Details

Time bar (total: 9.1s)

sample28.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
8.0ms234×body80nan

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01620
13220
28820
324520
450420
580320
6102120
7104420
done104420

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))))))

rewrite82.0ms

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:
33.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
11.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
6.0ms
(* 6.0 (* v v))
27.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series807.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
105.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
24.0ms
(* 6.0 (* v v))
409.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify1.3s

Counts
135 → 135
Iterations

Useful iterations: 2 (483.0ms)

IterNodesCost
03303068
19512820
240922433
done50002433

prune299.0ms

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)

rewrite90.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 162
Calls
4 calls:
12.0ms
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
6.0ms
(* 6.0 (* v v))
29.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
34.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

series1.7s

Counts
4 → 12
Calls
4 calls:
353.0ms
(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))
425.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
924.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

simplify370.0ms

Counts
174 → 174
Iterations

Useful iterations: done (363.0ms)

IterNodesCost
04005925
111795113
done50004739

prune477.0ms

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 (* (+ (* 1.0 (* 3.0 PI)) (- (* 3.0 (* (pow v 2) PI)))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite37.0ms

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×expm1-log1p-u frac-times unpow-prod-down pow-prod-down log1p-expm1-u 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 → 102
Calls
4 calls:
11.0ms
(* 3.0 (* (pow v 2) PI))
6.0ms
(* 6.0 (* v v))
6.0ms
(* (pow v 2) PI)
12.0ms
(/ 4.0 (* (+ (* 1.0 (* 3.0 PI)) (- (* 3.0 (* (pow v 2) PI)))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series544.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* 3.0 (* (pow v 2) PI))
31.0ms
(* 6.0 (* v v))
25.0ms
(* (pow v 2) PI)
448.0ms
(/ 4.0 (* (+ (* 1.0 (* 3.0 PI)) (- (* 3.0 (* (pow v 2) PI)))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify1.0s

Counts
114 → 114
Iterations

Useful iterations: 2 (482.0ms)

IterNodesCost
02571940
16781781
227301509
done50001509

prune295.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes56.0ms

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

sample763.0ms

Algorithm
intervals
Results
304.0ms8000×body80valid
274.0ms8044×body80nan