Details

Time bar (total: 7.2s)

sample31.0ms

Algorithm
intervals
Results
10.0ms275×body80nan
10.0ms256×body80valid

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03210
19110
227510
367210
4130310
5173710
6180210
7180210

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize16.0ms

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)))))
0.1b
(* 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)))
11.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
12.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
303.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
278.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
31.0ms
(* 6.0 (* v v))
430.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify119.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
09551468
146961282
250011281

prune291.0ms

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
40×associate-*r/ associate-/r/
38×add-exp-log add-cbrt-cube
36×cbrt-prod
30×unpow-prod-down flip3-- sqrt-div cube-prod flip--
20×frac-times
18×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
15×times-frac prod-exp cbrt-unprod
10×pow1 associate-*l/
8×cbrt-undiv div-exp
5×pow-exp div-inv rem-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*l* pow-prod-down associate-/l*
2×cube-div cube-mult unpow3 sqr-pow
1×pow-to-exp cbrt-div pow-pow frac-2neg pow1/3 associate-*r* clear-num associate-/r* *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 162
Calls
4 calls:
7.0ms
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
6.0ms
(* 6.0 (* v v))
12.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
15.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

series1.7s

Counts
4 → 12
Calls
4 calls:
343.0ms
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
30.0ms
(* 6.0 (* v v))
428.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
923.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

simplify66.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
011902718
150022574

prune466.0ms

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
196×add-exp-log add-cbrt-cube
103×prod-exp cbrt-unprod
57×associate-*r/
56×associate-/r/
52×cbrt-undiv div-exp
42×flip3-- sqrt-div flip--
29×frac-times
21×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
15×swap-sqr associate-*r* associate-*l* associate-*l/
11×pow1
9×associate-/l*
7×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/r*
1×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 219
Calls
4 calls:
13.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
19.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
13.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
31.0ms
(* (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
443.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
436.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
445.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
278.0ms
(* (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
011565131
150023827

prune740.0ms

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
02433
12433

end0.0ms

sample776.0ms

Algorithm
intervals
Results
303.0ms8000×body80valid
290.0ms8031×body80nan