Details

Time bar (total: 8.7s)

sample97.0ms

Algorithm
intervals
Results
74.0ms723×body80valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
05515
117914
256113
3182413
4500213

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite60.0ms

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:
28.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
13.0ms
(* (* a a) (+ 1.0 a))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
4.0ms
(* (* a a) (+ 1.0 a))
22.0ms
(pow (+ (* a a) (* b b)) 2.0)
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify75.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
0564828
12826724
25001715

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
0.1b
(* (* a a) (+ 1.0 a))
0.2b
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.6b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
16×pow1 add-exp-log add-cbrt-cube
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt associate-*r*
7×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
6×prod-diff
5×associate-*l*
4×expm1-log1p-u flip3-+ frac-add flip-+ log1p-expm1-u add-log-exp
3×flip3-- *-commutative flip-- unswap-sqr
2×sub-neg
1×fma-udef distribute-lft-out
Counts
4 → 97
Calls
4 calls:
35.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
13.0ms
(* (* a a) (+ 1.0 a))
0.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))
4.0ms
(* (* a a) (+ 1.0 a))
34.0ms
(fma (pow (+ (* a a) (* b b)) (/ 2.0 2)) (pow (+ (* a a) (* b b)) (/ 2.0 2)) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify99.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06661047
13763904
25001897

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* b b) (- 1.0 (* 3.0 a)))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log unpow-prod-down add-cbrt-cube
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* pow-prod-down prod-exp cbrt-unprod sqr-pow
2×sub-neg associate-*r/
1×flip3-- associate-*l* *-commutative flip-- unswap-sqr
Counts
4 → 84
Calls
4 calls:
12.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
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))

series121.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
39.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
37.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
37.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0315769
11231692
25002681

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

8.9b
(cbrt (pow (+ (* a a) (* b b)) (/ 2.0 2)))
8.9b
(cbrt (pow (+ (* a a) (* b b)) (/ 2.0 2)))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))
16.1b
(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
12×add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp sqr-pow
Counts
4 → 68
Calls
4 calls:
4.0ms
(cbrt (pow (+ (* a a) (* b b)) (/ 2.0 2)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) (/ 2.0 2)))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

series153.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(cbrt (pow (+ (* a a) (* b b)) (/ 2.0 2)))
37.0ms
(cbrt (pow (+ (* a a) (* b b)) (/ 2.0 2)))
39.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))
38.0ms
(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0163728
1392678
21340660
35001660

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes425.0ms

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
02821
12821

end0.0ms

sample2.5s

Algorithm
intervals
Results
2.1s20670×body80valid