Details

Time bar (total: 9.7s)

sample30.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
9.0ms272×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)))
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))))))

rewrite84.0ms

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:
11.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
31.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
9.0ms
(* 6.0 (* v v))
28.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series809.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
272.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
27.0ms
(* 6.0 (* v v))
407.0ms
(/ 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 (490.0ms)

IterNodesCost
03303068
19512820
240902433
done50002433

prune319.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
46×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
37×add-exp-log add-cbrt-cube
30×sqrt-prod
18×associate-*r/ associate-/r/
14×pow1
12×prod-exp cbrt-unprod associate-/l*
10×cbrt-undiv flip3-- div-exp flip--
9×div-inv
7×associate-/r*
6×prod-diff pow-prod-down
5×distribute-rgt-in distribute-lft-in associate-*r*
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
2×sub-neg frac-2neg sqrt-div clear-num *-commutative
1×associate-/l/ difference-of-squares unswap-sqr
Counts
4 → 173
Calls
4 calls:
16.0ms
(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
11.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
8.0ms
(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms
(* 6.0 (* v v))

series661.0ms

Counts
4 → 12
Calls
4 calls:
427.0ms
(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
104.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
105.0ms
(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
26.0ms
(* 6.0 (* v v))

simplify1.3s

Counts
185 → 185
Iterations

Useful iterations: 2 (527.0ms)

IterNodesCost
03784647
19964300
240113934
done50013934

prune397.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
486×times-frac
204×add-sqr-sqrt
203×add-cube-cbrt *-un-lft-identity
99×sqrt-prod
62×associate-/r/
52×add-exp-log add-cbrt-cube
36×associate-/l*
35×div-inv
26×flip3-+ flip-+
22×cbrt-undiv div-exp
18×associate-/r*
12×prod-exp cbrt-unprod
9×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* pow-prod-down clear-num associate-/l/
2×flip3-- sqrt-div associate-*r/ flip--
1×associate-*r* *-commutative unswap-sqr
Counts
4 → 365
Calls
4 calls:
28.0ms
(/ (/ 4.0 (/ (* (* 3.0 PI) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
14.0ms
(/ 4.0 (/ (* (* 3.0 PI) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v))))
20.0ms
(/ (* (* 3.0 PI) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v)))
7.0ms
(* 6.0 (* v v))

series998.0ms

Counts
4 → 12
Calls
4 calls:
628.0ms
(/ (/ 4.0 (/ (* (* 3.0 PI) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
136.0ms
(/ 4.0 (/ (* (* 3.0 PI) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v))))
209.0ms
(/ (* (* 3.0 PI) (- (* 1.0 1.0) (pow v 4))) (+ 1.0 (* v v)))
24.0ms
(* 6.0 (* v v))

simplify616.0ms

Counts
377 → 377
Iterations

Useful iterations: 1 (267.0ms)

IterNodesCost
066415800
1173814804
done500014804

prune1.1s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02128
12528
done2528

end0.0ms

sample760.0ms

Algorithm
intervals
Results
295.0ms8000×body80valid
279.0ms8079×body80nan