Details

Time bar (total: 3.8s)

sample29.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
9.0ms245×body80nan

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03210
19110
227510
367210
4130310
5173710
6180210
7180210

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

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))))))

rewrite41.0ms

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:
7.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
12.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
5.0ms
(* 6.0 (* v v))
12.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series825.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
270.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
29.0ms
(* 6.0 (* v v))
420.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify117.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
09551468
146961282
250011281

prune313.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

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))))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
82×times-frac
80×add-sqr-sqrt
64×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×prod-diff associate-/r* associate-/r/ associate-/l* unswap-sqr
5×distribute-rgt-in distribute-lft-in associate-*r/
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u add-log-exp
3×*-commutative div-inv
2×sub-neg
1×frac-times sqrt-undiv frac-2neg associate-*l/ clear-num difference-of-squares
Counts
4 → 208
Calls
4 calls:
7.0ms
(* (* 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)))))
26.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

series970.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
25.0ms
(* 6.0 (* v v))
219.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
623.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011702781
150012456

prune542.0ms

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

sample790.0ms

Algorithm
intervals
Results
305.0ms8000×body80valid
296.0ms8249×body80nan