Details

sample54.0ms

Algorithm

intervals

Results

35.0ms

643×

body

valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.3b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`prod-diff` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `fma-def` `flip3-+` `associate-l` `pow-exp` `sum-log` `*-commutative` `flip--` `flip-+` `fma-udef` `unswap-sqr` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

4.0ms	(+ (* a a) (* b b))
1.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
8.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series247.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* a a) (* b b))
52.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
54.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
110.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	422	576
1	1971	501
2	5001	486

prune286.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	7	89

Merged error: 0.1b

Counts

89 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 117

Calls

4 calls:

14.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series598.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
147.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
151.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	217	1556
1	702	1473
2	3308	1390
3	5001	1383

prune553.0ms

Filtered

129 candidates to 96 candidates (74.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	126	10	136

Merged error: 0.0b

Counts

136 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

31×	`cbrt-prod`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
10×	`sqrt-prod`
5×	`pow1` `sqr-pow`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1`
1×	`pow1/2`

Counts

4 → 77

Calls

4 calls:

6.0ms	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series596.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (cbrt (pow (+ (* a a) (* b b)) 2.0)))
151.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
146.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
152.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	157	734
1	354	691
2	1149	684
3	4997	674
4	5001	674

prune501.0ms

Filtered

89 candidates to 75 candidates (84.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	88	11	99

Merged error: 0.0b

Counts

99 → 11

localize55.0ms

Local error

Found 4 expressions with local error:

8.9b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
8.9b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.4b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
18×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

8.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
5.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series619.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
156.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
157.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify135.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	179	814
1	384	760
2	1210	750
3	4950	740
4	5001	740

prune540.0ms

Filtered

86 candidates to 72 candidates (83.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	86	11	97

Merged error: 0.0b

Counts

97 → 11

regimes190.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

20683×

body

valid