Details

Time bar (total: 25.0s)

sample43.0ms

Algorithm
intervals
Results
14.0ms281×body80nan
13.0ms256×body80valid

simplify4.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01419
12719
27019
319219
440019
575319
6105819
7120219
8131219
9131819
done131819

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
26×associate-*l*
24×add-cube-cbrt *-un-lft-identity
23×add-exp-log add-cbrt-cube
22×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
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative
2×cbrt-undiv sub-neg div-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 div-inv difference-of-squares
Counts
4 → 142
Calls
4 calls:
15.0ms
(sqrt (- 1.0 (* 3.0 (* v v))))
55.0ms
(* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
114.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
20.0ms
(* 3.0 (* v v))

series877.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(sqrt (- 1.0 (* 3.0 (* v v))))
279.0ms
(* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
433.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
42.0ms
(* 3.0 (* v v))

simplify2.4s

Counts
154 → 154
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03013466
18583174
231892946
done50002938

prune651.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize38.0ms

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)

rewrite197.0ms

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
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow-prod-down
8×cbrt-prod
6×prod-diff
5×distribute-rgt-in distribute-lft-in associate-*r*
4×expm1-log1p-u associate-*l* pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×pow-unpow pow-pow
2×cbrt-undiv cube-mult sub-neg unpow-prod-down unpow3 cube-prod div-exp *-commutative sqr-pow
1×pow-to-exp pow1/3 rem-cbrt-cube difference-of-squares unswap-sqr
Counts
4 → 153
Calls
4 calls:
83.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
12.0ms
(cbrt (pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3))
19.0ms
(* 3.0 (* v v))
75.0ms
(pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3)

series2.2s

Counts
4 → 12
Calls
4 calls:
477.0ms
(* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v)))
389.0ms
(cbrt (pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3))
46.0ms
(* 3.0 (* v v))
1.2s
(pow (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))) 3)

simplify826.0ms

Counts
165 → 165
Iterations

Useful iterations: done (812.0ms)

IterNodesCost
03825501
111864661
done50014439

prune918.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize23.0ms

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

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
34×cube-div
18×frac-times
17×cbrt-div
16×add-exp-log sqrt-div add-cbrt-cube
15×flip3-- flip--
13×pow1 associate-*l/
12×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow-unpow associate-*r/
5×unpow-prod-down cube-prod pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×pow-pow associate-*l*
2×cube-mult pow-to-exp unpow3 difference-of-squares sqr-pow
1×cbrt-undiv cbrt-prod pow1/3 div-exp associate-*r* *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 110
Calls
4 calls:
32.0ms
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (- 1.0 (* v v)) 3)))
15.0ms
(pow (- 1.0 (* v v)) 3)
34.0ms
(* 3.0 (* v v))
46.0ms
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

series1.6s

Counts
4 → 12
Calls
4 calls:
379.0ms
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (- 1.0 (* v v)) 3)))
69.0ms
(pow (- 1.0 (* v v)) 3)
34.0ms
(* 3.0 (* v v))
1.1s
(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
03032740
17792421
234972260
done50002257

prune680.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow (- 1.0 (* v v)) (* (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 (* v v)) (* (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)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log
15×add-cbrt-cube
13×unpow-prod-down
12×pow1 add-sqr-sqrt
10×cube-div add-cube-cbrt *-un-lft-identity
9×pow-unpow associate-*l/
8×sqrt-div
7×pow-exp
5×cbrt-div prod-exp cbrt-unprod
4×cbrt-prod expm1-log1p-u frac-times flip3-- pow-prod-down flip-- log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow associate-*l* rem-cube-cbrt sqr-pow
2×associate-*r/
1×cbrt-undiv cube-mult pow1/3 unpow3 cube-prod div-exp associate-*r* *-commutative difference-of-squares unswap-sqr
Counts
4 → 97
Calls
4 calls:
25.0ms
(pow (pow (- 1.0 (* v v)) (* (cbrt 3) (cbrt 3))) (cbrt 3))
32.0ms
(cbrt (* (pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3) (pow (pow (- 1.0 (* v v)) (* (cbrt 3) (cbrt 3))) (cbrt 3))))
16.0ms
(* 3.0 (* v v))
21.0ms
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

series3.2s

Counts
4 → 12
Calls
4 calls:
833.0ms
(pow (pow (- 1.0 (* v v)) (* (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 (* v v)) (* (cbrt 3) (cbrt 3))) (cbrt 3))))
42.0ms
(* 3.0 (* v v))
682.0ms
(pow (* (sqrt (- 1.0 (* 3.0 (* v v)))) (/ (sqrt 2.0) 4.0)) 3)

simplify1.8s

Counts
109 → 109
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03472751
19522507
236242268
done50012242

prune676.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02131
12431
done2431

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s8000×body80valid
673.0ms7943×body80nan