Details

Time bar (total: 6.0s)

sample69.0ms

Algorithm
intervals
Results
50.0ms723×body80valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
0268
1518
2887
31537
43577
515727
650027

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
11×add-log-exp
10×pow1 add-exp-log
9×prod-diff add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×unpow-prod-down pow-unpow fma-neg associate-*l* pow-prod-down prod-exp cbrt-unprod
2×diff-log sum-log
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow fma-def flip3-+ associate-*r* pow-exp associate--l+ *-commutative flip-- flip-+ distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 84
Calls
4 calls:
164.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
3.0ms
(+ (* a a) (* b b))
6.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series47.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
5.0ms
(+ (* a a) (* b b))
2.0ms
(* 4.0 (* b b))
23.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify50.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0404753
11693603
25001587

prune589.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a a) (* b b))
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)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×prod-diff
7×add-log-exp
4×pow1 add-exp-log
3×expm1-log1p-u unpow-prod-down pow-unpow fma-neg add-cbrt-cube log1p-expm1-u
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow fma-def flip3-+ diff-log pow-exp associate--l+ sum-log flip-- flip-+ fma-udef distribute-lft-out-- difference-of-squares sqr-pow
Counts
3 → 62
Calls
3 calls:
3.0ms
(+ (* a a) (* b b))
3.0ms
(- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series42.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* a a) (* b b))
14.0ms
(- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0)
23.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify43.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0326624
11302504
25001490

prune543.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
8.9b
(cbrt (+ (* a a) (* b b)))
8.9b
(cbrt (+ (* a a) (* b b)))
8.9b
(cbrt (+ (* a a) (* b b)))

rewrite27.0ms

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:
18.0ms
(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
2.0ms
(cbrt (+ (* a a) (* b b)))
2.0ms
(cbrt (+ (* a a) (* b b)))
2.0ms
(cbrt (+ (* a a) (* b b)))

series83.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
22.0ms
(cbrt (+ (* a a) (* b b)))
19.0ms
(cbrt (+ (* a a) (* b b)))
19.0ms
(cbrt (+ (* a a) (* b b)))

simplify140.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02341025
11005960
24315899
35001899

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (fma (* 4.0 b) b (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
0.0b
(* 2.0 (pow a 2))
1.3b
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
9×prod-diff
8×add-exp-log associate-*r*
5×add-cbrt-cube add-log-exp
4×unpow-prod-down unswap-sqr
3×pow1 expm1-log1p-u fma-neg associate-*l* prod-exp log1p-expm1-u
2×fma-udef unpow2 sqr-pow
1×pow-to-exp sub-neg flip3-- diff-log pow-exp associate--l+ *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
3 → 68
Calls
3 calls:
3.0ms
(- (fma (* 4.0 b) b (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
6.0ms
(* 2.0 (pow a 2))
0.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series29.0ms

Counts
3 → 9
Calls
3 calls:
13.0ms
(- (fma (* 4.0 b) b (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
2.0ms
(* 2.0 (pow a 2))
14.0ms
(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify40.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0267667
1983535
25001525

prune554.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02419
12619
22619

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s20670×body80valid