Details

Time bar (total: 1.4m)

sample863.0ms

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: 43.5b

localize81.0ms

Local error

Found 3 expressions with local error:

58.7b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(+ (exp x) (exp (- x)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
19×associate-*l*
16×times-frac
13×add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×add-log-exp
5×pow1
4×distribute-lft-out-- difference-of-squares
3×associate-*r* insert-posit16
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv +-commutative sum-log sub-neg flip3-+ flip3-- diff-log div-exp pow-prod-down associate-*l/ *-commutative flip-+ div-inv flip-- distribute-lft-out
Counts
3 → 67
Calls
3 calls:
Slowest
45.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
18.0ms
(+ (exp x) (exp (- x)))
18.0ms
(- (exp x) (exp (- x)))

series236.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
140.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
71.0ms
(- (exp x) (exp (- x)))
25.0ms
(+ (exp x) (exp (- x)))

simplify3.4s

Counts
46 → 76
Calls
46 calls:
Slowest
858.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
252.0ms
(* 1/2 (* (- (exp x) (exp (* -1 x))) (sin y)))
249.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
186.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))
166.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize146.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/3 x)
0.1b
(* x (* 1/3 x))
0.1b
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
0.0b
(* (pow x 5) 1/60)

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×associate-*l*
21×add-exp-log
18×*-un-lft-identity add-cbrt-cube add-cube-cbrt
13×pow1
10×times-frac associate-*r*
9×prod-exp
7×cbrt-unprod
6×unswap-sqr
5×pow-prod-down
4×unpow-prod-down *-commutative insert-posit16 add-log-exp
2×sqr-pow
1×pow-to-exp cbrt-undiv div-exp associate-*l/ pow-exp div-inv
Counts
4 → 97
Calls
4 calls:
Slowest
96.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
25.0ms
(* x (* 1/3 x))
16.0ms
(* (pow x 5) 1/60)
11.0ms
(* 1/3 x)

series275.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
93.0ms
(* (pow x 5) 1/60)
34.0ms
(* x (* 1/3 x))
19.0ms
(* 1/3 x)

simplify8.6s

Counts
72 → 109
Calls
72 calls:
Slowest
518.0ms
(/ (* (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))) (sqrt 2))
516.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
512.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) 1)
471.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (cbrt 2) (cbrt 2)))
463.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize123.0ms

Local error

Found 4 expressions with local error:

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

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
51×add-sqr-sqrt add-exp-log
49×*-un-lft-identity add-cube-cbrt
33×sqrt-prod
31×add-cbrt-cube
25×associate-*l*
21×prod-exp
13×pow1 div-exp
12×associate-/r*
11×cbrt-unprod
7×cbrt-undiv
6×associate-/l*
4×rec-exp 1-exp associate-*r* pow-prod-down insert-posit16 add-log-exp
3×associate-*l/ div-inv pow-flip
2×clear-num frac-2neg *-commutative associate-/l/
1×frac-times sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ inv-pow unswap-sqr
Counts
4 → 162
Calls
4 calls:
Slowest
98.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
82.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
10.0ms
(* 1/3 x)
5.0ms
(/ 1 (sqrt 2))

series538.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
302.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
207.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
29.0ms
(* 1/3 x)
0.0ms
(/ 1 (sqrt 2))

simplify24.6s

Counts
162 → 172
Calls
162 calls:
Slowest
1.0s
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
996.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
943.0ms
(* (* (* (/ 1 (sqrt 2)) (/ 1 (sqrt 2))) (/ 1 (sqrt 2))) (* (/ (* (* (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
700.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt 2) (sqrt 2)) (sqrt 2))) (* (* (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))) (* (* (sin y) (sin y)) (sin y))))
647.0ms
(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (sqrt 2)))

prune3.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize142.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
59×add-sqr-sqrt
57×*-un-lft-identity add-cube-cbrt
18×add-cbrt-cube add-exp-log
16×associate-/r*
11×pow1
6×associate-*r* div-inv associate-/l*
4×cbrt-undiv div-exp associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 add-log-exp
2×clear-num frac-2neg *-commutative associate-/l/
1×flip3-+ associate-/r/ flip-+ unswap-sqr
Counts
4 → 139
Calls
4 calls:
Slowest
71.0ms
(/ (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))) (/ 2 (sin y)))
18.0ms
(* (* x 1/3) x)
9.0ms
(* x 1/3)
4.0ms
(/ 2 (sin y))

series203.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(/ (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))) (/ 2 (sin y)))
46.0ms
(* (* x 1/3) x)
28.0ms
(/ 2 (sin y))
21.0ms
(* x 1/3)

simplify23.3s

Counts
154 → 151
Calls
154 calls:
Slowest
582.0ms
(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (/ (sqrt 2) (cbrt (sin y))))
564.0ms
(sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2))))
556.0ms
(* (* (* (* x 1/3) (* x 1/3)) (* x 1/3)) (* (* x x) x))
521.0ms
(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (/ (sqrt 2) 1))
520.0ms
(/ (sqrt (+ (* (pow x 5) 1/60) (* x (+ (* (* x 1/3) x) 2)))) (cbrt (/ 2 (sin y))))

prune3.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes179.0ms

Accuracy

0% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch10.0ms

end0.0ms

sample11.7s

Algorithm
halfpoints
Results