Details

Time bar (total: 1.7m)

sample490.0ms

Algorithm
halfpoints
Results

simplify240.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
240.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 47.2b

localize108.0ms

Local error

Found 4 expressions with local error:

58.1b
(- (exp x) (exp (- x)))
0.2b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(+ (exp x) (exp (- x)))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite165.0ms

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
66.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
64.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
20.0ms
(+ (exp x) (exp (- x)))
13.0ms
(- (exp x) (exp (- x)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
94.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
62.0ms
(- (exp x) (exp (- x)))
27.0ms
(+ (exp x) (exp (- x)))

simplify7.1s

Counts
99 → 138
Calls
99 calls:
Slowest
878.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
425.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
279.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
244.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
235.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize112.0ms

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
17×*-un-lft-identity
16×associate-*l*
15×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×times-frac
8×pow1
6×associate-*r* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def prod-exp cbrt-unprod fma-udef unswap-sqr
2×pow-prod-down *-commutative
1×distribute-rgt-in cbrt-undiv +-commutative sum-log distribute-lft-in flip3-+ div-exp associate-*l/ flip-+ div-inv distribute-lft-out
Counts
4 → 87
Calls
4 calls:
Slowest
19.0ms
(+ (exp x) (exp (- x)))
13.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
6.0ms
(* x (fma 1/3 (* x x) 2))
0.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2) (sin y))
109.0ms
(* x (fma 1/3 (* x x) 2))
85.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))
44.0ms
(+ (exp x) (exp (- x)))

simplify9.2s

Counts
53 → 99
Calls
53 calls:
Slowest
778.0ms
(* (* (* x x) x) (* (* (fma 1/3 (* x x) 2) (fma 1/3 (* x x) 2)) (fma 1/3 (* x x) 2)))
593.0ms
(+ (- (log (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (log 2)) (log (sin y)))
507.0ms
(* (sqrt (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) 2)) (sqrt (sin y)))
501.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)
468.0ms
(fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (sqrt 2))
0.5b
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.4b
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
0.3b
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
69×add-sqr-sqrt
61×*-un-lft-identity add-cube-cbrt
54×add-exp-log
44×associate-*l*
43×sqrt-prod
34×add-cbrt-cube
22×prod-exp
14×div-exp
13×pow1
12×associate-/r* cbrt-unprod
8×cbrt-undiv
6×associate-/l*
4×expm1-log1p-u rec-exp 1-exp associate-*r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-flip unswap-sqr
2×clear-num frac-2neg *-commutative
1×frac-times sqrt-pow1 pow1/2 associate-*r/ inv-pow
Counts
4 → 192
Calls
4 calls:
Slowest
56.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
27.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
5.0ms
(/ 1 (sqrt 2))
5.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))

series705.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
317.0ms
(* (/ 1 (sqrt 2)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
218.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
170.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms
(/ 1 (sqrt 2))

simplify29.1s

Counts
187 → 202
Calls
187 calls:
Slowest
726.0ms
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
644.0ms
(* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))) (* (* (sin y) (sin y)) (sin y)))
631.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
582.0ms
(/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
568.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))))

prune4.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize139.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1/2 (sqrt 2))
0.5b
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.4b
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
0.3b
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
70×add-sqr-sqrt
62×*-un-lft-identity add-cube-cbrt
47×associate-*l*
43×sqrt-prod
22×cbrt-prod add-exp-log
19×add-cbrt-cube
12×associate-/r*
11×pow1
7×prod-exp cbrt-unprod
6×associate-/l*
4×expm1-log1p-u cbrt-undiv div-exp associate-*r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×unswap-sqr
2×cbrt-div clear-num frac-2neg *-commutative
1×frac-times associate-*r/
Counts
4 → 177
Calls
4 calls:
Slowest
60.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
16.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
10.0ms
(/ 1/2 (sqrt 2))
10.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))

series1.1s

Counts
4 → 10
Calls
4 calls:
Slowest
751.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y)))
208.0ms
(* (/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2)) (sin y))
177.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
0.0ms
(/ 1/2 (sqrt 2))

simplify25.2s

Counts
175 → 187
Calls
175 calls:
Slowest
867.0ms
(/ (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (sqrt 2))
552.0ms
(/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
498.0ms
(/ (sqrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) 1)
492.0ms
(* (/ 1/2 (sqrt 2)) (* (/ (* (* (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
491.0ms
(/ (cbrt (fma 1/60 (pow x 5) (* x (fma 1/3 (* x x) 2)))) (sqrt 2))

prune4.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes159.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch4.0ms

end0.0ms

sample12.2s

Algorithm
halfpoints
Results