Details

Time bar (total: 1.6m)

sample478.0ms

Algorithm
halfpoints
Results

simplify216.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
216.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 46.0b

localize90.0ms

Local error

Found 3 expressions with local error:

58.8b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
43×*-un-lft-identity
35×associate-*l*
29×times-frac add-cube-cbrt
13×add-cbrt-cube add-exp-log
9×prod-diff
7×pow1
6×associate-*r*
5×add-log-exp
4×prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
3×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u distribute-lft-out
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 108
Calls
3 calls:
Slowest
77.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
52.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
12.0ms
(- (exp x) (exp (- x)))

series246.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
117.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
65.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
63.0ms
(- (exp x) (exp (- x)))

simplify15.6s

Counts
131 → 117
Calls
131 calls:
Slowest
989.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (sin y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))) (* (/ (- (exp x) (exp (- x))) 2) (sin y)))
854.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
584.0ms
(* (* (- (exp x) (exp (- x))) (- (exp x) (exp (- x)))) (- (exp x) (exp (- x))))
550.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
492.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (+ (exp x) (exp (- x))) 2) (cos y))) (* (/ (+ (exp x) (exp (- x))) 2) (cos y)))

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize114.0ms

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

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
32×associate-*l*
29×*-un-lft-identity
23×times-frac add-cube-cbrt
16×add-cbrt-cube add-exp-log
10×pow1
9×associate-*r*
5×prod-exp cbrt-unprod unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down *-commutative fma-udef distribute-lft-out
2×cbrt-undiv div-exp associate-*l/ div-inv
1×distribute-rgt-in distribute-lft-in
Counts
4 → 107
Calls
4 calls:
Slowest
52.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
21.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
14.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/3 (* x x) 2)

series442.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(* x (fma 1/3 (* x x) 2))
120.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
95.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
72.0ms
(fma 1/3 (* x x) 2)

simplify18.7s

Counts
123 → 119
Calls
123 calls:
Slowest
1.0s
(* (* (* x (fma 1/3 (* x x) 2)) (* x (fma 1/3 (* x x) 2))) (* x (fma 1/3 (* x x) 2)))
750.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
706.0ms
(* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y)))
564.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) 1)
512.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (+ (exp x) (exp (- x))) 2) (cos y))) (* (/ (+ (exp x) (exp (- x))) 2) (cos y)))

prune2.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize132.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
0.4b
(* x (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
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
33×associate-*l*
32×*-un-lft-identity
26×add-cube-cbrt
23×times-frac
21×add-cbrt-cube add-exp-log
18×associate-*r*
15×pow1
8×prod-exp cbrt-unprod
7×sqrt-prod
6×pow-prod-down unswap-sqr
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×distribute-lft-out
2×cbrt-undiv div-exp associate-*l/ div-inv
Counts
4 → 122
Calls
4 calls:
Slowest
47.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
26.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
19.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
11.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
108.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
99.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
74.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify19.4s

Counts
136 → 134
Calls
136 calls:
Slowest
753.0ms
(* (* (* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y)) (* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))) (* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y)))
536.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (+ (exp x) (exp (- x))) 2) (cos y))) (* (/ (+ (exp x) (exp (- x))) 2) (cos y)))
520.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
485.0ms
(* (/ (+ (exp x) (exp (- x))) (cbrt 2)) (cos y))
392.0ms
(* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sin y))

prune2.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize145.0ms

Local error

Found 4 expressions with local error:

0.4b
(* x (sqrt (fma 1/3 (* x x) 2)))
0.3b
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
0.2b
(* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
0.1b
(* (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))) 2) (sin y))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
27×associate-*r*
25×add-cbrt-cube add-exp-log
22×pow1 sqrt-prod
21×*-un-lft-identity add-cube-cbrt
18×associate-*l*
12×prod-exp cbrt-unprod
11×pow-prod-down
10×times-frac
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
1×cbrt-undiv div-exp associate-*l/ div-inv
Counts
4 → 117
Calls
4 calls:
Slowest
132.0ms
(* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
39.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
24.0ms
(* (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))) 2) (sin y))
7.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))

series685.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
258.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
183.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
139.0ms
(* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
105.0ms
(* (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))) 2) (sin y))

simplify20.1s

Counts
129 → 129
Calls
129 calls:
Slowest
847.0ms
(* (* (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))) (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))))
518.0ms
(* (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))))
507.0ms
(- (+ (* 9/2 (/ (exp (* 1/4 (- (log 1/27) (* 6 (log (/ -1 x)))))) x)) (* x (exp (* 1/4 (- (log 1/27) (* 6 (log (/ -1 x)))))))) (* 27/8 (/ (exp (* 1/4 (- (log 1/27) (* 6 (log (/ -1 x)))))) (pow x 3))))
389.0ms
(- (+ (* 9/2 (/ (exp (* 1/4 (- (log 1/27) (* 6 (log (/ 1 x)))))) x)) (* x (exp (* 1/4 (- (log 1/27) (* 6 (log (/ 1 x)))))))) (* 27/8 (/ (exp (* 1/4 (- (log 1/27) (* 6 (log (/ 1 x)))))) (pow x 3))))
372.0ms
(* (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))) (sqrt 2)) (sin y))

prune2.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes182.0ms

Accuracy

0% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 0.8b

bsearch4.0ms

end0.0ms

sample12.0s

Algorithm
halfpoints
Results