Details

Time bar (total: 22.0s)

sample465.0ms

Algorithm
halfpoints

simplify6.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
01624
13011
24811
38311
411711
518811
633111
755611
8100611
9137511
10169111
11177511
12179511
done179511

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize52.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.7b
(- (exp x) (exp (- x)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×*-un-lft-identity
19×associate-*l*
16×times-frac
12×add-cube-cbrt
7×add-exp-log add-cbrt-cube
4×pow1 distribute-lft-out-- add-log-exp difference-of-squares
3×associate-*r*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv sub-neg flip3-- diff-log div-exp pow-prod-down associate-*l/ *-commutative flip-- div-inv
Counts
2 → 52
Calls
2 calls:
86.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
29.0ms
(- (exp x) (exp (- x)))

series182.0ms

Counts
2 → 6
Calls
2 calls:
112.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
69.0ms
(- (exp x) (exp (- x)))

simplify2.0s

Counts
58 → 58
Iterations

Useful iterations: 3 (872.0ms)

IterNodesCost
0121770
1290755
2749669
32404668
done5001668

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1/60 (pow x 5)) (* 2 x))
0.1b
(* 1/60 (pow x 5))
0.1b
(* 1/3 (pow x 3))
0.2b
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
22×associate-*r*
19×add-exp-log add-cube-cbrt *-un-lft-identity associate-*l*
13×add-cbrt-cube
10×times-frac
9×unswap-sqr
8×unpow-prod-down prod-exp
6×pow1 add-log-exp
4×cube-prod cbrt-unprod sqr-pow
3×*-commutative
2×pow-to-exp pow-exp
1×cbrt-undiv +-commutative cube-mult flip3-+ unpow3 div-exp pow-prod-down associate-*l/ sum-log flip-+ div-inv
Counts
4 → 99
Calls
4 calls:
13.0ms
(+ (* 1/60 (pow x 5)) (* 2 x))
22.0ms
(* 1/60 (pow x 5))
18.0ms
(* 1/3 (pow x 3))
119.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series515.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(+ (* 1/60 (pow x 5)) (* 2 x))
101.0ms
(* 1/60 (pow x 5))
57.0ms
(* 1/3 (pow x 3))
124.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify1.1s

Counts
111 → 111
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01931563
14721469
214651303
done50011302

prune585.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
0.4b
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b
(/ 1 (sqrt 2.0))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
69×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
54×add-exp-log
44×associate-*l*
43×sqrt-prod
34×add-cbrt-cube
22×prod-exp
14×div-exp
13×pow1
12×associate-/r* cbrt-unprod
8×cbrt-undiv
6×associate-/l*
4×rec-exp 1-exp associate-*r* pow-prod-down associate-*l/ div-inv add-log-exp
3×pow-flip unswap-sqr
2×frac-2neg clear-num *-commutative associate-/l/
1×frac-times sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ inv-pow
Counts
4 → 182
Calls
4 calls:
107.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
170.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
156.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
7.0ms
(/ 1 (sqrt 2.0))

series814.0ms

Counts
4 → 10
Calls
4 calls:
281.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
346.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
186.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify1.5s

Counts
192 → 192
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02564878
16534529
223403872
done50013848

prune945.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite570.0ms

Algorithm
rewrite-expression-head
Rules
1128×sqrt-prod
1116×times-frac
592×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
283×associate-*l*
79×add-exp-log
49×add-cbrt-cube
37×associate-/l*
32×div-exp
25×prod-exp
24×associate-/r*
23×pow1 div-inv
20×sqrt-pow1
17×cbrt-undiv
15×cbrt-unprod
14×pow-flip
10×pow1/2 pow-div
5×rec-exp 1-exp
4×add-log-exp
3×frac-2neg pow-prod-down associate-*l/ clear-num associate-/l/
2×inv-pow
1×frac-times flip3-+ associate-*r/ associate-*r* *-commutative flip-+
Counts
4 → 767
Calls
4 calls:
290.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
109.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
34.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
16.0ms
(/ 1 (sqrt (sqrt 2.0)))

series543.0ms

Counts
4 → 8
Calls
4 calls:
321.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
221.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify2.4s

Counts
775 → 775
Iterations

Useful iterations: done (2.4s)

IterNodesCost
061620777
1167217920
2391216102
done500015684

prune2.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes129.0ms

bsearch1.0ms