Details

Time bar (total: 23.5s)

sample39.0ms

Algorithm
intervals
Results
13.0ms281×body80nan
12.0ms256×body80valid

simplify2.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01419
12719
27019
318019
435619
565719
693519
7105219
8113319
done113319

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* 3.0 (* v v))))
0.0b
(* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
0.0b
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
0.2b
(* 3.0 (* v v))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
26×associate-*l*
23×add-exp-log add-cbrt-cube
22×add-cube-cbrt *-un-lft-identity times-frac
20×sqrt-prod
18×frac-times sqrt-div
17×pow1
15×flip3-- flip--
11×associate-*r*
10×associate-*r/ prod-exp cbrt-unprod
9×associate-*l/
7×pow-prod-down unswap-sqr
4×add-log-exp
3×*-commutative
2×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in div-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 div-inv difference-of-squares
Counts
4 → 128
Calls
4 calls:
11.0ms
(sqrt (- 1.0 (* 3.0 (* v v))))
50.0ms
(* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
96.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
28.0ms
(* 3.0 (* v v))

series958.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(sqrt (- 1.0 (* 3.0 (* v v))))
322.0ms
(* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
461.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
49.0ms
(* 3.0 (* v v))

simplify2.1s

Counts
140 → 140
Iterations

Useful iterations: 2 (729.0ms)

IterNodesCost
02783102
17962836
229712648
done50012648

prune647.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
0.0b
(cbrt (pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3))
0.2b
(* 3.0 (* v v))
1.0b
(pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3)

rewrite663.0ms

Algorithm
rewrite-expression-head
Rules
48×frac-times
36×flip3-- sqrt-div flip--
34×cube-div
28×add-exp-log add-cbrt-cube
24×associate-*r/ associate-*l/
20×pow1
17×cbrt-div
13×prod-exp cbrt-unprod
10×add-sqr-sqrt
9×pow-prod-down
8×cbrt-prod add-cube-cbrt *-un-lft-identity
5×associate-*r*
4×associate-*l* pow-exp add-log-exp rem-cube-cbrt
3×pow-unpow pow-pow
2×cbrt-undiv distribute-rgt-in cube-mult sub-neg unpow-prod-down distribute-lft-in unpow3 cube-prod div-exp *-commutative sqr-pow
1×pow-to-exp pow1/3 rem-cbrt-cube difference-of-squares unswap-sqr
Counts
4 → 139
Calls
4 calls:
93.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
25.0ms
(cbrt (pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3))
443.0ms
(* 3.0 (* v v))
91.0ms
(pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3)

series1.9s

Counts
4 → 12
Calls
4 calls:
457.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
276.0ms
(cbrt (pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3))
42.0ms
(* 3.0 (* v v))
1.2s
(pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3)

simplify745.0ms

Counts
151 → 151
Iterations

Useful iterations: done (735.0ms)

IterNodesCost
03595093
111224322
done50004182

prune914.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (- 1.0 (pow v 2)) 3)))
0.0b
(pow (- 1.0 (pow v 2)) 3)
0.2b
(* 3.0 (* v v))
1.0b
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
34×cube-div
22×add-sqr-sqrt
18×frac-times
17×cbrt-div
16×add-exp-log sqrt-div add-cbrt-cube
15×flip3-- flip--
13×pow1 *-un-lft-identity associate-*l/
11×unpow-prod-down
9×add-cube-cbrt cube-prod
8×difference-of-squares
6×pow-unpow associate-*r/
5×pow-prod-down prod-exp cbrt-unprod
4×pow-exp add-log-exp rem-cube-cbrt sqr-pow
3×pow-pow associate-*l*
2×cube-mult pow-to-exp unpow3 distribute-lft-out-- unpow2
1×cbrt-undiv cbrt-prod pow1/3 div-exp associate-*r* *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 110
Calls
4 calls:
41.0ms
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (- 1.0 (pow v 2)) 3)))
23.0ms
(pow (- 1.0 (pow v 2)) 3)
20.0ms
(* 3.0 (* v v))
17.0ms
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

series1.2s

Counts
4 → 12
Calls
4 calls:
375.0ms
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (- 1.0 (pow v 2)) 3)))
81.0ms
(pow (- 1.0 (pow v 2)) 3)
49.0ms
(* 3.0 (* v v))
677.0ms
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

simplify2.2s

Counts
122 → 122
Iterations

Useful iterations: done (2.2s)

IterNodesCost
03132762
18132463
234902301
done50012298

prune817.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow (- 1.0 (pow v 2)) (* (cbrt 3) (cbrt 3))) (cbrt 3))
0.0b
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (pow (- 1.0 (pow v 2)) (* (cbrt 3) (cbrt 3))) (cbrt 3))))
0.2b
(* 3.0 (* v v))
1.0b
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-down
17×add-exp-log add-sqr-sqrt
15×add-cbrt-cube
12×pow1 *-un-lft-identity
10×cube-div add-cube-cbrt
9×pow-unpow associate-*l/
8×sqrt-div
7×pow-exp
5×cbrt-div prod-exp cbrt-unprod
4×cbrt-prod frac-times flip3-- pow-prod-down flip-- add-log-exp difference-of-squares sqr-pow
3×pow-to-exp pow-pow associate-*l* rem-cube-cbrt
2×associate-*r/
1×cbrt-undiv cube-mult pow1/3 unpow3 cube-prod div-exp associate-*r* *-commutative distribute-lft-out-- unpow2 unswap-sqr
Counts
4 → 93
Calls
4 calls:
47.0ms
(pow (pow (- 1.0 (pow v 2)) (* (cbrt 3) (cbrt 3))) (cbrt 3))
54.0ms
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (pow (- 1.0 (pow v 2)) (* (cbrt 3) (cbrt 3))) (cbrt 3))))
26.0ms
(* 3.0 (* v v))
16.0ms
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

series3.1s

Counts
4 → 12
Calls
4 calls:
746.0ms
(pow (pow (- 1.0 (pow v 2)) (* (cbrt 3) (cbrt 3))) (cbrt 3))
1.6s
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (pow (- 1.0 (pow v 2)) (* (cbrt 3) (cbrt 3))) (cbrt 3))))
41.0ms
(* 3.0 (* v v))
738.0ms
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

simplify1.9s

Counts
105 → 105
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03622735
19842498
235782249
done50022228

prune662.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02331
12631
done2631

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s8000×body80valid
747.0ms7943×body80nan