Details

Time bar (total: 1.4m)

sample396.0ms

Algorithm
halfpoints
Results

simplify190.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
190.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.2b

localize90.0ms

Local error

Found 4 expressions with local error:

57.4b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.0b
(+ (exp x) (exp (- x)))

rewrite167.0ms

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 insert-posit16 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 → 103
Calls
4 calls:
Slowest
73.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
62.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
18.0ms
(+ (exp x) (exp (- x)))
11.0ms
(- (exp x) (exp (- x)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
89.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
84.0ms
(- (exp x) (exp (- x)))
27.0ms
(+ (exp x) (exp (- x)))

simplify5.7s

Counts
77 → 115
Calls
77 calls:
Slowest
970.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
409.0ms
(/ 1 (sqrt 2))
376.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
312.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
265.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize143.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/3 x)
0.1b
(* x (* 1/3 x))
0.1b
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
0.1b
(* (pow x 5) 1/60)

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×associate-*l*
21×add-exp-log
18×*-un-lft-identity add-cbrt-cube add-cube-cbrt
13×pow1
10×times-frac associate-*r*
9×prod-exp
7×cbrt-unprod
6×unswap-sqr
5×pow-prod-down
4×unpow-prod-down *-commutative insert-posit16 add-log-exp
2×sqr-pow
1×pow-to-exp cbrt-undiv div-exp associate-*l/ pow-exp div-inv
Counts
4 → 97
Calls
4 calls:
Slowest
60.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
14.0ms
(* x (* 1/3 x))
8.0ms
(* (pow x 5) 1/60)
5.0ms
(* 1/3 x)

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
98.0ms
(* (pow x 5) 1/60)
54.0ms
(* x (* 1/3 x))
30.0ms
(* 1/3 x)

simplify9.1s

Counts
72 → 109
Calls
72 calls:
Slowest
565.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (cbrt 2) (cbrt 2)))
562.0ms
(/ (* (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))) 1)
543.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
541.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
530.0ms
(/ (* (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))) (sqrt 2))

prune2.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt 2))
0.4b
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
0.4b
(* 1/3 x)
0.3b
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
51×add-sqr-sqrt add-exp-log
49×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
31×add-cbrt-cube
25×associate-*l*
21×prod-exp
13×pow1 div-exp
12×associate-/r*
11×cbrt-unprod
7×cbrt-undiv
6×associate-/l*
4×rec-exp 1-exp associate-*r* pow-prod-down insert-posit16 add-log-exp
3×associate-*l/ div-inv pow-flip
2×clear-num frac-2neg *-commutative associate-/l/
1×frac-times sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ inv-pow unswap-sqr
Counts
4 → 162
Calls
4 calls:
Slowest
75.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
69.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
10.0ms
(* 1/3 x)
6.0ms
(/ 1 (sqrt 2))

series462.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
268.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
167.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
27.0ms
(* 1/3 x)
0.0ms
(/ 1 (sqrt 2))

simplify24.3s

Counts
162 → 172
Calls
162 calls:
Slowest
1.1s
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
1.0s
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
913.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt 1))
637.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
612.0ms
(- (log (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (log (sqrt 2)))

prune3.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize140.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1/2 (sqrt 2))
0.4b
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
0.4b
(* 1/3 x)
0.3b
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
52×add-sqr-sqrt
50×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
28×associate-*l*
22×cbrt-prod
19×add-exp-log
16×add-cbrt-cube
12×associate-/r*
11×pow1
6×prod-exp cbrt-unprod associate-/l*
4×associate-*r* pow-prod-down insert-posit16 add-log-exp
3×cbrt-undiv div-exp associate-*l/ div-inv
2×cbrt-div clear-num frac-2neg *-commutative associate-/l/
1×frac-times flip3-+ associate-*r/ flip-+ unswap-sqr
Counts
4 → 147
Calls
4 calls:
Slowest
109.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
79.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
10.0ms
(* 1/3 x)
8.0ms
(/ 1/2 (sqrt 2))

series992.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
797.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
162.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
33.0ms
(* 1/3 x)
0.0ms
(/ 1/2 (sqrt 2))

simplify20.1s

Counts
150 → 157
Calls
150 calls:
Slowest
898.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (* (cbrt 2) (cbrt 2))))
865.0ms
(* (/ 1/2 (sqrt 2)) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
650.0ms
(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (cbrt 2)))
592.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
560.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

prune3.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes218.0ms

Accuracy

47.7% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.9b

bsearch222.0ms

end0.0ms

sample11.7s

Algorithm
halfpoints
Results