Details

Time bar (total: 4.8s)

sample40.0ms

Algorithm
intervals
Results
23.0ms623×body80valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
0268
1518
2887
31537
43577
515727
650027

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
4×pow1 add-exp-log
3×expm1-log1p-u unpow-prod-down pow-unpow add-cbrt-cube log1p-expm1-u
1×+-commutative pow-to-exp pow-pow fma-def flip3-+ pow-exp sum-log flip-+ fma-udef sqr-pow
Counts
3 → 43
Calls
3 calls:
0.0ms
(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
8.0ms
(+ (* a a) (* b b))
13.0ms
(pow (+ (* a a) (* b b)) 2.0)

series212.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(fma (* 4.0 b) b (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
28.0ms
(+ (* a a) (* b b))
105.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify112.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0226319
1972282
23693275
35001274

prune150.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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)))
18.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite113.0ms

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:
82.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series618.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
155.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
158.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
153.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify96.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
02171556
17021473
233081390
350011383

prune397.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (pow (pow (+ (* a a) (* b b)) 2.0) 1/3))
18.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.3b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
21.4b
(pow (pow (+ (* a a) (* b b)) 2.0) 1/3)

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
50×unpow-prod-down
44×add-sqr-sqrt
36×cbrt-prod
20×unswap-sqr sqr-pow
17×add-cube-cbrt *-un-lft-identity
14×add-exp-log
11×associate-*r*
10×associate-*l*
8×pow-exp
5×pow1/3 prod-exp add-cbrt-cube
4×pow1 expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×pow-unpow
2×unpow1/3 cbrt-unprod
1×pow-pow pow-prod-down pow-sqr *-commutative pow-prod-up
Counts
4 → 121
Calls
4 calls:
112.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (pow (pow (+ (* a a) (* b b)) 2.0) 1/3))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
9.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
18.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 1/3)

series622.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (pow (pow (+ (* a a) (* b b)) 2.0) 1/3))
161.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
152.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
156.0ms
(pow (pow (+ (* a a) (* b b)) 2.0) 1/3)

simplify43.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03461519
111191247
250011206

prune449.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow a 4)) (pow b 4))
0.0b
(* 2 (pow a 2))
2.8b
(fma (* 2 (pow a 2)) (pow b 2) (pow a 4))

rewrite24.0ms

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:
9.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow a 4)) (pow b 4))
13.0ms
(* 2 (pow a 2))
0.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow a 4))

series142.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ (fma (* 2 (pow a 2)) (pow b 2) (pow a 4)) (pow b 4))
26.0ms
(* 2 (pow a 2))
59.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow a 4))

simplify35.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0215372
1958344
25002344

prune161.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes55.0ms

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)

IterNodesCost
0147
1147

end0.0ms

sample1.2s

Algorithm
intervals
Results
785.0ms20611×body80valid