Details

Time bar (total: 36.2s)

sample673.0ms

Algorithm
halfpoints

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01624
13011
24811
38311
411811
523111
697911
done500011

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.9b

localize80.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.9b
(- (exp x) (exp (- x)))

rewrite131.0ms

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:
104.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
24.0ms
(- (exp x) (exp (- x)))

series221.0ms

Counts
2 → 6
Calls
2 calls:
157.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
64.0ms
(- (exp x) (exp (- x)))

simplify964.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (252.0ms)

IterNodesCost
0121770
1307755
21228669
done5001669

prune445.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 3 expressions with local error:

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

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
22×associate-*r*
19×associate-*l*
18×add-exp-log add-cube-cbrt *-un-lft-identity
12×add-cbrt-cube
10×times-frac
9×unswap-sqr
8×unpow-prod-down prod-exp
5×pow1
4×cube-prod cbrt-unprod sqr-pow
3×*-commutative add-log-exp
2×pow-to-exp pow-exp
1×cbrt-undiv cube-mult unpow3 div-exp pow-prod-down associate-*l/ div-inv
Counts
3 → 88
Calls
3 calls:
24.0ms
(* 1/60 (pow x 5))
31.0ms
(* 1/3 (pow x 3))
144.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series334.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(* 1/60 (pow x 5))
70.0ms
(* 1/3 (pow x 3))
162.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify1.5s

Counts
97 → 97
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01741355
14291284
217751134
done50001133

prune801.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

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))

rewrite492.0ms

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:
156.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
173.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
136.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
12.0ms
(/ 1 (sqrt 2.0))

series951.0ms

Counts
4 → 10
Calls
4 calls:
305.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
401.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
244.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify4.8s

Counts
192 → 192
Iterations

Useful iterations: 2 (992.0ms)

IterNodesCost
02564878
17304621
244384014
done50004014

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize101.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0)))
0.3b
(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0))))
0.5b
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b
(/ (sqrt 1) (sqrt (sqrt 2.0)))

rewrite493.0ms

Algorithm
rewrite-expression-head
Rules
228×sqrt-prod
153×times-frac
133×add-sqr-sqrt
110×*-un-lft-identity
107×add-cube-cbrt
58×associate-*l*
49×add-exp-log add-cbrt-cube
24×associate-/r*
18×cbrt-undiv div-exp
14×prod-exp cbrt-unprod
13×associate-*r*
10×associate-/l* unswap-sqr
6×pow1
5×div-inv
4×add-log-exp
3×frac-2neg clear-num associate-/l/
2×associate-*l/
1×frac-times sqrt-undiv flip3-+ associate-*r/ pow-prod-down *-commutative flip-+
Counts
4 → 268
Calls
4 calls:
64.0ms
(/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0)))
234.0ms
(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0))))
153.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
20.0ms
(/ (sqrt 1) (sqrt (sqrt 2.0)))

series1.3s

Counts
4 → 10
Calls
4 calls:
601.0ms
(/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0)))
404.0ms
(* (/ (sqrt 1) (sqrt (sqrt 2.0))) (/ (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0))))
249.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms
(/ (sqrt 1) (sqrt (sqrt 2.0)))

simplify882.0ms

Counts
278 → 278
Iterations

Useful iterations: done (856.0ms)

IterNodesCost
03278386
19137552
done50016629

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes278.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01820
12420
done2420

end0.0ms

sample16.1s

Algorithm
halfpoints