Details

Time bar (total: 59.8s)

sample555.0ms

Algorithm
halfpoints
Results

simplify2.9s

Counts
1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize148.0ms

Local error

Found 4 expressions with local error:

57.6b
(- (exp x) (exp (- x)))
0.1b
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
0.0b
(+ (exp x) (exp (- x)))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))

rewrite150.0ms

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
67.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
46.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
20.0ms
(- (exp x) (exp (- x)))
16.0ms
(+ (exp x) (exp (- x)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(* (/ (+ (exp x) (exp (- x))) 2) (cos y))
94.0ms
(* (/ (- (exp x) (exp (- x))) 2) (sin y))
48.0ms
(- (exp x) (exp (- x)))
32.0ms
(+ (exp x) (exp (- x)))

simplify698.0ms

Counts
115 → 115

prune1.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize160.0ms

Local error

Found 4 expressions with local error:

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

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1
28×add-sqr-sqrt add-exp-log
25×add-cbrt-cube
22×associate-*l*
17×*-un-lft-identity add-cube-cbrt
14×prod-exp
12×associate-*r* cbrt-unprod
10×times-frac pow-prod-down
6×unswap-sqr
5×pow-prod-up
4×unpow-prod-down *-commutative insert-posit16 add-log-exp
2×sqr-pow
1×pow2 pow-to-exp cbrt-undiv pow-plus cube-unmult div-exp associate-*l/ pow-exp pow-sqr div-inv
Counts
4 → 106
Calls
4 calls:
Slowest
97.0ms
(* (/ (+ (+ (* 2 x) (* 1/3 (* x (* x x)))) (* 1/60 (pow x 5))) 2) (sin y))
45.0ms
(* 1/3 (* x (* x x)))
26.0ms
(* x (* x x))
16.0ms
(* 1/60 (pow x 5))

series351.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(* (/ (+ (+ (* 2 x) (* 1/3 (* x (* x x)))) (* 1/60 (pow x 5))) 2) (sin y))
72.0ms
(* 1/60 (pow x 5))
71.0ms
(* 1/3 (* x (* x x)))
57.0ms
(* x (* x x))

simplify2.4s

Counts
118 → 118

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize168.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.7s

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
54×add-exp-log
52×times-frac
43×*-un-lft-identity
41×add-cube-cbrt
34×add-cbrt-cube
32×sqrt-prod
25×associate-*l*
18×div-exp prod-exp
13×associate-*r*
12×associate-/r*
10×pow1 cbrt-undiv cbrt-unprod
6×unswap-sqr
4×rec-exp 1-exp insert-posit16 div-inv associate-/l* add-log-exp
3×associate-*l/ pow-flip
2×clear-num frac-2neg pow-prod-down *-commutative associate-/l/
1×frac-times sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+ inv-pow
Counts
4 → 163
Calls
4 calls:
Slowest
2.3s
(* (/ 1 (sqrt 2)) (/ (* (+ (+ (* 1/60 (* x (* (* x x) (* x x)))) (+ x x)) (* (* 1/3 x) (* x x))) (sin y)) (sqrt 2)))
1.4s
(/ (* (+ (+ (* 1/60 (* x (* (* x x) (* x x)))) (+ x x)) (* (* 1/3 x) (* x x))) (sin y)) (sqrt 2))
11.0ms
(/ 1 (sqrt 2))
5.0ms
(* 1/3 x)

series529.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
274.0ms
(* (/ 1 (sqrt 2)) (/ (* (+ (+ (* 1/60 (* x (* (* x x) (* x x)))) (+ x x)) (* (* 1/3 x) (* x x))) (sin y)) (sqrt 2)))
223.0ms
(/ (* (+ (+ (* 1/60 (* x (* (* x x) (* x x)))) (+ x x)) (* (* 1/3 x) (* x x))) (sin y)) (sqrt 2))
32.0ms
(* 1/3 x)
0.0ms
(/ 1 (sqrt 2))

simplify1.6s

Counts
173 → 173

prune3.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize168.0ms

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
(* 1/3 x)
0.3b
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (* (+ (+ (* 1/60 (* x (* (* x x) (* x x)))) (+ x x)) (* (* 1/3 x) (* x x))) (sin y)) (sqrt 2)))

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
1158×sqrt-prod
1143×times-frac
659×add-sqr-sqrt
591×*-un-lft-identity
582×add-cube-cbrt
286×associate-*l*
79×add-exp-log
49×add-cbrt-cube
36×div-exp
34×associate-/l*
24×div-inv unswap-sqr
22×pow1
21×prod-exp
20×sqrt-pow1
19×cbrt-undiv
18×associate-/r*
14×pow-flip
13×associate-*r* cbrt-unprod
10×pow1/2 pow-div
5×rec-exp 1-exp
4×insert-posit16 add-log-exp
2×clear-num frac-2neg pow-prod-down *-commutative inv-pow
1×frac-times associate-*l/ associate-*r/ associate-/l/
Counts
4 → 779
Calls
4 calls:
Slowest
2.7s
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (* (+ (+ (* 1/60 (* x (* (* x x) (* x x)))) (+ x x)) (* (* 1/3 x) (* x x))) (sin y)) (sqrt 2)))
14.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
6.0ms
(/ 1 (sqrt (sqrt 2)))
5.0ms
(* 1/3 x)

series344.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
297.0ms
(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (* (+ (+ (* 1/60 (* x (* (* x x) (* x x)))) (+ x x)) (* (* 1/3 x) (* x x))) (sin y)) (sqrt 2)))
47.0ms
(* 1/3 x)
0.0ms
(/ (/ 1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms
(/ 1 (sqrt (sqrt 2)))

simplify1.8s

Counts
787 → 787

prune20.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes180.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch5.0ms

end0.0ms

sample11.7s

Algorithm
halfpoints
Results