Details

Time bar (total: 1.0m)

sample415.0ms

Algorithm
halfpoints
Results

simplify231.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
231.0ms
(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: 42.9b

localize122.0ms

Local error

Found 4 expressions with local error:

57.7b
(- (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)))

rewrite147.0ms

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
53.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
46.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
34.0ms
(- (exp x) (exp (- x)))
12.0ms
(+ (exp x) (exp (- x)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
77.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
61.0ms
(- (exp x) (exp (- x)))
25.0ms
(+ (exp x) (exp (- x)))

simplify7.3s

Counts
99 → 138
Calls
99 calls:
Slowest
813.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
509.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
324.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
286.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
248.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize125.0ms

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
(+ (exp x) (exp (- x)))
0.0b
(* x (fma 1/3 (* x x) 2))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
32×*-un-lft-identity associate-*l*
24×add-cube-cbrt
23×times-frac
16×add-cbrt-cube add-exp-log
10×pow1
9×associate-*r*
6×add-log-exp
5×prod-exp cbrt-unprod unswap-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out
3×fma-def pow-prod-down *-commutative
2×cbrt-undiv div-exp associate-*l/ fma-udef div-inv
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+
Counts
4 → 114
Calls
4 calls:
Slowest
79.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
26.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
20.0ms
(+ (exp x) (exp (- x)))
12.0ms
(* x (fma 1/3 (* x x) 2))

series415.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
121.0ms
(* x (fma 1/3 (* x x) 2))
91.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
40.0ms
(+ (exp x) (exp (- x)))

simplify10.2s

Counts
81 → 126
Calls
81 calls:
Slowest
807.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
508.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
502.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
487.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
466.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))

prune2.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize154.0ms

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)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
20×*-un-lft-identity
18×add-cube-cbrt
17×associate-*l*
16×add-cbrt-cube add-exp-log
15×associate-*r*
13×pow1
10×times-frac
7×sqrt-prod
6×prod-exp cbrt-unprod add-log-exp
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×fma-def *-commutative
1×cbrt-undiv +-commutative sum-log flip3-+ div-exp associate-*l/ flip-+ div-inv distribute-lft-out
Counts
4 → 102
Calls
4 calls:
Slowest
26.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
24.0ms
(* (/ (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
(+ (exp x) (exp (- x)))
9.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
129.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))
119.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))
30.0ms
(+ (exp x) (exp (- x)))

simplify7.4s

Counts
68 → 114
Calls
68 calls:
Slowest
493.0ms
(fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
393.0ms
(* (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) (sin y))
292.0ms
(+ (- (log (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))) (log 2)) (log (sin y)))
272.0ms
(* (* (* x x) x) (* (* (sqrt (fma 1/3 (* x x) 2)) (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2))))
254.0ms
(* (/ (fma 1/60 (pow x 5) (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (fma 1/3 (* x x) 2)))) 2) (sin y))

prune2.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize148.0ms

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))

rewrite173.0ms

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
111.0ms
(* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
27.0ms
(* (* 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))
8.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
248.0ms
(* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2))))
157.0ms
(* x (sqrt (fma 1/3 (* x x) 2)))
131.0ms
(* (/ (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))
118.0ms
(* (* (* x (sqrt (fma 1/3 (* x x) 2))) (sqrt (sqrt (fma 1/3 (* x x) 2)))) (sqrt (sqrt (fma 1/3 (* x x) 2))))

simplify12.2s

Counts
86 → 129
Calls
86 calls:
Slowest
807.0ms
(* (* (* (* x (sqrt (fma 1/3 (* x x) 2))) (* x (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)))) (sqrt (sqrt (fma 1/3 (* x x) 2)))))
551.0ms
(* (cbrt (/ (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)) (cbrt (/ (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)))
547.0ms
(/ (sqrt (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))
492.0ms
(/ (* (cbrt (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)))))) (cbrt (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))
488.0ms
(sqrt (/ (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))

prune3.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes251.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch4.0ms

end0.0ms

sample11.7s

Algorithm
halfpoints
Results