Details

Time bar (total: 10.0s)

sample30.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
9.0ms272×body80nan

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01620
13220
28820
324720
452620
587520
6112720
7115620
done115620

prune3.0ms

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))))))

rewrite113.0ms

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:
15.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
42.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
9.0ms
(* 6.0 (* v v))
40.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
349.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
32.0ms
(* 6.0 (* v v))
535.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify1.6s

Counts
135 → 135
Iterations

Useful iterations: 2 (354.0ms)

IterNodesCost
03303068
19592848
243422441
done50002441

prune383.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4)))))
1.0b
(* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0)
1.0b
(* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log add-cbrt-cube
36×distribute-rgt-in distribute-lft-in
28×prod-diff
23×pow1 add-sqr-sqrt
20×prod-exp cbrt-unprod
18×add-cube-cbrt *-un-lft-identity associate-*l/
16×associate-*r/
14×sqrt-div
13×flip3-- flip--
12×unpow-prod-down pow-prod-down
10×associate-*l*
8×frac-times associate-/r/
5×cbrt-undiv div-exp associate-*r*
4×expm1-log1p-u sub-neg sqrt-prod log1p-expm1-u add-log-exp sqr-pow
3×times-frac *-commutative associate-/l* unswap-sqr
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 152
Calls
4 calls:
11.0ms
(* 6.0 (* v v))
42.0ms
(/ 4.0 (* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4)))))
11.0ms
(* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0)
56.0ms
(* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4))))

series852.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 6.0 (* v v))
390.0ms
(/ 4.0 (* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4)))))
134.0ms
(* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0)
303.0ms
(* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4))))

simplify509.0ms

Counts
164 → 164
Iterations

Useful iterations: done (503.0ms)

IterNodesCost
04505138
112784511
done50004412

prune486.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4)))))
1.0b
(* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0)
1.0b
(* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log add-cbrt-cube
36×distribute-rgt-in distribute-lft-in
28×prod-diff
23×pow1 add-sqr-sqrt
20×prod-exp cbrt-unprod
18×add-cube-cbrt *-un-lft-identity associate-*l/
16×associate-*r/
14×sqrt-div
13×flip3-- flip--
12×unpow-prod-down pow-prod-down
10×associate-*l*
8×frac-times associate-/r/
5×cbrt-undiv div-exp associate-*r*
4×expm1-log1p-u sub-neg sqrt-prod log1p-expm1-u add-log-exp sqr-pow
3×times-frac *-commutative associate-/l* unswap-sqr
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 152
Calls
4 calls:
7.0ms
(* 6.0 (* v v))
33.0ms
(/ 4.0 (* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4)))))
9.0ms
(* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0)
44.0ms
(* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4))))

series909.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 6.0 (* v v))
386.0ms
(/ 4.0 (* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4)))))
189.0ms
(* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0)
309.0ms
(* (* (sqrt (- 2.0 (* 6.0 (* v v)))) 3.0) (* PI (- (* 1.0 1.0) (pow v 4))))

simplify544.0ms

Counts
164 → 164
Iterations

Useful iterations: done (534.0ms)

IterNodesCost
04505138
112784511
done50004412

prune518.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02330
12930
done2930

end0.0ms

sample893.0ms

Algorithm
intervals
Results
356.0ms8000×body80valid
335.0ms8079×body80nan