Details

Time bar (total: 9.5s)

sample38.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
11.0ms243×body80nan

simplify923.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01928
14428
216128
378328
4345128
done500028

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.3b
(* PI t)
0.3b
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
0.5b
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
18×associate-*r/
16×pow1
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
8×flip3-- sqrt-div associate-*r* associate-/r/ flip--
7×associate-*l* pow-prod-down
4×cbrt-undiv frac-times div-exp add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-*l/ associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 94
Calls
4 calls:
6.0ms
(* 5.0 (* v v))
3.0ms
(* PI t)
55.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
14.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series868.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 5.0 (* v v))
20.0ms
(* PI t)
618.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
205.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify1.2s

Counts
106 → 106
Iterations

Useful iterations: 2 (295.0ms)

IterNodesCost
02502389
17582248
239671908
done50001908

prune341.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.3b
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
0.3b
(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
0.4b
(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log associate-*r/ add-cbrt-cube
16×pow1
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity sqrt-div
9×flip3-- associate-*l* flip--
8×associate-/r/
7×pow-prod-down
6×associate-*r*
4×cbrt-undiv frac-times div-exp add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-*l/ associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 96
Calls
4 calls:
6.0ms
(* 5.0 (* v v))
95.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
30.0ms
(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
11.0ms
(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series1.0s

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 5.0 (* v v))
618.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
198.0ms
(* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))))
160.0ms
(* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify1.0s

Counts
108 → 108
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
02582663
17802498
236482144
done50012144

prune369.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(pow (* 3.0 (* v v)) 3)
0.4b
(/ (/ (- 1.0 (* 5.0 (* v v))) PI) (* (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (- (* 1.0 1.0) (pow v 4))))
0.4b
(* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
38×add-exp-log add-cbrt-cube
31×times-frac
25×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
18×associate-*r/
17×pow1
13×prod-exp cbrt-unprod associate-/l*
9×cbrt-undiv div-exp
8×sqrt-div associate-/r/
7×flip3-- pow-prod-down flip--
6×associate-*l*
5×associate-*r*
4×frac-times add-log-exp
3×pow-unpow pow-pow pow-exp div-inv rem-cube-cbrt
2×div-sub associate-*l/ *-commutative unswap-sqr
1×cube-mult pow-to-exp unpow-prod-down frac-2neg unpow3 cube-prod clear-num associate-/r* sqrt-prod associate-/l/ sqr-pow
Counts
4 → 124
Calls
4 calls:
6.0ms
(* 5.0 (* v v))
6.0ms
(pow (* 3.0 (* v v)) 3)
136.0ms
(/ (/ (- 1.0 (* 5.0 (* v v))) PI) (* (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (- (* 1.0 1.0) (pow v 4))))
33.0ms
(* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

series676.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 5.0 (* v v))
57.0ms
(pow (* 3.0 (* v v)) 3)
398.0ms
(/ (/ (- 1.0 (* 5.0 (* v v))) PI) (* (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (- (* 1.0 1.0) (pow v 4))))
196.0ms
(* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

simplify1.1s

Counts
136 → 136
Iterations

Useful iterations: 2 (295.0ms)

IterNodesCost
02983778
18523490
236293044
done50003044

prune738.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(pow (* 3.0 (* v v)) 3)
0.4b
(/ (/ (- 1.0 (* 5.0 (* v v))) PI) (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))
0.4b
(* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
29×add-exp-log add-cbrt-cube
25×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
17×pow1
13×associate-/l*
9×prod-exp cbrt-unprod
8×associate-*r/
7×pow-prod-down
6×cbrt-undiv div-exp associate-*l*
5×associate-*r*
4×sqrt-div add-log-exp
3×pow-unpow pow-pow pow-exp div-inv rem-cube-cbrt
2×flip3-- div-sub associate-/r/ *-commutative flip-- unswap-sqr
1×cube-mult pow-to-exp unpow-prod-down frac-2neg unpow3 cube-prod clear-num associate-/r* sqrt-prod associate-/l/ sqr-pow
Counts
4 → 114
Calls
4 calls:
6.0ms
(* 5.0 (* v v))
6.0ms
(pow (* 3.0 (* v v)) 3)
41.0ms
(/ (/ (- 1.0 (* 5.0 (* v v))) PI) (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))
34.0ms
(* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 5.0 (* v v))
56.0ms
(pow (* 3.0 (* v v)) 3)
337.0ms
(/ (/ (- 1.0 (* 5.0 (* v v))) PI) (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))
194.0ms
(* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))

simplify55.0ms

Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
02512706