Details

Time bar (total: 4.7s)

sample39.0ms

Algorithm
intervals
Results
24.0ms654×body80valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0258
1418
2678
31198
43098
514948
650018

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
9×add-cbrt-cube
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
3×unpow-prod-down pow-unpow associate-*l* pow-prod-down prod-exp cbrt-unprod
2×+-commutative flip3-+ sum-log flip-+
1×pow-to-exp pow-pow associate-*r* pow-exp *-commutative unswap-sqr sqr-pow
Counts
4 → 58
Calls
4 calls:
4.0ms
(+ (* a a) (* b b))
6.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
5.0ms
(* 4.0 (* b b))
4.0ms
(pow (+ (* a a) (* b b)) 2.0)

series222.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(+ (* a a) (* b b))
60.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
30.0ms
(* 4.0 (* b b))
101.0ms
(pow (+ (* a a) (* b b)) 2.0)

simplify40.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0322413
11353379
25001379

prune159.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite39.0ms

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 (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series685.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
183.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
183.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
184.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify144.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 3 (123.0ms)

IterNodesCost
02621815
19421694
242611539
350011529

prune311.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
0.0b
(* 2 (* (pow a 2) (pow b 2)))
0.0b
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
3.6b
(* (pow a 2) (pow b 2))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
39×add-exp-log
28×prod-exp
25×add-sqr-sqrt
16×unswap-sqr
14×unpow-prod-down
12×pow-to-exp pow-exp
11×*-un-lft-identity associate-*l* add-cbrt-cube add-log-exp
10×unpow2 sqr-pow
9×add-cube-cbrt associate-*r*
6×pow1
4×sum-log cbrt-unprod
2×+-commutative flip3-+ pow-prod-down *-commutative flip-+
1×associate-+r+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
11.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
7.0ms
(* 2 (* (pow a 2) (pow b 2)))
4.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms
(* (pow a 2) (pow b 2))

series176.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
35.0ms
(* 2 (* (pow a 2) (pow b 2)))
55.0ms
(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
31.0ms
(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0375699
11611622
25002616

prune239.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
12.4b
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
32.3b
(cbrt (+ (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)) (- (* (* 4.0 (* b b)) (* 4.0 (* b b))) (* (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))))
33.5b
(cbrt (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
10×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt cbrt-div
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
1×sum-cubes distribute-lft-out
Counts
4 → 54
Calls
4 calls:
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
6.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
17.0ms
(cbrt (+ (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)) (- (* (* 4.0 (* b b)) (* 4.0 (* b b))) (* (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))))
14.0ms
(cbrt (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)))

series727.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
180.0ms
(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
202.0ms
(cbrt (+ (* (pow (+ (* a a) (* b b)) 2.0) (pow (+ (* a a) (* b b)) 2.0)) (- (* (* 4.0 (* b b)) (* 4.0 (* b b))) (* (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))))
160.0ms
(cbrt (+ (pow (pow (+ (* a a) (* b b)) 2.0) 3) (pow (* 4.0 (* b b)) 3)))

simplify53.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03121363
111061259
250021224

prune374.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes140.0ms

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
0158
1158

end0.0ms

sample1.1s

Algorithm
intervals
Results
752.0ms20313×body80valid