Details

Time bar (total: 1.5m)

sample470.0ms

Algorithm
halfpoints
Results

simplify177.0ms

Calls
1 calls:
Slowest
177.0ms
(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: 41.6b

localize109.0ms

Local error

Found 3 expressions with local error:

57.7b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(+ (exp x) (exp (- x)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
31×*-un-lft-identity
21×add-cube-cbrt
19×associate-*l*
16×times-frac
9×prod-diff
8×add-cbrt-cube add-exp-log
7×add-log-exp
5×pow1
4×distribute-lft-out-- difference-of-squares
3×expm1-log1p-u fma-def fma-neg associate-*r* insert-posit16 log1p-expm1-u
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative sum-log sub-neg flip3-+ flip3-- diff-log div-exp pow-prod-down associate-*l/ *-commutative flip-+ div-inv flip-- distribute-lft-out
Calls
3 calls:
Slowest
53.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
20.0ms
(- (exp x) (exp (- x)))
11.0ms
(+ (exp x) (exp (- x)))

series209.0ms

Calls
3 calls:
Slowest
108.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
70.0ms
(- (exp x) (exp (- x)))
31.0ms
(+ (exp x) (exp (- x)))

simplify5.3s

Calls
68 calls:
Slowest
789.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
335.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
255.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
244.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
238.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
13×associate-*l* add-cube-cbrt
10×times-frac
9×add-cbrt-cube add-exp-log
6×pow1 add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r*
2×prod-exp cbrt-unprod fma-udef unswap-sqr
1×cbrt-undiv +-commutative sum-log flip3-+ div-exp pow-prod-down associate-*l/ *-commutative flip-+ div-inv distribute-lft-out
Calls
4 calls:
Slowest
13.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
10.0ms
(+ (exp x) (exp (- x)))
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
0.0ms
(fma 1/3 (* x x) 2)

series369.0ms

Calls
4 calls:
Slowest
141.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
102.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
78.0ms
(fma 1/3 (* x x) 2)
47.0ms
(+ (exp x) (exp (- x)))

simplify7.5s

Calls
41 calls:
Slowest
819.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
498.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
471.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
441.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))
393.0ms
(sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize132.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt 2))
0.4b
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.4b
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
0.2b
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
69×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
54×add-exp-log
44×associate-*l*
43×sqrt-prod
34×add-cbrt-cube
22×prod-exp
14×div-exp
13×pow1
12×associate-/r* cbrt-unprod
8×cbrt-undiv
6×associate-/l*
4×expm1-log1p-u rec-exp 1-exp associate-*r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-flip unswap-sqr
2×clear-num frac-2neg *-commutative
1×frac-times sqrt-pow1 pow1/2 associate-*r/ inv-pow
Calls
4 calls:
Slowest
46.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
28.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
5.0ms
(/ 1 (sqrt 2))
5.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))

series715.0ms

Calls
4 calls:
Slowest
303.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
226.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
186.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms
(/ 1 (sqrt 2))

simplify29.5s

Calls
187 calls:
Slowest
792.0ms
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))))
691.0ms
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
660.0ms
(/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
651.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
534.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt (sqrt 2)))

prune4.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize120.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
57×*-un-lft-identity
55×add-sqr-sqrt add-cube-cbrt
16×associate-/r*
11×add-cbrt-cube add-exp-log
6×div-inv associate-/l* add-log-exp
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×fma-def
2×clear-num frac-2neg
1×+-commutative sum-log flip3-+ associate-/r/ flip-+ fma-udef distribute-lft-out
Calls
4 calls:
Slowest
10.0ms
(/ (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))) (/ 2 (sin y)))
10.0ms
(+ (exp x) (exp (- x)))
5.0ms
(/ 2 (sin y))
0.0ms
(fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))

series255.0ms

Calls
4 calls:
Slowest
121.0ms
(/ (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))) (/ 2 (sin y)))
81.0ms
(fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))
30.0ms
(+ (exp x) (exp (- x)))
22.0ms
(/ 2 (sin y))

simplify23.1s

Calls
139 calls:
Slowest
817.0ms
(/ (sqrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ 2 (sin y)))
535.0ms
(/ (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ 2 (sin y)))
498.0ms
(/ (sqrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ (sqrt 2) 1))
483.0ms
(/ (sqrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (/ 2 (sin y)))
479.0ms
(/ (* (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))) (cbrt (fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2))))) (/ 1 1))

prune2.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch7.0ms

end0.0ms

sample11.6s

Algorithm
halfpoints
Results