Details

Time bar (total: 27.2s)

sample494.0ms

Algorithm
halfpoints

simplify909.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01624
13011
24811
38311
411811
523111
697911
done500011

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize78.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.7b
(- (exp x) (exp (- x)))

rewrite99.0ms

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:
70.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
25.0ms
(- (exp x) (exp (- x)))

series188.0ms

Counts
2 → 6
Calls
2 calls:
121.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
66.0ms
(- (exp x) (exp (- x)))

simplify681.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
0121770
1307755
21228669
done5001669

prune241.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 3 expressions with local error:

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

rewrite174.0ms

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))
126.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
18.0ms
(* 1/3 (pow x 3))

series249.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(* 1/60 (pow x 5))
137.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
43.0ms
(* 1/3 (pow x 3))

simplify891.0ms

Counts
97 → 97
Iterations

Useful iterations: done (888.0ms)

IterNodesCost
01741355
14291282
217601138
done50011137

prune483.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize67.0ms

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))
0.3b
(* (/ 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))

rewrite404.0ms

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:
127.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
161.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
97.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
7.0ms
(/ 1 (sqrt 2.0))

series653.0ms

Counts
4 → 10
Calls
4 calls:
240.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
271.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
142.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify3.4s

Counts
192 → 192
Iterations

Useful iterations: 2 (580.0ms)

IterNodesCost
02564878
17304621
244384014
done50004014

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/3 (pow x 3))
0.2b
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b
(* (pow 2.0 -1/2) (* (/ (+ (* 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))

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×add-exp-log
39×add-cube-cbrt *-un-lft-identity
38×times-frac
32×associate-*l*
22×sqrt-prod add-cbrt-cube
20×prod-exp
16×associate-*r*
8×cbrt-unprod
7×unpow-prod-down unswap-sqr
6×pow1 associate-/r*
5×div-exp
4×pow-to-exp cube-prod pow-exp add-log-exp
3×cbrt-undiv *-commutative associate-/l* sqr-pow
2×associate-*l/ div-inv associate-/l/
1×cube-mult frac-2neg flip3-+ unpow3 associate-*r/ pow-prod-down clear-num flip-+
Counts
4 → 143
Calls
4 calls:
15.0ms
(* 1/3 (pow x 3))
106.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
160.0ms
(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
111.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

series741.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* 1/3 (pow x 3))
215.0ms
(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
292.0ms
(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
155.0ms
(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify2.1s

Counts
155 → 155
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02603877
16973736
233083357
done50023356

prune898.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01820
12420
done2420

end0.0ms

sample12.6s

Algorithm
halfpoints