Details

Time bar (total: 59.2s)

sample453.0ms

Algorithm
halfpoints
Results

simplify228.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
228.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.5b

localize113.0ms

Local error

Found 3 expressions with local error:

58.7b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(+ (exp x) (exp (- x)))

rewrite113.0ms

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
Counts
3 → 88
Calls
3 calls:
Slowest
60.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
28.0ms
(- (exp x) (exp (- x)))
21.0ms
(+ (exp x) (exp (- x)))

series260.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
143.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
74.0ms
(- (exp x) (exp (- x)))
43.0ms
(+ (exp x) (exp (- x)))

simplify5.2s

Counts
68 → 97
Calls
68 calls:
Slowest
776.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
275.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
254.0ms
(fma 1 (exp x) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
236.0ms
(fma (sqrt (exp x)) (sqrt (exp x)) (- (* (cbrt (exp (- x))) (* (cbrt (exp (- x))) (cbrt (exp (- x)))))))
230.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize156.0ms

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×associate-*l*
14×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×times-frac
8×pow1
6×associate-*r*
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod unswap-sqr
2×pow-prod-down *-commutative
1×distribute-rgt-in cbrt-undiv distribute-lft-in div-exp associate-*l/ div-inv
Counts
4 → 80
Calls
4 calls:
Slowest
14.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
7.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
0.0ms
(fma 1/3 (* x x) 2)

series443.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
112.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
111.0ms
(* x (fma 1/3 (* x x) 2))
75.0ms
(fma 1/3 (* x x) 2)

simplify9.4s

Counts
49 → 92
Calls
49 calls:
Slowest
826.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
825.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
495.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)
490.0ms
(sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2))
472.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize178.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
17×*-un-lft-identity associate-*l* add-cube-cbrt
16×add-cbrt-cube add-exp-log
15×associate-*r*
13×pow1
10×times-frac
7×sqrt-prod
6×prod-exp cbrt-unprod
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
1×cbrt-undiv div-exp associate-*l/ fma-udef div-inv
Counts
4 → 95
Calls
4 calls:
Slowest
43.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
27.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
16.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
0.0ms
(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))

series566.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
153.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
153.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
81.0ms
(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))

simplify8.1s

Counts
64 → 107
Calls
64 calls:
Slowest
438.0ms
(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
382.0ms
(* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sin y))
338.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
272.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
267.0ms
(* (* (* x x) x) (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))

prune2.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize214.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
39×*-un-lft-identity add-cube-cbrt
36×times-frac
31×sqrt-prod
17×add-exp-log
15×add-cbrt-cube
13×pow1
12×associate-/r* associate-*r*
6×associate-/l*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-exp pow-flip
2×cbrt-undiv clear-num frac-2neg *-commutative div-inv unswap-sqr
1×rec-exp sqrt-pow1 pow1/2 1-exp inv-pow
Counts
4 → 139
Calls
4 calls:
Slowest
23.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
15.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
11.0ms
(/ 1 (sqrt 2))
10.0ms
(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))

series457.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
179.0ms
(/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sqrt 2))
161.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
117.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
0.0ms
(/ 1 (sqrt 2))

simplify11.2s

Counts
133 → 149
Calls
133 calls:
Slowest
662.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (sqrt (sqrt 2)))
441.0ms
(/ (* (* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
273.0ms
(* (* (* x x) x) (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
267.0ms
(/ (* (cbrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (cbrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
258.0ms
(/ (cbrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (sqrt (sqrt 2)))

prune3.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes244.0ms

Accuracy

0% (0.7b remaining)

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

bsearch4.0ms

end0.0ms

sample12.3s

Algorithm
halfpoints
Results