Details

Time bar (total: 4.7s)

sample67.0ms

Algorithm
intervals
Results
48.0ms658×body80valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.2b

Counts
2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.1b
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
12×add-cube-cbrt
7×distribute-rgt-in fma-def distribute-lft-in associate-*r*
6×unpow-prod-down prod-diff pow-prod-down prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr sqr-pow
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out
Counts
4 → 100
Calls
4 calls:
8.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
8.0ms
(* (* a a) (+ 1.0 a))
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms
(pow (+ (* a a) (* b b)) 2.0)

series303.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
51.0ms
(* (* a a) (+ 1.0 a))
47.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
102.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify72.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0564828
12826724
25001715

prune286.0ms

Filtered
112 candidates to 80 candidates (71.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1057112
Fresh000
Picked101
Done000
Total1067113

Merged error: 0.0b

Counts
113 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
0.1b
(* (* a a) (- (* 1.0 1.0) (* a a)))
0.1b
(* (* b b) (- 1.0 (* 3.0 a)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
23×add-cbrt-cube
18×add-sqr-sqrt
16×*-un-lft-identity
15×pow1
12×add-cube-cbrt
9×prod-exp cbrt-unprod
8×distribute-rgt-in distribute-lft-in prod-diff
7×associate-*r*
6×associate-*r/ pow-prod-down
5×times-frac associate-/r*
4×expm1-log1p-u sub-neg flip3-- flip-- log1p-expm1-u add-log-exp
3×cbrt-undiv unpow-prod-down pow-unpow div-exp difference-of-squares
2×associate-*l* associate-/r/ *-commutative associate-/l/ distribute-lft-out-- unswap-sqr
1×pow-to-exp pow-pow frac-2neg pow-exp clear-num div-inv associate-/l* sqr-pow
Counts
4 → 115
Calls
4 calls:
15.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
8.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
8.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series336.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (- 1.0 a))
76.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
46.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
98.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify99.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0651943
13489802
25001799

prune335.0ms

Filtered
127 candidates to 85 candidates (66.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1261127
Fresh156
Picked011
Done000
Total1277134

Merged error: 0.0b

Counts
134 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
0.0b
(* 2 (pow a 2))
0.1b
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.0b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
9×add-exp-log prod-diff
8×associate-*r*
6×add-cbrt-cube add-log-exp
4×pow1 expm1-log1p-u unpow-prod-down log1p-expm1-u unswap-sqr
3×fma-neg associate-*l* prod-exp fma-udef
2×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
4 → 78
Calls
4 calls:
4.0ms
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
6.0ms
(* 2 (pow a 2))
1.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
1.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series219.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
24.0ms
(* 2 (pow a 2))
61.0ms
(fma (pow a 3) a (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
70.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify48.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0276764
11144636
25001628

prune242.0ms

Filtered
90 candidates to 61 candidates (67.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh055
Picked101
Done011
Total90797

Merged error: 0.0b

Counts
97 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (pow a 4) (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
0.0b
(+ (pow a 4) (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
0.0b
(* 2 (pow a 2))
1.0b
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
25×add-sqr-sqrt
17×add-cube-cbrt
12×prod-diff
11×add-log-exp
9×add-exp-log
8×associate-*r*
7×unpow-prod-down fma-def
6×add-cbrt-cube distribute-lft-out
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u unswap-sqr
3×associate-*l* prod-exp sqr-pow
2×diff-log sum-log fma-udef distribute-lft-out-- unpow2
1×+-commutative pow-to-exp sub-neg associate-+r+ flip3-- flip3-+ pow-exp associate--l+ *-commutative flip-- cbrt-unprod flip-+ difference-of-squares
Counts
4 → 96
Calls
4 calls:
8.0ms
(- (+ (pow a 4) (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
5.0ms
(+ (pow a 4) (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
6.0ms
(* 2 (pow a 2))
1.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series197.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (+ (pow a 4) (fma (* 2 (pow a 2)) (pow b 2) (pow b 4))) 1.0)
51.0ms
(+ (pow a 4) (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)))
24.0ms
(* 2 (pow a 2))
70.0ms
(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify49.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0324887
11364747
25001746

prune227.0ms

Filtered
108 candidates to 71 candidates (65.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1080108
Fresh055
Picked011
Done011
Total1087115

Merged error: 0.0b

Counts
115 → 7

regimes114.0ms

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
02919
12919

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.5s20498×body80valid