Details

sample43.0ms

Algorithm

intervals

Results

28.0ms

618×

body

valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ (* a a) (* b b))
7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series221.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a a) (* b b))
67.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
25.0ms	(* 4.0 (* b b))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	339	438
1	1458	396
2	5002	385

prune199.0ms

Filtered

86 candidates to 66 candidates (76.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.0b

Counts

87 → 4

localize14.0ms

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)))
18.7b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.7b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.7b	(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))
5.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series600.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
154.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
151.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
147.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (92.0ms)

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

prune358.0ms

Filtered

129 candidates to 96 candidates (74.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	128	5	133

Merged error: 0b

Counts

133 → 5

localize25.0ms

Local error

Found 4 expressions with local error:

10.0b	(cbrt (+ (* a a) (* b b)))
16.0b	(cbrt (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0))
18.7b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.7b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`unpow-prod-down`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`cbrt-div`
1×	`flip3-+` `flip-+`

Counts

4 → 64

Calls

4 calls:

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

series556.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (* a a) (* b b)))
154.0ms	(cbrt (pow (* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b)))) 2.0))
149.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
154.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	274	737
1	864	681
2	3001	672
3	5002	666

prune363.0ms

Filtered

76 candidates to 67 candidates (88.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	76	5	81

Merged error: 0b

Counts

81 → 5

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (pow a 2))
0.0b	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
1.4b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-def` `associate-l` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

3 → 57

Calls

3 calls:

6.0ms	(* 2 (pow a 2))
5.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
1.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series145.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* 2 (pow a 2))
53.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
68.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify38.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	215	381
1	1025	344
2	5002	343

prune165.0ms

Filtered

66 candidates to 46 candidates (69.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	66	5	71

Merged error: 0b

Counts

71 → 5

regimes102.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	20
1	16	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

947.0ms

20562×

body

valid