Details

Time bar (total: 6.2s)

sample51.0ms

Algorithm
intervals
Results
31.0ms603×body80valid

simplify77.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05114
115514
243014
3119514
4252614
5500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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) (+ 3.0 a)))))
0.1b
(* (* a a) (- 1.0 a))
0.2b
(* (* b b) (+ 3.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
12×add-sqr-sqrt *-un-lft-identity
9×associate-*r*
8×add-cube-cbrt
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×unpow-prod-down pow-unpow
2×sub-neg associate-+r+ flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×+-commutative pow-to-exp flip3-- pow-pow pow-exp sum-log flip-- distribute-lft-out distribute-lft-out-- difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
52.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
29.0ms
(* (* a a) (- 1.0 a))
31.0ms
(* (* b b) (+ 3.0 a))
10.0ms
(pow (+ (* a a) (* b b)) 2.0)

series307.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
51.0ms
(* (* a a) (- 1.0 a))
37.0ms
(* (* b b) (+ 3.0 a))
106.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify67.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
0506651
12520583
25001583

prune254.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
0.1b
(* (* a a) (- (* 1.0 1.0) (* a a)))
0.2b
(* (* b b) (+ 3.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
23×add-cbrt-cube
16×*-un-lft-identity
15×pow1
12×add-sqr-sqrt
10×add-cube-cbrt
9×prod-exp cbrt-unprod
8×associate-*r*
6×associate-*r/ pow-prod-down
4×times-frac associate-/r* add-log-exp
3×cbrt-undiv distribute-rgt-in unpow-prod-down pow-unpow distribute-lft-in div-exp distribute-lft-out
2×sub-neg flip3-- flip3-+ associate-*l* associate-/r/ *-commutative flip-- flip-+ associate-/l/ unswap-sqr
1×pow-to-exp pow-pow frac-2neg pow-exp clear-num div-inv associate-/l* difference-of-squares sqr-pow
Counts
4 → 96
Calls
4 calls:
36.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
37.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
28.0ms
(* (* b b) (+ 3.0 a))
12.0ms
(pow (+ (* a a) (* b b)) 2.0)

series331.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (* (* a a) (- (* 1.0 1.0) (* a a))) (+ 1.0 a))
80.0ms
(* (* a a) (- (* 1.0 1.0) (* a a)))
33.0ms
(* (* b b) (+ 3.0 a))
106.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify84.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
0565735
13088616
25001616

prune312.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (- (* 1.0 1.0) (* a a)))
0.1b
(* (* a a) (* (cbrt (- (* 1.0 1.0) (* a a))) (cbrt (- (* 1.0 1.0) (* a a)))))
0.2b
(* (* b b) (+ 3.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
38×pow1
22×add-exp-log
17×pow-prod-down add-cbrt-cube
14×cbrt-div
12×associate-*r/
11×prod-exp cbrt-unprod
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt
7×flip3-- flip--
5×associate-*r*
4×cbrt-prod frac-times pow-plus pow-prod-up add-log-exp
3×unpow-prod-down pow-unpow
2×pow2 associate-*l* associate-*l/ pow-sqr *-commutative unswap-sqr
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in flip3-+ pow1/3 pow-exp flip-+ distribute-lft-out difference-of-squares sqr-pow
Counts
4 → 92
Calls
4 calls:
6.0ms
(cbrt (- (* 1.0 1.0) (* a a)))
85.0ms
(* (* a a) (* (cbrt (- (* 1.0 1.0) (* a a))) (cbrt (- (* 1.0 1.0) (* a a)))))
29.0ms
(* (* b b) (+ 3.0 a))
12.0ms
(pow (+ (* a a) (* b b)) 2.0)

series561.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(cbrt (- (* 1.0 1.0) (* a a)))
238.0ms
(* (* a a) (* (cbrt (- (* 1.0 1.0) (* a a))) (cbrt (- (* 1.0 1.0) (* a a)))))
33.0ms
(* (* b b) (+ 3.0 a))
106.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify80.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0655936
12853817
25003806

prune388.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
8.6b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.6b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
8.6b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

rewrite328.0ms

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:
235.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
29.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
28.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
32.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

series794.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))))
192.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
191.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))
191.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03433024
111932795
250012567

prune396.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03329
13329

end0.0ms

sample1.4s

Algorithm
intervals
Results
975.0ms20441×body80valid