Details

sample78.0ms

Algorithm

intervals

Results

62.0ms

650×

body

valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

0.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series168.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
98.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	137	245
1	492	221
2	1863	214
3	5001	213

prune110.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

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)))
19.9b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.9b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.9b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite50.0ms

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))

series563.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
143.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
141.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
139.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 3 (83.0ms)

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

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2.0 (pow a 2))
0.0b	(fma (* 4.0 b) b (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
0.9b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

5.0ms	(* 2.0 (pow a 2))
0.0ms	(fma (* 4.0 b) b (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
0.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series166.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* 2.0 (pow a 2))
71.0ms	(fma (* 4.0 b) b (- (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) 1.0))
72.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify121.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	172	328
1	661	285
2	3351	281
3	5001	279

prune178.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.1b	(pow (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
12.8b	(cbrt (pow (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp`
1×	`pow1/3` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 77

Calls

4 calls:

0.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
1.0ms	(pow (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
2.0ms	(cbrt (pow (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

series665.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
418.0ms	(pow (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3)
101.0ms	(pow (+ (* a a) (* b b)) 2.0)
73.0ms	(cbrt (pow (fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0)) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	259	842
1	1049	788
2	5002	773

prune227.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes74.0ms

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	18	20
1	18	20

end0.0ms

sample2.3s

Algorithm

intervals

Results

2.0s

20311×

body

valid