Details

Time bar (total: 6.2s)

sample60.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
23.0ms258×body80nan

simplify57.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 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))))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
18×pow1
16×associate-*r/
15×prod-exp cbrt-unprod
13×flip3-- flip--
12×sqrt-div
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity pow-prod-down
8×frac-times associate-/r/
7×associate-*r*
6×add-log-exp
4×cbrt-undiv div-exp associate-*l* associate-*l/
3×times-frac sqrt-prod associate-/l*
2×*-commutative
1×sub-neg frac-2neg diff-log clear-num associate-/r* div-inv unswap-sqr
Counts
4 → 96
Calls
4 calls:
2.0ms
(- 2.0 (* 6.0 (* v v)))
29.0ms
(* (* (* 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))))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- 2.0 (* 6.0 (* v v)))
280.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
25.0ms
(* 6.0 (* v v))
445.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify94.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08361265
139441110
250021108

prune257.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
106×add-exp-log
52×add-cbrt-cube
50×prod-exp
46×add-sqr-sqrt
44×times-frac
37×add-cube-cbrt *-un-lft-identity
29×div-exp
25×associate-*r*
22×sqrt-prod
20×cbrt-unprod
17×pow1
14×cbrt-undiv
12×associate-*l*
9×rec-exp 1-exp
8×associate-/r/
7×pow-prod-down associate-/r*
6×associate-/l*
5×associate-*r/
4×flip3-- sqrt-div flip-- div-inv add-log-exp unswap-sqr
3×pow-flip
2×frac-2neg clear-num *-commutative
1×frac-times associate-*l/ inv-pow
Counts
4 → 171
Calls
4 calls:
16.0ms
(/ 1 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms
(* 6.0 (* v v))
4.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))
267.0ms
(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1 (* (* 3.0 PI) (- 1.0 (* v v))))
25.0ms
(* 6.0 (* v v))
165.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))
430.0ms
(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010602014
150011721

prune349.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))
1.0b
(* (cbrt (pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3)) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b
(pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3)
1.0b
(cbrt (pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
64×times-frac
60×cbrt-prod
48×add-cube-cbrt *-un-lft-identity
33×add-exp-log
30×unpow-prod-down cube-prod
27×associate-*l*
26×sqrt-prod
24×associate-*r*
19×add-cbrt-cube
16×associate-/r/
15×unswap-sqr
13×pow1 associate-*r/
11×prod-exp
10×pow-exp
8×flip3-- div-exp flip-- div-inv
6×associate-/r* sqr-pow
5×cbrt-undiv pow-pow cbrt-unprod
4×cube-div sqrt-div pow-prod-down add-log-exp rem-cube-cbrt
3×cube-mult rec-exp pow-unpow cbrt-div pow-flip 1-exp unpow3 associate-/l*
1×frac-times pow-to-exp frac-2neg pow1/3 associate-*l/ clear-num *-commutative rem-cbrt-cube inv-pow
Counts
4 → 209
Calls
4 calls:
5.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))
45.0ms
(* (cbrt (pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3)) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
15.0ms
(pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3)
5.0ms
(cbrt (pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3))

series968.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))
446.0ms
(* (cbrt (pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3)) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
249.0ms
(pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3)
101.0ms
(cbrt (pow (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) 3))

simplify52.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010772620
150012472

prune503.0ms

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
02713
12713

end0.0ms

sample1.7s

Algorithm
intervals
Results
805.0ms8000×body80valid
723.0ms8033×body80nan