Details

Time bar (total: 1.1m)

sample481.0ms

Algorithm
halfpoints
Results

simplify165.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
165.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.1b

localize83.0ms

Local error

Found 4 expressions with local error:

59.1b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
0.0b
(+ (exp x) (exp (- x)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
47×*-un-lft-identity
35×associate-*l*
31×add-cube-cbrt
29×times-frac
14×add-cbrt-cube add-exp-log
9×prod-diff
8×pow1 add-log-exp
6×associate-*r*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
3×fma-def fma-neg
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip--
Counts
4 → 126
Calls
4 calls:
Slowest
68.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
53.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
19.0ms
(+ (exp x) (exp (- x)))
17.0ms
(- (exp x) (exp (- x)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
82.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
70.0ms
(- (exp x) (exp (- x)))
42.0ms
(+ (exp x) (exp (- x)))

simplify7.5s

Counts
99 → 138
Calls
99 calls:
Slowest
842.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
461.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
298.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
292.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
285.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))

prune2.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize141.0ms

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

rewrite83.0ms

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
51.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
25.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
5.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
111.0ms
(* x (fma 1/3 (* x x) 2))
91.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
74.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify11.2s

Counts
77 → 119
Calls
77 calls:
Slowest
699.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
523.0ms
(sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2))
495.0ms
(* (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)))
478.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
475.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))

prune2.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize109.0ms

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))

rewrite99.0ms

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
53.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
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))
19.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
7.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
198.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
137.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
119.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
90.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify9.1s

Counts
92 → 134
Calls
92 calls:
Slowest
500.0ms
(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
485.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
266.0ms
(* (/ (sqrt (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (sqrt 2)) (sqrt (sin y)))
258.0ms
(- (* 1/2 (/ 1 (* (pow x 2) (pow (sqrt 1/3) 3)))) (+ (/ 1 (sqrt 1/3)) (* (pow x 2) (sqrt 1/3))))
257.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize142.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))
0.4b
(* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
0.2b
(* x (sqrt (sqrt (fma 1/3 (* x x) 2))))
0.1b
(* (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
27×associate-*r*
25×add-cbrt-cube add-exp-log
24×sqrt-prod
22×pow1
21×*-un-lft-identity add-cube-cbrt
18×associate-*l*
12×prod-exp cbrt-unprod
11×pow-prod-down
10×times-frac
5×unswap-sqr
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv div-exp associate-*l/ div-inv
Counts
4 → 118
Calls
4 calls:
Slowest
102.0ms
(* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))
46.0ms
(* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
12.0ms
(* (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
8.0ms
(* x (sqrt (sqrt (fma 1/3 (* x x) 2))))

series687.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
270.0ms
(* x (sqrt (sqrt (fma 1/3 (* x x) 2))))
176.0ms
(* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
129.0ms
(* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))
111.0ms
(* (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))

simplify13.5s

Counts
88 → 130
Calls
88 calls:
Slowest
657.0ms
(* (* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (* x (sqrt (sqrt (fma 1/3 (* x x) 2))))) (* x (sqrt (sqrt (fma 1/3 (* x x) 2))))) (* (* (sqrt (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))))
514.0ms
(- (+ (* 1/24 (* (pow x 3) (pow 2 1/4))) (* x (pow 2 1/4))) (* 1/384 (* (pow x 5) (pow 2 1/4))))
504.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))) 2)) (sqrt (sin y)))
499.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2))))) 1)
491.0ms
(- (+ (* 3/2 (/ (exp (* 1/4 (- (log 1/3) (* 2 (log (/ -1 x)))))) x)) (* x (exp (* 1/4 (- (log 1/3) (* 2 (log (/ -1 x)))))))) (* 27/8 (/ (exp (* 1/4 (- (log 1/3) (* 2 (log (/ -1 x)))))) (pow x 3))))

prune2.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes267.0ms

Accuracy

0% (0.7b remaining)

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

bsearch7.0ms

end0.0ms

sample11.7s

Algorithm
halfpoints
Results