Details

sample50.0ms

Algorithm

intervals

Results

9.0ms	33×	body	2560	valid
8.0ms	39×	body	1280	valid
8.0ms	166×	body	80	valid
6.0ms	22×	body	640	valid
3.0ms	77×	body	80	nan
2.0ms	12×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

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: 35.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b	(- (* b b) (* (* 3.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

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:

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

series216.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

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

prune236.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 11.9b

Counts

93 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
0.6b	(- (* b b) (* (* 3.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite17.0ms

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` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

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

series233.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(- (* b b) (* (* 3.0 a) c))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify89.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	170	540
1	665	506
2	2968	498
3	5001	488

prune247.0ms

Filtered

78 candidates to 62 candidates (79.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	78	10	88

Merged error: 11.9b

Counts

88 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
13.2b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))
20.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite18.0ms

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:

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

series267.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* 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))))))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (35.0ms)

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

prune262.0ms

Filtered

87 candidates to 72 candidates (82.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	87	10	97

Merged error: 11.9b

Counts

97 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
11.2b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
21.5b	(cbrt (- (* b b) (* (* 3.0 a) c)))
21.5b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`fma-def` `add-log-exp`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `flip3--` `distribute-rgt-neg-in` `flip--`
2×	`pow1/3` `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 → 71

Calls

4 calls:

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

series359.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
117.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
102.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	366	849
1	1532	766
2	5002	749

prune305.0ms

Filtered

83 candidates to 73 candidates (88.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	82	11	93

Merged error: 11.9b

Counts

93 → 11

regimes378.0ms

Accuracy

84.5% (3.5b remaining)

Error of 16.0b against oracle of 12.5b and baseline of 35.1b

bsearch77.0ms

Steps

Iters	Range		Point
9	5.157801608255442e-100	9.252074768315096e-95	8.946318171081371e-95
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	40	25
1	40	25

end0.0ms

sample1.5s

Algorithm

intervals

Results

330.0ms	1133×	body	2560	valid
308.0ms	5778×	body	80	valid
219.0ms	895×	body	1280	valid
140.0ms	2864×	body	80	nan
90.0ms	464×	body	640	valid
38.0ms	107×	body	5120	valid
36.0ms	248×	body	320	valid
10.0ms	110×	body	160	valid