Details

Time bar (total: 6.1s)

sample30.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
9.0ms272×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
(* (* 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))))))

rewrite84.0ms

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))
30.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series840.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
285.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
23.0ms
(* 6.0 (* v v))
425.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify108.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08881350
144081176
250021174

prune266.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

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:
13.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
7.0ms
(* 6.0 (* v v))
6.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
57.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

series945.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
24.0ms
(* 6.0 (* v v))
216.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
598.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011082661
150012348

prune506.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* v v) (* v v))
0.2b
(* 6.0 (* v v))
1.0b
(* (/ (sqrt 4.0) (/ (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))

rewrite308.0ms

Algorithm
rewrite-expression-head
Rules
166×times-frac
142×add-sqr-sqrt
122×pow1 sqrt-prod
89×add-cube-cbrt *-un-lft-identity
68×add-exp-log add-cbrt-cube
63×associate-*l*
44×associate-*r*
36×pow-prod-up
27×pow-prod-down prod-exp cbrt-unprod
22×pow-sqr
20×cbrt-undiv div-exp
18×pow-plus
17×associate-/r/ unswap-sqr
13×pow2
9×div-inv
6×flip3-+ associate-/r* flip-+ associate-/l*
4×sqrt-div add-log-exp
3×*-commutative
2×flip3-- flip--
1×frac-times sqrt-undiv frac-2neg associate-*r/ swap-sqr associate-*l/ clear-num
Counts
4 → 293
Calls
4 calls:
12.0ms
(* (* v v) (* v v))
7.0ms
(* 6.0 (* v v))
267.0ms
(* (/ (sqrt 4.0) (/ (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))
6.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))

series950.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* v v) (* v v))
24.0ms
(* 6.0 (* v v))
671.0ms
(* (/ (sqrt 4.0) (/ (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (+ (* 1.0 1.0) (+ (* (* v v) (* v v)) (* 1.0 (* v v)))))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))
218.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014665603
150014912

prune972.0ms

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
03424
13424

end0.0ms

sample775.0ms

Algorithm
intervals
Results
313.0ms8000×body80valid
282.0ms8079×body80nan