Details

Time bar (total: 34.0s)

sample462.0ms

Algorithm
halfpoints

simplify5.5s

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01624
13011
24811
38311
412711
520011
637311
760811
8110511
9152111
10185511
11193911
12195911
done195911

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize90.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.9b
(- (exp x) (exp (- x)))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
43×*-un-lft-identity
35×associate-*l*
29×add-cube-cbrt times-frac
13×add-exp-log add-cbrt-cube
9×prod-diff
7×pow1
6×associate-*r*
5×add-log-exp
4×prod-exp cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
3×expm1-log1p-u fma-neg log1p-expm1-u distribute-lft-out
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 105
Calls
3 calls:
98.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
103.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
30.0ms
(- (exp x) (exp (- x)))

series265.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
108.0ms
(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
70.0ms
(- (exp x) (exp (- x)))

simplify1.6s

Counts
114 → 114
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02181732
15321573
215121344
done50001289

prune762.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize135.0ms

Local error

Found 2 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt associate-*l*
25×*-un-lft-identity
23×times-frac
19×add-cube-cbrt
12×add-exp-log add-cbrt-cube
6×pow1 associate-*r*
4×prod-exp cbrt-unprod unswap-sqr
3×distribute-lft-out
2×cbrt-undiv expm1-log1p-u div-exp pow-prod-down associate-*l/ *-commutative log1p-expm1-u div-inv add-log-exp
Counts
2 → 71
Calls
2 calls:
73.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
38.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series253.0ms

Counts
2 → 6
Calls
2 calls:
74.0ms
(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
179.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify4.0s

Counts
77 → 77
Iterations

Useful iterations: done (4.0s)

IterNodesCost
01661407
14001393
211991211
340201208
done50001207

prune614.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize118.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.3b
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b
(/ 1 (sqrt 2.0))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
74×times-frac
69×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
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/ log1p-expm1-u div-inv add-log-exp
3×pow-flip unswap-sqr
2×frac-2neg clear-num *-commutative
1×frac-times sqrt-pow1 pow1/2 associate-*r/ inv-pow
Counts
4 → 188
Calls
4 calls:
49.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
102.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
7.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
8.0ms
(/ 1 (sqrt 2.0))

series746.0ms

Counts
4 → 10
Calls
4 calls:
228.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
347.0ms
(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
171.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt 2.0))

simplify1.4s

Counts
198 → 198
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02544584
16014231
219843619
done50013595

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt (sqrt 2.0))) (/ (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0))))
0.3b
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.5b
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
107×times-frac
103×add-sqr-sqrt
100×sqrt-prod
81×*-un-lft-identity
78×add-cube-cbrt
75×add-exp-log
53×associate-*l*
45×add-cbrt-cube
28×div-exp
26×prod-exp
16×associate-*r*
15×cbrt-undiv associate-/r*
14×cbrt-unprod
11×pow1
10×unswap-sqr
6×associate-/l*
5×rec-exp pow-flip 1-exp div-inv
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
2×frac-2neg pow1/2 pow-prod-down associate-*l/ clear-num *-commutative
1×frac-times associate-*r/ inv-pow
Counts
4 → 235
Calls
4 calls:
128.0ms
(* (/ 1 (sqrt (sqrt 2.0))) (/ (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0))))
41.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
14.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
19.0ms
(/ 1 (sqrt (sqrt 2.0)))

series726.0ms

Counts
4 → 10
Calls
4 calls:
307.0ms
(* (/ 1 (sqrt (sqrt 2.0))) (/ (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)) (sqrt (sqrt 2.0))))
243.0ms
(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
176.0ms
(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify1.7s

Counts
245 → 245
Iterations

Useful iterations: 2 (702.0ms)

IterNodesCost
03326521
18025950
227125027
done50005027

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes157.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02531
12931
done2931

end0.0ms

sample11.3s

Algorithm
halfpoints