Details

Time bar (total: 22.7s)

sample77.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
19.0ms284×body80nan

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01620
13220
29020
326820
463320
5119120
6147820
7149620
done149620

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize29.0ms

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))))))

rewrite294.0ms

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:
27.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
112.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
32.0ms
(* 6.0 (* v v))
115.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
194.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
384.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
34.0ms
(* 6.0 (* v v))
709.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify2.3s

Counts
135 → 135
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03303068
19322820
238392441
done50012432

prune539.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt 4.0) (* (* 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))))))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
91×sqrt-prod
88×times-frac
80×add-sqr-sqrt
65×add-cube-cbrt *-un-lft-identity
52×add-exp-log add-cbrt-cube
43×associate-*r*
20×prod-exp cbrt-unprod
15×associate-*l*
14×cbrt-undiv div-exp
12×associate-/l*
11×pow1
8×associate-/r/
7×associate-/r*
6×unswap-sqr
5×associate-*r/
4×expm1-log1p-u flip3-- sqrt-div pow-prod-down flip-- log1p-expm1-u div-inv add-log-exp
2×frac-2neg clear-num *-commutative
1×frac-times sqrt-undiv associate-*l/
Counts
4 → 208
Calls
4 calls:
24.0ms
(/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v))))
34.0ms
(* 6.0 (* v v))
17.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
123.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
282.0ms
(/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v))))
54.0ms
(* 6.0 (* v v))
332.0ms
(/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v)))))
921.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (/ (sqrt 4.0) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify2.7s

Counts
220 → 220
Iterations

Useful iterations: done (2.7s)

IterNodesCost
04015490
111254810
246924329
done50004325

prune820.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 6.0 (* v v))
1.0b
(cbrt (- 2.0 (* 6.0 (* v v))))
1.0b
(cbrt (- 2.0 (* 6.0 (* v v))))
1.0b
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (* (/ (fabs (cbrt 4.0)) (fabs (cbrt (- 2.0 (* 6.0 (* v v)))))) (/ (sqrt (cbrt 4.0)) (sqrt (cbrt (- 2.0 (* 6.0 (* v v))))))))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
111×add-exp-log add-cbrt-cube
54×prod-exp cbrt-unprod
31×cbrt-undiv div-exp
15×associate-*l*
14×pow1
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
7×associate-*r/
6×cbrt-prod times-frac pow-prod-down
5×frac-times
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×flip3-- associate-*l/ sqrt-prod flip--
2×pow1/3 associate-*r* associate-/r/ *-commutative
1×div-inv unswap-sqr
Counts
4 → 123
Calls
4 calls:
17.0ms
(* 6.0 (* v v))
3.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
3.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
224.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (* (/ (fabs (cbrt 4.0)) (fabs (cbrt (- 2.0 (* 6.0 (* v v)))))) (/ (sqrt (cbrt 4.0)) (sqrt (cbrt (- 2.0 (* 6.0 (* v v))))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
39.0ms
(* 6.0 (* v v))
384.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
365.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
1.0s
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (* (/ (fabs (cbrt 4.0)) (fabs (cbrt (- 2.0 (* 6.0 (* v v)))))) (/ (sqrt (cbrt 4.0)) (sqrt (cbrt (- 2.0 (* 6.0 (* v v))))))))

simplify1.0s

Counts
135 → 135
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03876113
111295739
done50004162

prune846.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 6.0 (* v v))
1.0b
(cbrt (- 2.0 (* 6.0 (* v v))))
1.0b
(cbrt (- 2.0 (* 6.0 (* v v))))
1.0b
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (* (/ (fabs (cbrt 4.0)) (fabs (cbrt (- 2.0 (* 6.0 (* v v)))))) (/ (sqrt (cbrt 4.0)) (sqrt (cbrt (- 2.0 (* 6.0 (* v v))))))))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
111×add-exp-log add-cbrt-cube
54×prod-exp cbrt-unprod
31×cbrt-undiv div-exp
15×associate-*l*
14×pow1
11×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
7×associate-*r/
6×cbrt-prod times-frac pow-prod-down
5×frac-times
4×expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×flip3-- associate-*l/ sqrt-prod flip--
2×pow1/3 associate-*r* associate-/r/ *-commutative
1×div-inv unswap-sqr
Counts
4 → 123
Calls
4 calls:
26.0ms
(* 6.0 (* v v))
3.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
3.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
213.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (* (/ (fabs (cbrt 4.0)) (fabs (cbrt (- 2.0 (* 6.0 (* v v)))))) (/ (sqrt (cbrt 4.0)) (sqrt (cbrt (- 2.0 (* 6.0 (* v v))))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
44.0ms
(* 6.0 (* v v))
344.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
393.0ms
(cbrt (- 2.0 (* 6.0 (* v v))))
971.0ms
(* (/ (sqrt 4.0) (* (* 3.0 PI) (- 1.0 (* v v)))) (* (/ (fabs (cbrt 4.0)) (fabs (cbrt (- 2.0 (* 6.0 (* v v)))))) (/ (sqrt (cbrt 4.0)) (sqrt (cbrt (- 2.0 (* 6.0 (* v v))))))))

simplify864.0ms

Counts
135 → 135
Iterations

Useful iterations: done (851.0ms)

IterNodesCost
03876113
111295739
done50004162

prune835.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02742
13242
done3242

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s8000×body80valid
701.0ms8253×body80nan