Details

Time bar (total: 4.7s)

sample48.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
16.0ms243×body80nan

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03210
19110
226310
362010
4113810
5147010
6151010
7151010

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize12.0ms

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))))))

rewrite83.0ms

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:
10.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
31.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
31.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series846.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
277.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
31.0ms
(* 6.0 (* v v))
432.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify118.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
08881350
144081176
250021174

prune267.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
91×sqrt-prod
88×times-frac
80×add-sqr-sqrt
65×add-cube-cbrt *-un-lft-identity
52×add-exp-log add-cbrt-cube
43×associate-*r*
20×prod-exp cbrt-unprod
15×associate-*l*
14×cbrt-undiv div-exp
12×associate-/l*
11×pow1
8×associate-/r/
7×associate-/r*
6×unswap-sqr
5×associate-*r/
4×flip3-- sqrt-div pow-prod-down flip-- div-inv add-log-exp
2×frac-2neg clear-num *-commutative
1×frac-times sqrt-undiv associate-*l/
Counts
4 → 200
Calls
4 calls:
9.0ms
(/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms
(* 6.0 (* v v))
6.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
61.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v))))
31.0ms
(* 6.0 (* v v))
209.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
618.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011472816
150012486

prune717.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02213
12213

end0.0ms

sample1.4s

Algorithm
intervals
Results
616.0ms8000×body80valid
538.0ms8041×body80nan