Details

Time bar (total: 1.1m)

sample513.0ms

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))))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.4b

localize132.0ms

Local error

Found 4 expressions with local error:

58.3b
(- (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)))

rewrite103.0ms

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
38.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
36.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
16.0ms
(- (exp x) (exp (- x)))
10.0ms
(+ (exp x) (exp (- x)))

series300.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
89.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
55.0ms
(- (exp x) (exp (- x)))
40.0ms
(+ (exp x) (exp (- x)))

simplify7.5s

Counts
99 → 138
Calls
99 calls:
Slowest
850.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
468.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
357.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
262.0ms
(* (/ (* (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))) (+ (exp x) (exp (- x)))) (* (* 2 2) 2)) (* (* (cos y) (cos y)) (cos y)))
258.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))

prune2.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

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

rewrite71.0ms

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
50.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
12.0ms
(* (/ (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)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(* x (fma 1/3 (* x x) 2))
144.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
107.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
82.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

simplify11.3s

Counts
77 → 119
Calls
77 calls:
Slowest
844.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
736.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
476.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
463.0ms
(sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2))
462.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize159.0ms

Local error

Found 4 expressions with local error:

0.5b
(* 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
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite103.0ms

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
54.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
21.0ms
(* (* 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)))
12.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))

series498.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
119.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
112.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
81.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

simplify9.1s

Counts
92 → 134
Calls
92 calls:
Slowest
450.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
414.0ms
(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
310.0ms
(* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sin y))
284.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
264.0ms
(* (/ (* (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))) (+ (exp x) (exp (- x)))) (* (* 2 2) 2)) (* (* (cos y) (cos y)) (cos y)))

prune2.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize153.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))
0.3b
(* (* 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))

rewrite235.0ms

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
157.0ms
(* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))
27.0ms
(* (* x (sqrt (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 (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))
20.0ms
(* x (sqrt (sqrt (fma 1/3 (* x x) 2))))

series653.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
224.0ms
(* x (sqrt (sqrt (fma 1/3 (* x x) 2))))
170.0ms
(* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
144.0ms
(* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (fma 1/3 (* x x) 2)))
114.0ms
(* (/ (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))

simplify13.6s

Counts
88 → 130
Calls
88 calls:
Slowest
648.0ms
(* (* (* (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (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))))) (* (* x (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))) (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
611.0ms
(* (* (* (* 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)))))
516.0ms
(/ (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))))) (* (cbrt 2) (cbrt 2)))
503.0ms
(/ (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))))) (sqrt 2))
501.0ms
(- (+ (* 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))))

prune2.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes234.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch4.0ms

end0.0ms

sample12.0s

Algorithm
halfpoints
Results