Details

sample39.0ms

Algorithm

intervals

Results

24.0ms

656×

body

valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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:

6.0ms	(* 4.0 (* b b))
3.0ms	(+ (* a a) (* b b))
29.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series215.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 4.0 (* b b))
31.0ms	(+ (* a a) (* b b))
61.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
99.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

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

prune223.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize13.0ms

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)))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite53.0ms

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:

35.0ms	(* (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))

series604.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
144.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
164.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
145.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify103.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (88.0ms)

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

prune412.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

13.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
13.0b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
6×	`rem-sqrt-square` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 76

Calls

4 calls:

7.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms	(sqrt (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))

series588.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
143.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
146.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
154.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify117.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	147	644
1	323	600
2	1002	596
3	3983	592
4	5002	592

prune374.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (pow a 2))
0.8b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`associate-r`
7×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 39

Calls

2 calls:

6.0ms	(* 2 (pow a 2))
0.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series97.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(* 2 (pow a 2))
74.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify125.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	139	196
1	607	173
2	3092	173
3	5001	167

prune117.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes70.0ms

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	20	28
1	20	28

end0.0ms

sample1.1s

Algorithm

intervals

Results

755.0ms

20310×

body

valid