Details

sample46.0ms

Algorithm

intervals

Results

26.0ms

713×

body

valid

simplify50.0ms

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 1 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
2×	`pow1` `add-exp-log`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `sqr-pow`

Counts

1 → 19

Calls

1 calls:

10.0ms

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

series94.0ms

Counts

1 → 3

Calls

1 calls:

94.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	98	128
1	364	119
2	1356	114
3	5002	110

prune71.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
12.4b	(cbrt (+ (* a a) (* b b)))
12.4b	(cbrt (+ (* a a) (* b b)))
12.4b	(cbrt (+ (* a a) (* b b)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

43.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
5.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
88.0ms	(cbrt (+ (* a a) (* b b)))
88.0ms	(cbrt (+ (* a a) (* b b)))
87.0ms	(cbrt (+ (* a a) (* b b)))

simplify147.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	234	1025
1	1005	960
2	4315	899
3	5001	899

prune446.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

11.8b	(sqrt (+ (* a a) (* b b)))
11.8b	(sqrt (+ (* a a) (* b b)))
12.4b	(cbrt (+ (* a a) (* b b)))
12.4b	(cbrt (+ (* a a) (* b b)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `hypot-def`

Counts

4 → 66

Calls

4 calls:

7.0ms	(sqrt (+ (* a a) (* b b)))
7.0ms	(sqrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ (* a a) (* b b)))
38.0ms	(sqrt (+ (* a a) (* b b)))
88.0ms	(cbrt (+ (* a a) (* b b)))
87.0ms	(cbrt (+ (* a a) (* b b)))

simplify56.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	153	468
1	493	440
2	1626	434
3	5002	432

prune455.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

12.4b	(cbrt (+ (* a a) (* b b)))
12.4b	(cbrt (+ (* a a) (* b b)))
12.4b	(cbrt (+ (* a a) (* b b)))
12.4b	(cbrt (+ (* a a) (* b b)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
4.0ms	(cbrt (+ (* a a) (* b b)))
5.0ms	(cbrt (+ (* a a) (* b b)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ (* a a) (* b b)))
89.0ms	(cbrt (+ (* a a) (* b b)))
89.0ms	(cbrt (+ (* a a) (* b b)))
86.0ms	(cbrt (+ (* a a) (* b b)))

simplify51.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	132	524
1	449	488
2	1529	476
3	5001	476

prune394.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes209.0ms

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	14	7
1	14	7

end0.0ms

sample1.2s

Algorithm

intervals

Results

747.0ms

20279×

body

valid