Details

Time bar (total: 40.2s)

sample527.0ms

Algorithm
halfpoints

simplify6.7s

Counts
1 → 1
Iterations

Useful iterations: 6 (229.0ms)

IterNodesCost
016543
130363
248294
379294
4121294
5194294
6477293
71340293
83108293
done5001293

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.1b

localize96.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp x) (exp (- x)))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.6b
(- (exp x) (exp (- x)))

rewrite156.0ms

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 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 → 122
Calls
4 calls:
12.0ms
(+ (exp x) (exp (- x)))
52.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
56.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
32.0ms
(- (exp x) (exp (- x)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (exp x) (exp (- x)))
79.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
133.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.0ms
(- (exp x) (exp (- x)))

simplify3.0s

Counts
134 → 134
Iterations

Useful iterations: done (2.9s)

IterNodesCost
023155848
158252825
2190450508
done500244078

prune871.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (+ 2 (* 1/3 (* x x))))
0.0b
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b
(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* 1/3 (* x x))))) 2.0) (sin y))
0.2b
(* 1/3 (* x x))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
35×associate-*l*
30×*-un-lft-identity
24×add-cube-cbrt
23×times-frac
21×add-cbrt-cube add-exp-log
15×pow1
10×associate-*r*
8×prod-exp cbrt-unprod
6×pow-prod-down unswap-sqr
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×distribute-lft-out
2×cbrt-undiv div-exp associate-*l/ associate-*r/ div-inv
1×distribute-rgt-in distribute-lft-in flip3-+ flip-+
Counts
4 → 116
Calls
4 calls:
12.0ms
(* x (+ 2 (* 1/3 (* x x))))
62.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
14.0ms
(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* 1/3 (* x x))))) 2.0) (sin y))
13.0ms
(* 1/3 (* x x))

series407.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(* x (+ 2 (* 1/3 (* x x))))
91.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
124.0ms
(* (/ (fma (pow x 5) 1/60 (* x (+ 2 (* 1/3 (* x x))))) 2.0) (sin y))
30.0ms
(* 1/3 (* x x))

simplify2.6s

Counts
128 → 128
Iterations

Useful iterations: done (2.5s)

IterNodesCost
023651947
164848993
2236147116
done500246961

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1/3 (* x x))
0.2b
(* 1/3 (* x x))
0.4b
(* (* x (sqrt (+ 2 (* 1/3 (* x x))))) (sqrt (+ 2 (* 1/3 (* x x)))))
0.5b
(* x (sqrt (+ 2 (* 1/3 (* x x)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
21×pow1 add-cbrt-cube add-exp-log
17×add-sqr-sqrt
14×sqrt-div associate-*r*
11×*-un-lft-identity add-cube-cbrt
10×associate-*l* pow-prod-down prod-exp associate-*r/ cbrt-unprod
7×flip3-+ sqrt-prod flip-+
4×expm1-log1p-u frac-times *-commutative log1p-expm1-u add-log-exp unswap-sqr
2×associate-*l/
Counts
4 → 99
Calls
4 calls:
23.0ms
(* 1/3 (* x x))
14.0ms
(* 1/3 (* x x))
49.0ms
(* (* x (sqrt (+ 2 (* 1/3 (* x x))))) (sqrt (+ 2 (* 1/3 (* x x)))))
30.0ms
(* x (sqrt (+ 2 (* 1/3 (* x x)))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* 1/3 (* x x))
40.0ms
(* 1/3 (* x x))
121.0ms
(* (* x (sqrt (+ 2 (* 1/3 (* x x))))) (sqrt (+ 2 (* 1/3 (* x x)))))
152.0ms
(* x (sqrt (+ 2 (* 1/3 (* x x)))))

simplify2.5s

Counts
111 → 111
Iterations

Useful iterations: done (2.5s)

IterNodesCost
014531781
141924790
2186422590
done500122392

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0b

localize185.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1/3 (* x x))
0.2b
(* x (sqrt (sqrt (+ 2 (* 1/3 (* x x))))))
0.3b
(* (* x (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (sqrt (+ 2 (* 1/3 (* x x))))))
0.4b
(* (* (* x (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (+ 2 (* 1/3 (* x x)))))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
118×sqrt-div
36×associate-*r/
34×flip3-+ flip-+
32×frac-times
25×pow1 add-cbrt-cube associate-*r* add-exp-log
24×sqrt-prod
21×add-sqr-sqrt
16×associate-*l/
14×*-un-lft-identity add-cube-cbrt
13×pow-prod-down prod-exp cbrt-unprod
8×associate-*l*
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp unswap-sqr
Counts
4 → 137
Calls
4 calls:
17.0ms
(* 1/3 (* x x))
18.0ms
(* x (sqrt (sqrt (+ 2 (* 1/3 (* x x))))))
54.0ms
(* (* x (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (sqrt (+ 2 (* 1/3 (* x x))))))
207.0ms
(* (* (* x (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (+ 2 (* 1/3 (* x x)))))

series588.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 1/3 (* x x))
248.0ms
(* x (sqrt (sqrt (+ 2 (* 1/3 (* x x))))))
177.0ms
(* (* x (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (sqrt (+ 2 (* 1/3 (* x x))))))
125.0ms
(* (* (* x (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (sqrt (+ 2 (* 1/3 (* x x)))))) (sqrt (+ 2 (* 1/3 (* x x)))))

simplify4.3s

Counts
149 → 149
Iterations

Useful iterations: done (4.3s)

IterNodesCost
026274299
175058537
2334851720
done500050894

prune1.7s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes364.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
025932
131932
done31932

end0.0ms

sample12.5s

Algorithm
halfpoints