Details

Time bar (total: 7.7s)

sample68.0ms

Algorithm
intervals
Results
49.0ms723×body80valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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)

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log add-sqr-sqrt
9×*-un-lft-identity add-cbrt-cube
7×add-cube-cbrt
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×diff-log sum-log
1×+-commutative pow-to-exp sub-neg flip3-- pow-pow flip3-+ associate-*r* pow-exp associate--l+ *-commutative flip-- flip-+ distribute-lft-out-- difference-of-squares unswap-sqr sqr-pow
Counts
4 → 63
Calls
4 calls:
137.0ms
(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
2.0ms
(+ (* a a) (* b b))
6.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series224.0ms

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))
200.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0338488
11360446
25001439

prune452.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite468.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
32×*-un-lft-identity
28×cbrt-prod
18×add-cube-cbrt
14×pow1
12×cbrt-div
10×swap-sqr
9×add-exp-log unpow-prod-down pow-unpow
8×associate-*r* associate-*l*
6×flip3-- pow1/3 flip-- distribute-lft-out--
4×frac-times add-cbrt-cube add-log-exp difference-of-squares unswap-sqr
3×pow-to-exp pow-pow pow-exp sqr-pow
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 107
Calls
4 calls:
452.0ms
(* (cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series134.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (cbrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))
22.0ms
(pow (+ (* a a) (* b b)) 2.0)
22.0ms
(pow (+ (* a a) (* b b)) 2.0)
24.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify49.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
02821770
111061677
250011520

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.3b
(pow (+ (* a a) (* b b)) 2.0)
11.2b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
11.2b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1
6×add-exp-log unpow-prod-down pow-unpow sqrt-prod
4×sqrt-div add-cbrt-cube add-log-exp
2×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 pow-exp flip-+ sqr-pow
Counts
4 → 64
Calls
4 calls:
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
29.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
27.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(pow (+ (* a a) (* b b)) 2.0)
24.0ms
(pow (+ (* a a) (* b b)) 2.0)
19.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
19.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify101.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0202652
1753636
23003634
35002634

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

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×frac-times add-cbrt-cube 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 → 87
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)))

series80.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (cbrt (+ (* a a) (* b b))) (cbrt (+ (* a a) (* b b))))
18.0ms
(cbrt (+ (* a a) (* b b)))
18.0ms
(cbrt (+ (* a a) (* b b)))
21.0ms
(cbrt (+ (* a a) (* b b)))

simplify139.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
0222979
1943914
24107856
35001850

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes351.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02943
12943

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s20670×body80valid