Details

Time bar (total: 4.8s)

sample29.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
9.0ms273×body80nan

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03210
19110
226310
362010
4113810
5147010
6151010
7151010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 2.0 (* 6.0 (* 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))))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
19×pow1
16×associate-*r/
15×prod-exp cbrt-unprod
14×sqrt-div
13×flip3-- flip--
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow-prod-down
8×frac-times associate-/r/
7×associate-*r*
6×sqrt-prod
4×cbrt-undiv div-exp associate-*l* associate-*l/ add-log-exp
3×times-frac associate-/l*
2×*-commutative
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r* div-inv unswap-sqr
Counts
4 → 99
Calls
4 calls:
3.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
31.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
30.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series824.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
277.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
25.0ms
(* 6.0 (* v v))
440.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify308.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
08731328
141241178
250021175

prune263.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 2.0 (* 6.0 (* v v))))
0.2b
(* 6.0 (* v v))
1.0b
(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
85×add-exp-log
46×add-sqr-sqrt
43×add-cbrt-cube
41×times-frac prod-exp
36×add-cube-cbrt *-un-lft-identity
25×associate-*r* sqrt-prod
23×div-exp
17×cbrt-unprod
12×pow1 associate-*l*
11×cbrt-undiv
6×rec-exp sqrt-div 1-exp associate-/r* associate-/r/
4×flip3-- pow-prod-down flip-- add-log-exp unswap-sqr
3×associate-*r/ div-inv associate-/l*
2×*-commutative
1×frac-times rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*l/ clear-num
Counts
4 → 151
Calls
4 calls:
2.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
6.0ms
(* 6.0 (* v v))
67.0ms
(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
5.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

series698.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
25.0ms
(* 6.0 (* v v))
432.0ms
(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
162.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010201894
150011635

prune362.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* v v) (* v v))
0.2b
(* 6.0 (* v v))
1.0b
(* (/ 1 (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v))))) (* (+ 1.0 (* v v)) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))))
1.0b
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
149×add-exp-log
125×pow1
88×prod-exp
77×add-cbrt-cube
40×cbrt-unprod
36×pow-prod-up
29×div-exp pow-prod-down
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity pow-sqr
21×times-frac
18×pow-plus
14×cbrt-undiv
13×pow2 associate-*l*
12×sqrt-prod
9×frac-times rec-exp 1-exp associate-*r/
6×associate-/r*
5×associate-*l/
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×associate-*r* *-commutative associate-/l*
2×flip3-- sqrt-div flip-- div-inv unswap-sqr
1×frac-2neg swap-sqr clear-num
Counts
4 → 196
Calls
4 calls:
12.0ms
(* (* v v) (* v v))
6.0ms
(* 6.0 (* v v))
80.0ms
(* (/ 1 (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v))))) (* (+ 1.0 (* v v)) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))))
5.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

series681.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* v v) (* v v))
24.0ms
(* 6.0 (* v v))
455.0ms
(* (/ 1 (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v))))) (* (+ 1.0 (* v v)) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))))
170.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011472423
150011933

prune387.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03017
13017

end0.0ms

sample746.0ms

Algorithm
intervals
Results
293.0ms8000×body80valid
275.0ms8140×body80nan