Details

Time bar (total: 38.4s)

sample546.0ms

Algorithm
halfpoints
Results

simplify170.0ms

Calls
1 calls:
Slowest
170.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize126.0ms

Local error

Found 3 expressions with local error:

58.4b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
9×prod-diff
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log
6×associate-*r*
5×add-log-exp
3×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod div-inv
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
3 calls:
Slowest
25.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
25.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
13.0ms
(- (exp x) (exp (- x)))

series267.0ms

Calls
3 calls:
Slowest
113.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
87.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
66.0ms
(- (exp x) (exp (- x)))

simplify4.2s

Calls
53 calls:
Slowest
742.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
388.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
239.0ms
(* 1/2 (* (+ (exp x) (exp (- x))) (cos y)))
209.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
195.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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
(fma 1/3 (* x x) 2)
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×associate-*l*
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv
1×fma-udef
Calls
4 calls:
Slowest
18.0ms
(* (/ (+ (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))
3.0ms
(* (fma 1/3 (* x x) 2) x)
0.0ms
(fma 1/3 (* x x) 2)

series362.0ms

Calls
4 calls:
Slowest
128.0ms
(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
107.0ms
(* (fma 1/3 (* x x) 2) x)
65.0ms
(fma 1/3 (* x x) 2)
61.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify2.8s

Calls
34 calls:
Slowest
435.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
224.0ms
(* (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) (sin y))
210.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
178.0ms
(* (/ (fma 1/60 (pow x 5) (* (fma 1/3 (* x x) 2) x)) 2) (sin y))
173.0ms
(* 1/2 (* (+ (exp x) (exp (- x))) (cos y)))

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (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
(fma 1/3 (* x x) 2)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*l*
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×sqrt-prod
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-prod-down prod-exp cbrt-unprod
1×associate-*l/ fma-udef div-inv
Calls
4 calls:
Slowest
13.0ms
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
10.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
4.0ms
(* (sqrt (fma 1/3 (* x x) 2)) x)
0.0ms
(fma 1/3 (* x x) 2)

series471.0ms

Calls
4 calls:
Slowest
137.0ms
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))
136.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))
134.0ms
(* (sqrt (fma 1/3 (* x x) 2)) x)
64.0ms
(fma 1/3 (* x x) 2)

simplify3.9s

Calls
35 calls:
Slowest
652.0ms
(* (* (* (/ (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)))
505.0ms
(* (* (* (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)))
295.0ms
(- (+ (* 1/6 (/ (pow x 3) (sqrt 2))) (* (sqrt 2) x)) (* 1/72 (/ (pow x 5) (pow (sqrt 2) 3))))
294.0ms
(* (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) (sin y))
284.0ms
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (fma 1/3 (* x x) 2)) x))) 2) (sin y))

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b
(log1p (fma 1/3 (* x x) 2))
0.5b
(* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x)
0.4b
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))
0.1b
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))) 2) (sin y))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*l*
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×sqrt-prod
5×expm1-log1p-u
4×associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-prod-down prod-exp cbrt-unprod
1×log1p-udef associate-*l/ log1p-expm1 div-inv
Calls
4 calls:
Slowest
10.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))
6.0ms
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))) 2) (sin y))
6.0ms
(* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x)
1.0ms
(log1p (fma 1/3 (* x x) 2))

series1.4s

Calls
4 calls:
Slowest
676.0ms
(* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))
324.0ms
(* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))) 2) (sin y))
262.0ms
(* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x)
97.0ms
(log1p (fma 1/3 (* x x) 2))

simplify5.6s

Calls
36 calls:
Slowest
859.0ms
(* (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))) (* (* (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x)))
542.0ms
(* (* (* (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))) 2) (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))) 2)) (/ (fma 1/60 (pow x 5) (* (sqrt (fma 1/3 (* x x) 2)) (* (sqrt (expm1 (log1p (fma 1/3 (* x x) 2)))) x))) 2)) (* (* (sin y) (sin y)) (sin y)))
450.0ms
(- (+ (* (sqrt (/ 1 (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1))) (/ 1 (sqrt 1/3))) (+ (* 1/2 (* (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3))) (sqrt (/ 1 (pow (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1) 3))))) (* 25/8 (* (/ (pow (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 2) (* (pow (sqrt 1/3) 3) (pow x 2))) (sqrt (/ 1 (pow (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1) 3))))))) (+ (* 5/2 (* (/ (exp (- (log 1/3) (* 2 (log (/ -1 x))))) (* (pow (sqrt 1/3) 3) (pow x 2))) (sqrt (/ 1 (pow (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1) 3))))) (+ (* 5/2 (* (/ (exp (- (log 1/3) (* 2 (log (/ -1 x))))) (sqrt 1/3)) (sqrt (/ 1 (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1))))) (+ (* (* (pow x 2) (sqrt 1/3)) (sqrt (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1))) (* 9 (* (/ (exp (- (log 1/3) (* 2 (log (/ -1 x))))) (* (sqrt 1/3) (pow x 2))) (sqrt (/ 1 (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1)))))))))
379.0ms
(- (+ (* x (sqrt (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1))) (* 9/2 (* (/ (exp (- (log 1/3) (* 2 (log (/ -1 x))))) x) (sqrt (/ 1 (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1)))))) (* 81/8 (* (/ (pow (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 2) (pow x 3)) (sqrt (/ 1 (pow (- (exp (- (log 1/3) (* 2 (log (/ -1 x))))) 1) 3))))))
359.0ms
(- (+ (log 1/3) (* 9 (/ 1 (pow x 2)))) (+ (* 2 (log (/ -1 x))) (* 81/2 (/ 1 (pow x 4)))))

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes249.0ms

Accuracy

0% (0.8b remaining)

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

bsearch7.0ms

end0.0ms

sample12.1s

Algorithm
halfpoints
Results