Details

Time bar (total: 13.7s)

sample134.0ms

Algorithm
intervals
Results
58.0ms108×body2560valid
26.0ms72×body1280valid
14.0ms278×body80nan
10.0ms36×body640valid
3.0ms15×body320valid
2.0ms17×body160valid
1.0ms8×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09293
119293
241293
370293
4131293
5201293
6436293
71199293
84456293
done5114293

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b
(* 5.0 (* v v))
0.8b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac
10×add-cbrt-cube add-exp-log
8×pow1
4×associate-/r* difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×acos-asin cbrt-undiv clear-num frac-2neg div-sub div-exp associate-*r* *-commutative div-inv unswap-sqr
Counts
3 → 63
Calls
3 calls:
19.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
14.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
129.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
28.0ms
(* 5.0 (* v v))
5.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify1.8s

Counts
72 → 72
Iterations

Useful iterations: 2 (407.0ms)

IterNodesCost
013923037
135920471
2118020269
done500020269

prune320.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 5.0 (* v v)) (- (* v v) 1.0))
0.0b
(- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
0.1b
(* 5.0 (* v v))
0.8b
(acos (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
15×add-sqr-sqrt
9×pow1 *-un-lft-identity
7×add-cube-cbrt
6×prod-exp associate-/r/ cbrt-unprod add-log-exp
5×times-frac
4×associate-/r* flip3-- flip-- difference-of-squares
3×cbrt-undiv distribute-rgt-out-- div-exp associate-*l* pow-prod-down div-inv
1×acos-asin clear-num sub-neg frac-2neg diff-log associate-*r* *-commutative frac-sub associate-/l* distribute-lft-out-- sub-div unswap-sqr
Counts
4 → 74
Calls
4 calls:
38.0ms
(/ (* 5.0 (* v v)) (- (* v v) 1.0))
112.0ms
(- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
16.0ms
(* 5.0 (* v v))
50.0ms
(acos (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

series338.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (* 5.0 (* v v)) (- (* v v) 1.0))
179.0ms
(- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))
47.0ms
(* 5.0 (* v v))
11.0ms
(acos (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))

simplify2.5s

Counts
86 → 86
Iterations

Useful iterations: done (2.5s)

IterNodesCost
016327760
144722926
2155221919
done500321839

prune369.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 5.0 (* v v))
0.1b
(* 5.0 (* v v))
0.1b
(* 5.0 (* v v))
0.8b
(acos (cbrt (* (* (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))) (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×associate-*l* pow-prod-down prod-exp cbrt-unprod
7×*-un-lft-identity add-cube-cbrt
4×add-log-exp
3×associate-*r* *-commutative unswap-sqr
1×acos-asin
Counts
4 → 65
Calls
4 calls:
14.0ms
(* 5.0 (* v v))
16.0ms
(* 5.0 (* v v))
19.0ms
(* 5.0 (* v v))
1.0ms
(acos (cbrt (* (* (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))) (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

series127.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 5.0 (* v v))
33.0ms
(* 5.0 (* v v))
47.0ms
(* 5.0 (* v v))
9.0ms
(acos (cbrt (* (* (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))) (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0)))) (- (/ 1.0 (- (* v v) 1.0)) (/ (* 5.0 (* v v)) (- (* v v) 1.0))))))

simplify2.7s

Counts
77 → 77
Iterations

Useful iterations: 3 (510.0ms)

IterNodesCost
06116627
112714155
235413552
3140412272
done500012272

prune343.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
9.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series790.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(* (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
165.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
215.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
175.0ms
(cbrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify69.0ms

Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
06144615