Details

Time bar (total: 3.8s)

sample29.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
8.0ms245×body80nan

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03210
19110
226310
362010
4113810
5147010
6151010
7151010

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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))))))

rewrite82.0ms

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))))))

series831.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
272.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
24.0ms
(* 6.0 (* v v))
425.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify103.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
08881350
144081176
250021174

prune256.0ms

Filtered
121 candidates to 78 candidates (64.5%)
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
(* (* 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
85×sqrt-prod
82×times-frac
78×add-sqr-sqrt
62×add-cube-cbrt *-un-lft-identity
48×add-exp-log add-cbrt-cube
47×associate-*r*
20×prod-exp cbrt-unprod
16×pow1 associate-*l*
11×cbrt-undiv div-exp
7×pow-prod-down
6×associate-/r* associate-/r/ associate-/l* unswap-sqr
5×associate-*r/
4×flip3-- sqrt-div flip-- add-log-exp
3×*-commutative div-inv
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-times sqrt-undiv frac-2neg associate-*l/ clear-num difference-of-squares
Counts
4 → 194
Calls
4 calls:
10.0ms
(* (* 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)))))
59.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

series962.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
25.0ms
(* 6.0 (* v v))
221.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
609.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
011082661
150012348

prune502.0ms

Filtered
206 candidates to 131 candidates (63.6%)
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

sample783.0ms

Algorithm
intervals
Results
309.0ms8000×body80valid
285.0ms8249×body80nan