Details

Time bar (total: 36.5s)

sample432.0ms

Algorithm
halfpoints

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 6 (282.0ms)

IterNodesCost
016543
130363
248294
383294
4118294
5235294
6991293
done5001293

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.5b

localize82.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp x) (exp (- x)))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.4b
(- (exp x) (exp (- x)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
39×*-un-lft-identity
35×associate-*l*
29×times-frac
23×add-cube-cbrt
14×add-cbrt-cube add-exp-log
8×pow1 add-log-exp
6×associate-*r*
4×prod-exp cbrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 99
Calls
4 calls:
16.0ms
(+ (exp x) (exp (- x)))
49.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
58.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
19.0ms
(- (exp x) (exp (- x)))

series553.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (exp x) (exp (- x)))
68.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
106.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
344.0ms
(- (exp x) (exp (- x)))

simplify1.7s

Counts
111 → 111
Iterations

Useful iterations: 2 (648.0ms)

IterNodesCost
019945913
151743852
2232139757
done500239797

prune858.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize118.0ms

Local error

Found 4 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
34×pow1
28×add-sqr-sqrt add-exp-log
25×add-cbrt-cube
20×associate-*l*
17×*-un-lft-identity add-cube-cbrt
14×associate-*r* prod-exp
12×cbrt-unprod
10×times-frac pow-prod-down
6×pow-plus pow-prod-up unswap-sqr
4×unpow-prod-down *-commutative add-log-exp
2×pow2 pow-sqr sqr-pow
1×pow-to-exp cbrt-undiv div-exp pow3 associate-*l/ pow-exp div-inv
Counts
4 → 106
Calls
4 calls:
10.0ms
(* 1/60 (pow x 5))
15.0ms
(* (* x x) x)
71.0ms
(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) 2.0) (sin y))
54.0ms
(* 1/3 (* (* x x) x))

series352.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* 1/60 (pow x 5))
64.0ms
(* (* x x) x)
160.0ms
(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) 2.0) (sin y))
51.0ms
(* 1/3 (* (* x x) x))

simplify2.5s

Counts
118 → 118
Iterations

Useful iterations: 2 (925.0ms)

IterNodesCost
017842180
146438800
2243938002
done500138002

prune930.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize164.0ms

Local error

Found 4 expressions with local error:

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

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
69×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
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×clear-num frac-2neg *-commutative associate-/l/
1×frac-times sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ inv-pow
Counts
4 → 182
Calls
4 calls:
116.0ms
(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) (sqrt 2.0)) (sin y))
93.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) (sqrt 2.0)) (sin y)))
71.0ms
(/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) (sqrt 2.0))
8.0ms
(/ 1 (sqrt 2.0))

series728.0ms

Counts
4 → 10
Calls
4 calls:
243.0ms
(* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) (sqrt 2.0)) (sin y))
305.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) (sqrt 2.0)) (sin y)))
179.0ms
(/ (+ (* 2 x) (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x)))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify4.8s

Counts
192 → 192
Iterations

Useful iterations: 2 (1.6s)

IterNodesCost
0256132460
1726123265
24547121018
done5000121018

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize187.0ms

Local error

Found 4 expressions with local error:

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

rewrite508.0ms

Algorithm
rewrite-expression-head
Rules
70×add-exp-log
68×times-frac
63×add-sqr-sqrt
61×sqrt-prod
60×add-cbrt-cube
47×*-un-lft-identity add-cube-cbrt
35×associate-*r*
25×prod-exp cbrt-unprod
24×cbrt-undiv div-exp
16×associate-*l*
15×associate-/r*
8×pow1
7×unswap-sqr
5×div-inv
4×associate-/l* add-log-exp
2×clear-num frac-2neg pow-prod-down associate-*r/ *-commutative associate-/l/
1×frac-times flip3-+ associate-*l/ flip-+
Counts
4 → 182
Calls
4 calls:
142.0ms
(* (sin y) (/ (+ (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x))) (* 2 x)) (sqrt 2.0)))
181.0ms
(* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (+ (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x))) (* 2 x)) (sqrt 2.0))) (sqrt (sqrt 2.0))))
147.0ms
(/ (+ (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x))) (* 2 x)) (sqrt 2.0))
23.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 2.0)))

series1.1s

Counts
4 → 10
Calls
4 calls:
412.0ms
(* (sin y) (/ (+ (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x))) (* 2 x)) (sqrt 2.0)))
484.0ms
(* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 2.0))) (/ (* (sin y) (/ (+ (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x))) (* 2 x)) (sqrt 2.0))) (sqrt (sqrt 2.0))))
155.0ms
(/ (+ (+ (* 1/60 (pow x 5)) (* 1/3 (* (* x x) x))) (* 2 x)) (sqrt 2.0))
0.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 2.0)))

simplify2.6s

Counts
192 → 192
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0315154542
1957134034
done5000125690

prune1.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes201.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
027997
136997
done36997

end0.0ms

sample13.5s

Algorithm
halfpoints