Details

Time bar (total: 31.8s)

sample434.0ms

Algorithm
halfpoints
Results

simplify190.0ms

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize92.0ms

Local error

Found 4 expressions with local error:

58.5b
(- (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)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-sqr-sqrt
16×add-cube-cbrt
9×prod-diff
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-log-exp
6×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def fma-neg
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod div-inv
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
25.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
20.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
7.0ms
(- (exp x) (exp (- x)))
5.0ms
(+ (exp x) (exp (- x)))

series190.0ms

Calls
4 calls:
Slowest
73.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
48.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
44.0ms
(- (exp x) (exp (- x)))
24.0ms
(+ (exp x) (exp (- x)))

simplify3.6s

Calls
60 calls:
Slowest
569.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
360.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
175.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
175.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))
149.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
0.0b
(* (fma 1/3 (* x x) 2) x)
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.0b
(+ (exp x) (exp (- x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×associate-*l*
10×add-sqr-sqrt add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def *-commutative
2×pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv
1×+-commutative sum-log flip3-+ flip-+ distribute-lft-out
Calls
4 calls:
Slowest
13.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
6.0ms
(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
5.0ms
(+ (exp x) (exp (- x)))
4.0ms
(* (fma 1/3 (* x x) 2) x)

series202.0ms

Calls
4 calls:
Slowest
65.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
60.0ms
(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
39.0ms
(* (fma 1/3 (* x x) 2) x)
38.0ms
(+ (exp x) (exp (- x)))

simplify2.8s

Calls
38 calls:
Slowest
417.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
295.0ms
(* (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (sin y))
201.0ms
(* 1/2 (* (+ (exp x) (exp (- x))) (cos y)))
196.0ms
(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
160.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (fma 1/3 (* x x) 2)) x)
0.4b
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
0.1b
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
0.0b
(+ (exp x) (exp (- x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*l*
13×*-un-lft-identity
11×add-sqr-sqrt add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×sqrt-prod add-log-exp
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u
3×fma-def *-commutative
2×pow-prod-down prod-exp cbrt-unprod
1×+-commutative sum-log flip3-+ associate-*l/ flip-+ div-inv distribute-lft-out
Calls
4 calls:
Slowest
10.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
9.0ms
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
5.0ms
(+ (exp x) (exp (- x)))
3.0ms
(* (sqrt (fma 1/3 (* x x) 2)) x)

series171.0ms

Calls
4 calls:
Slowest
61.0ms
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
51.0ms
(* (sqrt (fma 1/3 (* x x) 2)) x)
35.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
24.0ms
(+ (exp x) (exp (- x)))

simplify3.8s

Calls
39 calls:
Slowest
596.0ms
(* (* (* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2)) (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2)) (* (* (sin y) (sin y)) (sin y)))
451.0ms
(* (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))) (* (* (* (sqrt (fma 1/3 (* x x) 2)) x) (* (sqrt (fma 1/3 (* x x) 2)) x)) (* (sqrt (fma 1/3 (* x x) 2)) x)))
317.0ms
(- (+ (* 1/6 (/ (pow x 3) (sqrt 2))) (* (sqrt 2) x)) (* 1/72 (/ (pow x 5) (pow (sqrt 2) 3))))
305.0ms
(* (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) (sin y))
295.0ms
(- (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))) (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))))

prune2.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin y))
0.6b
(cbrt (sin y))
0.6b
(cbrt (sin y))
0.5b
(* (cbrt (sin y)) (cbrt (sin y)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
7×pow1/3
6×associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
11.0ms
(* (cbrt (sin y)) (cbrt (sin y)))
1.0ms
(cbrt (sin y))
1.0ms
(cbrt (sin y))
1.0ms
(cbrt (sin y))

series634.0ms

Calls
4 calls:
Slowest
176.0ms
(cbrt (sin y))
175.0ms
(cbrt (sin y))
154.0ms
(* (cbrt (sin y)) (cbrt (sin y)))
129.0ms
(cbrt (sin y))

simplify662.0ms

Calls
41 calls:
Slowest
138.0ms
(- (pow y 1/3) (+ (* 1/18 (pow (pow y 7) 1/3)) (* 1/3240 (pow (pow y 13) 1/3))))
136.0ms
(- (+ (pow y 2/3) (* 1/405 (pow (pow y 14) 1/3))) (* 1/9 (pow (pow y 8) 1/3)))
124.0ms
(- (pow y 1/3) (+ (* 1/18 (pow (pow y 7) 1/3)) (* 1/3240 (pow (pow y 13) 1/3))))
121.0ms
(- (pow y 1/3) (+ (* 1/18 (pow (pow y 7) 1/3)) (* 1/3240 (pow (pow y 13) 1/3))))
6.0ms
(+ (log (cbrt (sin y))) (log (cbrt (sin y))))

prune1.7s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes304.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch8.0ms

end0.0ms

sample11.9s

Algorithm
halfpoints
Results