59 candidates (86.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.0b

localize23.0ms

Local error

Found 4 expressions with local error:

22.8b	(sqrt (* (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (- (* b b) (* (* 3.0 a) c)))))
23.6b	(cbrt (- (* b b) (* (* 3.0 a) c)))
23.6b	(cbrt (- (* b b) (* (* 3.0 a) c)))
23.6b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite46.0ms

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:

35.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c)))) (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)))
2.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (* (* (cbrt (- (* b b) (* (* 3.0 a) c))) (cbrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (- (* b b) (* (* 3.0 a) c)))))
96.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify193.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	363	1930
1	970	1879
2	4476	1859
3	5001	1859

prune351.0ms

Filtered

109 candidates to 76 candidates (69.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 9.0b

regimes337.0ms

Accuracy

86.9% (3.1b remaining)

Error of 14.0b against oracle of 10.9b and baseline of 34.9b

bsearch119.0ms

Steps

Iters	Range		Point
9	3.2956103981062554e-86	3.6842556330088986e-79	3.6227398529818415e-79
10	-5.288637106878427e+83	-2.355035228211621e+66	-2.4276688444363324e+79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	25
1	48	25
2	54	25
3	54	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

229.0ms	1081×	body	2560	valid
213.0ms	5782×	body	80	valid
156.0ms	927×	body	1280	valid
110.0ms	2977×	body	80	nan
60.0ms	451×	body	640	valid
27.0ms	104×	body	5120	valid
26.0ms	257×	body	320	valid
8.0ms	124×	body	160	valid