Details

Time bar (total: 1.9m)

sample487.0ms

Algorithm
halfpoints
Results

simplify195.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
195.0ms
(im (complex (* (/ (+ (exp x) (exp (- x))) 2) (cos y)) (* (/ (- (exp x) (exp (- x))) 2) (sin y))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.4b

localize109.0ms

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)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
39×*-un-lft-identity
35×associate-*l*
29×times-frac
23×add-cube-cbrt
14×add-cbrt-cube add-exp-log
8×pow1 add-log-exp
6×associate-*r*
4×prod-exp cbrt-unprod insert-posit16 distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
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 → 103
Calls
4 calls:
Slowest
54.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
48.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
28.0ms
(- (exp x) (exp (- x)))
9.0ms
(+ (exp x) (exp (- x)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
121.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
100.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
61.0ms
(- (exp x) (exp (- x)))
39.0ms
(+ (exp x) (exp (- x)))

simplify5.8s

Counts
77 → 115
Calls
77 calls:
Slowest
945.0ms
(* (* (* (/ (- (exp x) (exp (- x))) 2) (/ (- (exp x) (exp (- x))) 2)) (/ (- (exp x) (exp (- x))) 2)) (* (* (sin y) (sin y)) (sin y)))
460.0ms
(* (* (* (/ (+ (exp x) (exp (- x))) 2) (/ (+ (exp x) (exp (- x))) 2)) (/ (+ (exp x) (exp (- x))) 2)) (* (* (cos y) (cos y)) (cos y)))
305.0ms
(+ (* 2 x) (+ (* 1/3 (pow x 3)) (* 1/60 (pow x 5))))
289.0ms
(* 1/2 (* (+ (exp (* -1 x)) (exp x)) (cos y)))
262.0ms
(* 1/2 (* (- (exp x) (exp (- x))) (sin y)))

prune1.8s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize155.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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
56.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
15.0ms
(* x (* 1/3 x))
9.0ms
(* (pow x 5) 1/60)
5.0ms
(* 1/3 x)

series249.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2) (sin y))
91.0ms
(* (pow x 5) 1/60)
32.0ms
(* x (* 1/3 x))
16.0ms
(* 1/3 x)

simplify9.0s

Counts
72 → 109
Calls
72 calls:
Slowest
579.0ms
(/ (* (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)))) 1)
565.0ms
(/ (* (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))
535.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (cbrt 2) (cbrt 2)))
529.0ms
(* (sqrt (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) 2)) (sqrt (sin y)))
495.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) 1)

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize197.0ms

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

rewrite214.0ms

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
112.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
83.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
10.0ms
(* 1/3 x)
6.0ms
(/ 1 (sqrt 2))

series461.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
264.0ms
(* (/ 1 (sqrt 2)) (* (/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2)) (sin y)))
179.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
18.0ms
(* 1/3 x)
0.0ms
(/ 1 (sqrt 2))

simplify25.2s

Counts
162 → 172
Calls
162 calls:
Slowest
1.1s
(* (* (* (/ 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))))
1.1s
(* (/ (* (* 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))))
953.0ms
(/ (cbrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (cbrt 2)))
675.0ms
(* (/ (* (* 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))))
672.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (cbrt 2)))

prune3.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize169.0ms

Local error

Found 4 expressions with local error:

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

rewrite541.0ms

Algorithm
rewrite-expression-head
Rules
606×sqrt-prod
594×times-frac
331×add-sqr-sqrt
329×*-un-lft-identity add-cube-cbrt
37×associate-/l*
24×associate-/r*
21×add-exp-log
20×pow1 sqrt-pow1
15×add-cbrt-cube
14×pow-flip
13×div-inv
10×pow1/2 pow-div
9×div-exp
5×cbrt-undiv
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* associate-*l* associate-/l/
2×rec-exp 1-exp inv-pow
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 468
Calls
4 calls:
Slowest
405.0ms
(/ 1 (sqrt (sqrt 2)))
94.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
22.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
7.0ms
(* 1/3 x)

series219.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
203.0ms
(/ (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60)) (sqrt 2))
15.0ms
(* 1/3 x)
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify36.4s

Counts
756 → 476
Calls
756 calls:
Slowest
625.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
594.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (sqrt (sqrt 2)))
566.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (cbrt (sqrt 2)))
554.0ms
(- (log (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (log (sqrt 2)))
546.0ms
(/ (sqrt (+ (* x (+ (* x (* 1/3 x)) 2)) (* (pow x 5) 1/60))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

prune12.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes187.0ms

Accuracy

0% (0.8b remaining)

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

bsearch5.0ms

end0.0ms

sample11.6s

Algorithm
halfpoints
Results