Details

Time bar (total: 19.2s)

sample56.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
17.0ms262×body80nan

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01620
13220
29020
326820
463320
5119120
6147820
7149620
done149620

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize23.0ms

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

rewrite297.0ms

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:
52.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
110.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
31.0ms
(* 6.0 (* v v))
95.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
397.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
45.0ms
(* 6.0 (* v v))
674.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify2.0s

Counts
135 → 135
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03303068
19322820
238392441
done50012432

prune478.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
46×add-sqr-sqrt
43×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
28×add-exp-log add-cbrt-cube
16×associate-*r/ associate-/r/
15×pow1
10×flip3-- flip--
9×prod-exp cbrt-unprod associate-/l*
8×div-inv
7×cbrt-undiv div-exp
6×prod-diff pow-prod-down associate-/r*
5×distribute-rgt-in distribute-lft-in associate-*r*
4×expm1-log1p-u sqrt-div associate-*l* log1p-expm1-u add-log-exp
2×sub-neg *-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/ difference-of-squares unswap-sqr
Counts
4 → 163
Calls
4 calls:
46.0ms
(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
8.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
32.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
24.0ms
(* 6.0 (* v v))

series943.0ms

Counts
4 → 12
Calls
4 calls:
630.0ms
(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
106.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
160.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
47.0ms
(* 6.0 (* v v))

simplify2.3s

Counts
175 → 175
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03794432
19824088
235483792
done50003783

prune614.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite610.0ms

Algorithm
rewrite-expression-head
Rules
444×times-frac
184×add-sqr-sqrt
183×add-cube-cbrt *-un-lft-identity
120×pow1
99×sqrt-prod
51×associate-/r/
41×add-exp-log add-cbrt-cube
36×pow-prod-up
32×associate-/l*
29×div-inv
26×pow-prod-down
22×flip3-+ pow-sqr flip-+
18×pow-plus
14×prod-exp cbrt-unprod
13×pow2
12×cbrt-undiv div-exp
6×associate-/r* add-log-exp
4×expm1-log1p-u associate-*l* log1p-expm1-u
2×sqrt-div associate-*r* *-commutative unswap-sqr
1×+-commutative distribute-rgt-out flip3-- fma-def frac-2neg swap-sqr clear-num sum-log flip-- associate-/l/
Counts
4 → 356
Calls
4 calls:
458.0ms
(/ (/ 4.0 (/ (* 3.0 (* PI (- (pow 1.0 3) (pow v 6)))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
43.0ms
(+ (* (* v v) (* v v)) (* 1.0 (* v v)))
46.0ms
(* (* v v) (* v v))
19.0ms
(* 6.0 (* v v))

series924.0ms

Counts
4 → 12
Calls
4 calls:
698.0ms
(/ (/ 4.0 (/ (* 3.0 (* PI (- (pow 1.0 3) (pow v 6)))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
135.0ms
(+ (* (* v v) (* v v)) (* 1.0 (* v v)))
38.0ms
(* (* v v) (* v v))
52.0ms
(* 6.0 (* v v))

simplify1.1s

Counts
368 → 368
Iterations

Useful iterations: done (1.1s)

IterNodesCost
066919813
1170215658
done500015080

prune2.2s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02640
13240
done3240

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.2s7995×body80nan
788.0ms8000×body80valid