Details

Time bar (total: 22.6s)

sample77.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
27.0ms281×body80nan

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01620
13220
29020
326820
463320
5119120
6147820
7149620
done149620

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize20.0ms

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))))))

rewrite280.0ms

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:
45.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
94.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
20.0ms
(* 6.0 (* v v))
114.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
159.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
391.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
45.0ms
(* 6.0 (* v v))
630.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify2.8s

Counts
135 → 135
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03303068
19322820
238392441
done50012432

prune520.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 2.0 (* 6.0 (* v v))))
0.0b
(* (/ (/ (/ 4.0 (- (pow 1.0 3) (pow v 6))) (* 3.0 PI)) (sqrt (- 2.0 (* 6.0 (* v v))))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))
0.1b
(* (* v v) (* v v))
0.2b
(* 6.0 (* v v))

rewrite832.0ms

Algorithm
rewrite-expression-head
Rules
962×times-frac
566×add-sqr-sqrt
358×associate-*l*
286×*-un-lft-identity
250×add-cube-cbrt
216×difference-of-squares
178×sqrt-prod
126×unpow-prod-down sqr-pow
123×pow1
54×cube-prod
46×add-exp-log add-cbrt-cube
36×pow-prod-up
27×pow-prod-down
22×pow-sqr
19×prod-exp cbrt-unprod
18×pow-plus distribute-lft-out--
14×associate-/r/
13×pow2 div-inv
11×cbrt-undiv div-exp
8×flip3-- flip--
5×associate-*r* unswap-sqr
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×*-commutative
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 swap-sqr associate-*l/
Counts
4 → 493
Calls
4 calls:
13.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
665.0ms
(* (/ (/ (/ 4.0 (- (pow 1.0 3) (pow v 6))) (* 3.0 PI)) (sqrt (- 2.0 (* 6.0 (* v v))))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))
51.0ms
(* (* v v) (* v v))
19.0ms
(* 6.0 (* v v))

series805.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
615.0ms
(* (/ (/ (/ 4.0 (- (pow 1.0 3) (pow v 6))) (* 3.0 PI)) (sqrt (- 2.0 (* 6.0 (* v v))))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))
40.0ms
(* (* v v) (* v v))
43.0ms
(* 6.0 (* v v))

simplify1.8s

Counts
505 → 505
Iterations

Useful iterations: done (1.7s)

IterNodesCost
078218054
1315415221
done500114354

prune3.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (+ (pow (fma 1.0 (* v v) (pow v 4)) 3) (pow 1.0 6)) (/ (/ 4.0 (- (pow 1.0 3) (pow v 6))) (* 3.0 PI))) (* (fma (fma 1.0 (* v v) (pow v 4)) (fma (* v v) (fma v v 1.0) (- (* 1.0 1.0))) (pow 1.0 4)) (sqrt (- 2.0 (* 6.0 (* v v))))))
0.0b
(* (fma (fma 1.0 (* v v) (pow v 4)) (fma (* v v) (fma v v 1.0) (- (* 1.0 1.0))) (pow 1.0 4)) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.1b
(pow (fma 1.0 (* v v) (pow v 4)) 3)
0.2b
(* 6.0 (* v v))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log add-cbrt-cube
24×cbrt-undiv div-exp prod-exp cbrt-unprod
16×add-sqr-sqrt
12×pow1
11×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×associate-*l*
5×associate-*r/ associate-/l/
4×expm1-log1p-u sqrt-div pow-prod-down sqrt-prod log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod unswap-sqr
2×frac-times flip3-- flip3-+ associate-*l/ associate-/r/ *-commutative flip-- flip-+
1×cube-mult pow-to-exp pow-pow frac-2neg times-frac unpow3 pow-exp clear-num associate-/r* div-inv associate-/l* rem-cube-cbrt sqr-pow
Counts
4 → 118
Calls
4 calls:
104.0ms
(/ (* (+ (pow (fma 1.0 (* v v) (pow v 4)) 3) (pow 1.0 6)) (/ (/ 4.0 (- (pow 1.0 3) (pow v 6))) (* 3.0 PI))) (* (fma (fma 1.0 (* v v) (pow v 4)) (fma (* v v) (fma v v 1.0) (- (* 1.0 1.0))) (pow 1.0 4)) (sqrt (- 2.0 (* 6.0 (* v v))))))
26.0ms
(* (fma (fma 1.0 (* v v) (pow v 4)) (fma (* v v) (fma v v 1.0) (- (* 1.0 1.0))) (pow 1.0 4)) (sqrt (- 2.0 (* 6.0 (* v v)))))
3.0ms
(pow (fma 1.0 (* v v) (pow v 4)) 3)
17.0ms
(* 6.0 (* v v))

series1.4s

Counts
4 → 12
Calls
4 calls:
932.0ms
(/ (* (+ (pow (fma 1.0 (* v v) (pow v 4)) 3) (pow 1.0 6)) (/ (/ 4.0 (- (pow 1.0 3) (pow v 6))) (* 3.0 PI))) (* (fma (fma 1.0 (* v v) (pow v 4)) (fma (* v v) (fma v v 1.0) (- (* 1.0 1.0))) (pow 1.0 4)) (sqrt (- 2.0 (* 6.0 (* v v))))))
323.0ms
(* (fma (fma 1.0 (* v v) (pow v 4)) (fma (* v v) (fma v v 1.0) (- (* 1.0 1.0))) (pow 1.0 4)) (sqrt (- 2.0 (* 6.0 (* v v)))))
105.0ms
(pow (fma 1.0 (* v v) (pow v 4)) 3)
33.0ms
(* 6.0 (* v v))

simplify2.8s

Counts
130 → 130
Iterations

Useful iterations: done (2.8s)

IterNodesCost
03556635
110476293
245654615
done50004609

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes47.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03462
14262
done4262

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.3s8000×body80valid
796.0ms7943×body80nan