Details

Time bar (total: 5.0m)

sample509.0ms

Algorithm
halfpoints
Results

simplify165.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
164.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 46.0b

localize100.0ms

Local error

Found 3 expressions with local error:

58.8b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite123.0ms

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
61.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
39.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
21.0ms
(- (exp x) (exp (- x)))

series279.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
113.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
94.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
71.0ms
(- (exp x) (exp (- x)))

simplify12.8s

Counts
104 → 99
Calls
104 calls:
Slowest
860.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (sin y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))) (* (/ (- (exp x) (exp (- x))) 2) (sin y)))
830.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
521.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
499.0ms
(* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x))))
472.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (+ (exp x) (exp (- x))) 2) (cos y))) (* (/ (+ (exp x) (exp (- x))) 2) (cos y)))

prune1.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize129.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/3 x)
0.2b
(* x (* 1/3 x))
0.1b
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
0.0b
(* (pow x 5) 1/60)

rewrite103.0ms

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
68.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
20.0ms
(* x (* 1/3 x))
8.0ms
(* (pow x 5) 1/60)
5.0ms
(* 1/3 x)

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
96.0ms
(* (pow x 5) 1/60)
39.0ms
(* x (* 1/3 x))
16.0ms
(* 1/3 x)

simplify15.9s

Counts
111 → 109
Calls
111 calls:
Slowest
891.0ms
(* (/ (* (* (+ (* 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)))
634.0ms
(* (cbrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sin y))
562.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
557.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
527.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sin y))

prune2.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize170.0ms

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)))
0.4b
(* 1/3 x)

rewrite189.0ms

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
89.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
82.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
9.0ms
(/ 1 (sqrt 2))
5.0ms
(* 1/3 x)

series512.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
285.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
212.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
15.0ms
(* 1/3 x)
0.0ms
(/ 1 (sqrt 2))

simplify36.6s

Counts
209 → 172
Calls
209 calls:
Slowest
1.0s
(* (/ (* (* 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))))
756.0ms
(* (sqrt 2) (+ (* (* x (+ (* x (* 1/3 x)) 2)) (* x (+ (* x (* 1/3 x)) 2))) (- (* (* (pow x 5) 1/60) (* (pow x 5) 1/60)) (* (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))))
699.0ms
(* (/ (* (* 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))))
640.0ms
(* (* (/ (+ (* 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)))

prune3.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize132.0ms

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)))

rewrite226.0ms

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
105.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
60.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
12.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
6.0ms
(/ 1 (sqrt (sqrt 2)))

series894.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
718.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
176.0ms
(/ (+ (* 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)))

simplify3.2m

Counts
1105 → 779
Calls
1105 calls:
Slowest
1.3s
(* (/ (/ (* (* 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))))
1.1s
(* (/ (* (* (/ 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))))
988.0ms
(* (/ (/ (sqrt 1) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
915.0ms
(* (/ (/ (cbrt 1) (sqrt (sqrt 2))) (sqrt (sqrt (cbrt 2)))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
884.0ms
(* (/ (/ (cbrt 1) (sqrt (sqrt (cbrt 2)))) (sqrt (sqrt 2))) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))

prune19.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 0.8b

bsearch5.0ms

end0.0ms

sample11.4s

Algorithm
halfpoints
Results