Details

Time bar (total: 1.6m)

sample422.0ms

Algorithm
halfpoints
Results

simplify177.0ms

Counts
1 → 1
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: 45.4b

localize98.0ms

Local error

Found 2 expressions with local error:

58.7b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
27×*-un-lft-identity
19×associate-*l* add-cube-cbrt
16×times-frac
9×prod-diff
7×add-cbrt-cube add-exp-log
4×pow1 distribute-lft-out-- add-log-exp difference-of-squares
3×fma-neg associate-*r*
2×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
1×cbrt-undiv sub-neg flip3-- diff-log div-exp pow-prod-down associate-*l/ *-commutative div-inv flip--
Counts
2 → 70
Calls
2 calls:
Slowest
38.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
17.0ms
(- (exp x) (exp (- x)))

series176.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
111.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
65.0ms
(- (exp x) (exp (- x)))

simplify5.3s

Counts
61 → 76
Calls
61 calls:
Slowest
910.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
303.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
274.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
237.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
227.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize143.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×associate-*l*
13×*-un-lft-identity add-cube-cbrt
10×times-frac add-cbrt-cube add-exp-log
7×pow1
6×associate-*r*
3×expm1-log1p-u prod-exp cbrt-unprod fma-udef insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down *-commutative
1×distribute-rgt-in cbrt-undiv distribute-lft-in div-exp associate-*l/ div-inv
Counts
3 → 69
Calls
3 calls:
Slowest
13.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
6.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series376.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
148.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
138.0ms
(* x (fma 1/3 (* x x) 2))
91.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

simplify9.5s

Counts
46 → 78
Calls
46 calls:
Slowest
823.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
819.0ms
(sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2))
529.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))
527.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
504.0ms
(* (cbrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (cbrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)))

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize110.0ms

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))

rewrite122.0ms

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
Counts
4 → 192
Calls
4 calls:
Slowest
73.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
32.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
7.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
5.0ms
(/ 1 (sqrt 2))

series652.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
291.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
209.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
152.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms
(/ 1 (sqrt 2))

simplify29.5s

Counts
187 → 202
Calls
187 calls:
Slowest
909.0ms
(sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)))
693.0ms
(* (* (* (/ 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))))
685.0ms
(* (/ (* (* 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))))
659.0ms
(/ (* (* (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)))
551.0ms
(/ (cbrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))

prune4.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize143.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
70×add-sqr-sqrt
62×*-un-lft-identity add-cube-cbrt
47×associate-*l*
43×sqrt-prod
22×cbrt-prod add-exp-log
19×add-cbrt-cube
12×associate-/r*
11×pow1
7×prod-exp cbrt-unprod
6×associate-/l*
4×expm1-log1p-u cbrt-undiv div-exp associate-*r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×unswap-sqr
2×cbrt-div clear-num frac-2neg *-commutative
1×frac-times associate-*r/
Counts
4 → 177
Calls
4 calls:
Slowest
53.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
20.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
9.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
9.0ms
(/ 1/2 (sqrt 2))

series1.3s

Counts
4 → 10
Calls
4 calls:
Slowest
851.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
257.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
170.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms
(/ 1/2 (sqrt 2))

simplify25.5s

Counts
175 → 187
Calls
175 calls:
Slowest
724.0ms
(/ (* (* (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)))
610.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))
586.0ms
(* (/ (* (* (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))) (* (* (sin y) (sin y)) (sin y)))
582.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))
576.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt (sqrt 2)))

prune4.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes147.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch7.0ms

end0.0ms

sample11.6s

Algorithm
halfpoints
Results