Details

sample58.0ms

Algorithm

intervals

Results

39.0ms

742×

body

valid

simplify51.0ms

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

prune11.0ms

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

localize15.0ms

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)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite18.0ms

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))))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series243.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a a) (* b b))
50.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
55.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
105.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

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

prune241.0ms

Filtered

88 candidates to 63 candidates (71.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Merged error: 0.1b

Counts

89 → 5

localize19.0ms

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)))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite30.0ms

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:

13.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* 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))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series774.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
322.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
152.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
153.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify95.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (80.0ms)

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

prune460.0ms

Filtered

129 candidates to 96 candidates (74.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	7	129
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	123	11	134

Merged error: 0.0b

Counts

134 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

10.2b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
10.2b	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite20.0ms

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:

5.0ms	(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))

series625.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
149.0ms	(cbrt (pow (sqrt (+ (* a a) (* b b))) 2.0))
147.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
182.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify138.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (32.0ms)

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

prune427.0ms

Filtered

86 candidates to 72 candidates (83.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

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

series591.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
149.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
144.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
152.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	106	680
1	233	632
2	782	624
3	3284	616
4	5002	616

prune349.0ms

Filtered

80 candidates to 68 candidates (85.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	80	12	92

Merged error: 0.0b

Counts

92 → 12

regimes204.0ms

Accuracy

0% (0.2b 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

1.1s

20373×

body

valid