Details

Time bar (total: 6.6s)

sample31.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
8.0ms246×body80nan

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03210
19110
227510
367210
4130310
5173710
6180210
7180210

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.2b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
23×pow1
18×associate-*r/ prod-exp cbrt-unprod
14×add-sqr-sqrt
13×flip3-- flip--
12×add-cube-cbrt *-un-lft-identity sqrt-div pow-prod-down
11×associate-*r*
8×frac-times associate-/r/
6×prod-diff
5×distribute-rgt-in distribute-lft-in associate-*l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*l/ log1p-expm1-u add-log-exp
3×times-frac sqrt-prod *-commutative associate-/l*
2×sub-neg
1×frac-2neg clear-num associate-/r* div-inv difference-of-squares unswap-sqr
Counts
4 → 123
Calls
4 calls:
26.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
72.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
16.0ms
(* 6.0 (* v v))
66.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series974.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
447.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
23.0ms
(* 6.0 (* v v))
407.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify117.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
09551468
146961282
250011281

prune309.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4.0 (fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI))))))))
1.0b
(fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI)))))))
1.0b
(* 3.0 (sqrt 2.0))
1.0b
(pow (sqrt 2.0) 3)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
10×sqrt-prod
9×add-exp-log times-frac add-cbrt-cube
8×pow1
6×unpow-prod-down cube-prod associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow pow-pow associate-*l* associate-/r* associate-/l*
2×unswap-sqr
1×cbrt-undiv cube-mult pow-to-exp frac-2neg sqrt-pow1 pow1/2 unpow3 div-exp pow-prod-down pow-exp prod-exp clear-num *-commutative sqrt-pow2 cbrt-unprod fma-udef div-inv rem-cube-cbrt sqr-pow
Counts
4 → 97
Calls
4 calls:
5.0ms
(/ 4.0 (fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI))))))))
0.0ms
(fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI)))))))
9.0ms
(* 3.0 (sqrt 2.0))
4.0ms
(pow (sqrt 2.0) 3)

series1.3s

Counts
4 → 8
Calls
4 calls:
909.0ms
(/ 4.0 (fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI))))))))
373.0ms
(fma (* 3.0 (sqrt 2.0)) PI (- (* 9.0 (/ (* (pow v 4) PI) (sqrt 2.0))) (fma 9.0 (/ (* (pow v 2) PI) (sqrt 2.0)) (fma 13.5 (/ (* (pow v 4) PI) (pow (sqrt 2.0) 3)) (* 3.0 (* (sqrt 2.0) (* (pow v 2) PI)))))))
0.0ms
(* 3.0 (sqrt 2.0))
0.0ms
(pow (sqrt 2.0) 3)

simplify92.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
05482041
130531856
250011845

prune412.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.2b
(* 6.0 (* v v))
1.0b
(/ 4.0 (cbrt (pow (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))) 3)))
1.0b
(pow (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))) 3)

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
32×cbrt-prod
30×add-exp-log
29×add-sqr-sqrt add-cbrt-cube
28×pow1 add-cube-cbrt *-un-lft-identity
24×associate-*r/
18×flip3-- sqrt-div flip--
16×cube-div
15×pow-prod-down prod-exp cbrt-unprod
12×frac-times
11×associate-/r*
8×cbrt-div associate-/r/
7×associate-*r*
6×associate-*l/
5×cube-mult unpow-prod-down unpow3 cube-prod sqr-pow
4×expm1-log1p-u pow-pow associate-*l* pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×pow-unpow sqrt-prod associate-/l*
2×*-commutative
1×cbrt-undiv pow-to-exp frac-2neg div-exp clear-num div-inv unswap-sqr
Counts
4 → 162
Calls
4 calls:
74.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
16.0ms
(* 6.0 (* v v))
20.0ms
(/ 4.0 (cbrt (pow (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))) 3)))
66.0ms
(pow (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))) 3)

series1.3s

Counts
4 → 12
Calls
4 calls:
258.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
30.0ms
(* 6.0 (* v v))
401.0ms
(/ 4.0 (cbrt (pow (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))) 3)))
653.0ms
(pow (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))) 3)

simplify52.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012112654
150012540

prune556.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes44.0ms

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
03426
13426

end0.0ms

sample827.0ms

Algorithm
intervals
Results
306.0ms8000×body80valid
279.0ms7949×body80nan