Details

Time bar (total: 8.6s)

sample28.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
8.0ms234×body80nan

simplify972.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01620
13220
28820
323320
445420
567420
685020
786220
done86220

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b
(* (* 3.0 PI) (- 1.0 (* v v)))
0.1b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
23×pow1
18×associate-*r/ prod-exp cbrt-unprod
13×flip3-- flip--
12×add-sqr-sqrt sqrt-div pow-prod-down
11×associate-*r*
10×add-cube-cbrt *-un-lft-identity
8×frac-times associate-/r/
5×associate-*l*
4×cbrt-undiv div-exp associate-*l/ add-log-exp
3×times-frac sqrt-prod *-commutative associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-2neg clear-num associate-/r* div-inv difference-of-squares unswap-sqr
Counts
4 → 109
Calls
4 calls:
34.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
10.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
6.0ms
(* 6.0 (* v v))
29.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
267.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
106.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
24.0ms
(* 6.0 (* v v))
417.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify1.2s

Counts
121 → 121
Iterations

Useful iterations: 2 (414.0ms)

IterNodesCost
03072810
18852584
238402215
done50002215

prune278.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
0.1b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
40×associate-*r/ associate-/r/
38×add-exp-log add-cbrt-cube
36×cbrt-prod
30×unpow-prod-down flip3-- sqrt-div cube-prod flip--
20×frac-times
18×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
15×times-frac prod-exp cbrt-unprod
10×pow1 associate-*l/
8×cbrt-undiv div-exp
5×pow-exp div-inv rem-cube-cbrt
4×add-log-exp
3×pow-unpow associate-*l* pow-prod-down associate-/l*
2×cube-div cube-mult unpow3 sqr-pow
1×pow-to-exp cbrt-div pow-pow frac-2neg pow1/3 associate-*r* clear-num associate-/r* *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 154
Calls
4 calls:
12.0ms
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
7.0ms
(* 6.0 (* v v))
31.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
36.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

series1.8s

Counts
4 → 12
Calls
4 calls:
357.0ms
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
24.0ms
(* 6.0 (* v v))
431.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
944.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

simplify365.0ms

Counts
166 → 166
Iterations

Useful iterations: done (358.0ms)

IterNodesCost
03925777
111385031
done50004637

prune437.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 3.0 (* (pow v 2) PI))
0.1b
(* 6.0 (* v v))
0.2b
(* (pow v 2) PI)
1.0b
(/ 4.0 (* (+ (* (* 3.0 PI) 1.0) (- (* 3.0 (* (pow v 2) PI)))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
21×add-cbrt-cube
18×add-sqr-sqrt
14×associate-*l* prod-exp
11×pow1 add-cube-cbrt *-un-lft-identity
8×associate-/r/ cbrt-unprod
6×sqrt-div
5×associate-*r* unswap-sqr
4×frac-times unpow-prod-down pow-prod-down add-log-exp
3×flip3-- flip3-+ times-frac *-commutative flip-- flip-+ associate-/l*
2×cbrt-undiv pow-to-exp associate-*r/ div-exp associate-*l/ pow-exp unpow2 sqr-pow
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 94
Calls
4 calls:
8.0ms
(* 3.0 (* (pow v 2) PI))
6.0ms
(* 6.0 (* v v))
6.0ms
(* (pow v 2) PI)
13.0ms
(/ 4.0 (* (+ (* (* 3.0 PI) 1.0) (- (* 3.0 (* (pow v 2) PI)))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series553.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* 3.0 (* (pow v 2) PI))
31.0ms
(* 6.0 (* v v))
26.0ms
(* (pow v 2) PI)
456.0ms
(/ 4.0 (* (+ (* (* 3.0 PI) 1.0) (- (* 3.0 (* (pow v 2) PI)))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify849.0ms

Counts
106 → 106
Iterations

Useful iterations: 2 (295.0ms)

IterNodesCost
02491848
16591702
226601425
done50011425

prune266.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01923
12323
done2323

end0.0ms

sample757.0ms

Algorithm
intervals
Results
298.0ms8000×body80valid
281.0ms8044×body80nan