Details

Time bar (total: 5.4s)

sample30.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
9.0ms273×body80nan

simplify64.0ms

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

localize12.0ms

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))))))

rewrite78.0ms

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 expm1-log1p-u div-exp associate-*l* associate-*l/ log1p-expm1-u 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 → 107
Calls
4 calls:
4.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
32.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
32.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series773.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
261.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
27.0ms
(* 6.0 (* v v))
408.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify103.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
09051373
142751219
250011215

prune292.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

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
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 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)))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
88×sqrt-prod
82×times-frac
78×add-sqr-sqrt
62×add-cube-cbrt *-un-lft-identity
43×add-exp-log associate-*r* add-cbrt-cube
17×prod-exp cbrt-unprod
15×associate-*l*
12×pow1
11×cbrt-undiv div-exp
6×sqrt-div associate-/r* associate-/r/ associate-/l* unswap-sqr
4×expm1-log1p-u flip3-- pow-prod-down flip-- log1p-expm1-u add-log-exp
3×associate-*r/ div-inv
2×*-commutative
1×frac-times rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 associate-*l/ clear-num
Counts
4 → 192
Calls
4 calls:
3.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
7.0ms
(* 6.0 (* v v))
61.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 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)))))

series932.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(sqrt (- 2.0 (* 6.0 (* v v))))
36.0ms
(* 6.0 (* v v))
607.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))
207.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011252690
150012393

prune546.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

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) (- (* 1.0 1.0) (* (* v v) (* v v))))) (/ (* (fma v v 1.0) (sqrt 4.0)) (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b
(/ (* (fma v v 1.0) (sqrt 4.0)) (sqrt (- 2.0 (* 6.0 (* v v)))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
122×pow1
80×add-exp-log add-cbrt-cube
37×prod-exp cbrt-unprod
36×pow-prod-up
27×pow-prod-down
22×pow-sqr
19×cbrt-undiv div-exp
18×add-sqr-sqrt times-frac pow-plus
16×associate-*l*
15×add-cube-cbrt *-un-lft-identity
14×associate-*r*
13×pow2
12×sqrt-prod
6×associate-/r* associate-/r/
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×flip3-- associate-*r/ *-commutative flip-- div-inv unswap-sqr
1×frac-times frac-2neg swap-sqr associate-*l/ clear-num associate-/l*
Counts
4 → 180
Calls
4 calls:
13.0ms
(* (* v v) (* v v))
7.0ms
(* 6.0 (* v v))
58.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v))))) (/ (* (fma v v 1.0) (sqrt 4.0)) (sqrt (- 2.0 (* 6.0 (* v v))))))
7.0ms
(/ (* (fma v v 1.0) (sqrt 4.0)) (sqrt (- 2.0 (* 6.0 (* v v)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* v v) (* v v))
31.0ms
(* 6.0 (* v v))
678.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v))))) (/ (* (fma v v 1.0) (sqrt 4.0)) (sqrt (- 2.0 (* 6.0 (* v v))))))
272.0ms
(/ (* (fma v v 1.0) (sqrt 4.0)) (sqrt (- 2.0 (* 6.0 (* v v)))))

simplify59.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011302296
150021799

prune457.0ms

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
02718
12718

end0.0ms

sample750.0ms

Algorithm
intervals
Results
299.0ms8000×body80valid
271.0ms8140×body80nan