Details

Time bar (total: 2.5m)

sample371.0ms

Algorithm
halfpoints
Results

simplify250.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
249.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 46.0b

localize99.0ms

Local error

Found 3 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))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
36×*-un-lft-identity
35×associate-*l*
29×times-frac
22×add-cube-cbrt
13×add-cbrt-cube add-exp-log
7×pow1
6×associate-*r*
5×add-log-exp
4×prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
3×insert-posit16 distribute-lft-out
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 90
Calls
3 calls:
Slowest
66.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
42.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
10.0ms
(- (exp x) (exp (- x)))

series242.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
113.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
88.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
42.0ms
(- (exp x) (exp (- x)))

simplify5.5s

Counts
72 → 99
Calls
72 calls:
Slowest
902.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
424.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
291.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
262.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
259.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))

prune1.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize129.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 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)

rewrite110.0ms

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
83.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
13.0ms
(* x (* 1/3 x))
8.0ms
(* (pow x 5) 1/60)
6.0ms
(* 1/3 x)

series266.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
84.0ms
(* (pow x 5) 1/60)
38.0ms
(* x (* 1/3 x))
19.0ms
(* 1/3 x)

simplify9.6s

Counts
72 → 109
Calls
72 calls:
Slowest
1000.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) 1)
632.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
588.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
528.0ms
(* (/ (* (* (+ (* 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))) (* (* 2 2) 2)) (* (* (sin y) (sin y)) (sin y)))
513.0ms
(/ (* (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)

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize150.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt 2))
0.5b
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
0.4b
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
0.3b
(* 1/3 x)

rewrite140.0ms

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
73.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
54.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
5.0ms
(/ 1 (sqrt 2))
5.0ms
(* 1/3 x)

series470.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
290.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
152.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
27.0ms
(* 1/3 x)
0.0ms
(/ 1 (sqrt 2))

simplify26.2s

Counts
162 → 172
Calls
162 calls:
Slowest
1.2s
(* (/ (* (* 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))))
997.0ms
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (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))))
691.0ms
(* (/ (* (* 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))))
610.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))

prune3.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

localize128.0ms

Local error

Found 4 expressions with local error:

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

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
1128×sqrt-prod
1116×times-frac
592×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
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×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*l/ associate-/l/
2×inv-pow
1×frac-times flip3-+ associate-*r* associate-*r/ *-commutative flip-+
Counts
4 → 771
Calls
4 calls:
Slowest
131.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
64.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
24.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
10.0ms
(/ 1 (sqrt (sqrt 2)))

series538.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
334.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
203.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify1.1m

Counts
1060 → 779
Calls
1060 calls:
Slowest
1.0s
(* (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (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))))
974.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
968.0ms
(* (/ (/ (* (* 1 1) 1) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (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))))
959.0ms
(* (/ (* (* (/ 1 (sqrt (sqrt 2))) (/ 1 (sqrt (sqrt 2)))) (/ 1 (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y))))
812.0ms
(* (/ (/ (* (* 1 1) 1) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))) (* (* (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y))))

prune19.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes267.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch9.0ms

end0.0ms

sample11.6s

Algorithm
halfpoints
Results