Details

Time bar (total: 16.1s)

sample188.0ms

Algorithm
intervals
Results
102.0ms87×body1280valid
36.0ms52×body640valid
12.0ms25×body320valid
12.0ms82×body80valid
3.0ms10×body160valid

simplify766.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
03250
17450
218747
358747
4193547
done500047

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
184×add-sqr-sqrt
183×prod-diff
172×*-un-lft-identity
164×add-cube-cbrt
110×times-frac
82×distribute-rgt-in distribute-lft-in
14×sqrt-prod
12×associate-*r* div-inv
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
8×add-log-exp
7×associate-*l* difference-of-squares
6×sub-neg fma-neg
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod log1p-expm1-u distribute-lft-out--
2×diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 291
Calls
4 calls:
66.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
41.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series280.0ms

Counts
4 → 10
Calls
4 calls:
134.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
89.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
58.0ms
(- (cos x) (cos y))

simplify645.0ms

Counts
301 → 301
Iterations

Useful iterations: done (629.0ms)

IterNodesCost
073212252
1168810920
done500010000

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.7b
(cbrt (- (sin y) (/ (sin x) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×*-un-lft-identity
27×prod-diff
26×add-cube-cbrt
12×cbrt-prod
10×sqrt-prod
8×add-log-exp
7×difference-of-squares
6×fma-neg
4×pow1 add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out--
2×sub-neg times-frac pow1/3 diff-log
1×diff-cos
Counts
4 → 103
Calls
4 calls:
6.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
7.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series336.0ms

Counts
4 → 10
Calls
4 calls:
140.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
144.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
52.0ms
(- (cos x) (cos y))

simplify1.1s

Counts
113 → 113
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02271843
14581496
210171306
330751192
done50001189

prune671.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))
3.8b
(/ (* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (+ (sin x) (/ (sin y) 16.0)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
37×*-un-lft-identity
29×add-cube-cbrt prod-diff
26×associate-*r/
17×associate-/l/
15×add-exp-log add-cbrt-cube
14×frac-times sqrt-prod
12×flip3-- frac-sub flip-- sin-mult
9×associate-*l/
8×add-log-exp
6×pow1 fma-neg associate-*l*
4×expm1-log1p-u sub-neg times-frac associate-*r* prod-exp associate-/r* cbrt-unprod log1p-expm1-u difference-of-squares
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp
2×diff-log associate-/r/ distribute-lft-out distribute-lft-out-- unswap-sqr
1×frac-2neg flip3-+ pow-prod-down clear-num *-commutative flip-+ div-inv diff-cos associate-/l*
Counts
4 → 149
Calls
4 calls:
19.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
5.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))
72.0ms
(/ (* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (+ (sin x) (/ (sin y) 16.0)))

series390.0ms

Counts
4 → 10
Calls
4 calls:
110.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
0.0ms
(- 3.0 (sqrt 5.0))
51.0ms
(- (cos x) (cos y))
228.0ms
(/ (* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (+ (sin x) (/ (sin y) 16.0)))

simplify1.0s

Counts
159 → 159
Iterations

Useful iterations: 2 (343.0ms)

IterNodesCost
03494049
19213413
236202875
done50002875

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.7b
(cbrt (- (sin y) (/ (sin x) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.9b
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
12×cbrt-prod
10×sqrt-prod
6×add-log-exp difference-of-squares
4×pow1 add-exp-log expm1-log1p-u cbrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- fma-neg flip-- distribute-lft-out--
2×times-frac pow1/3
1×sub-neg diff-log fma-udef
Counts
4 → 84
Calls
4 calls:
6.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
7.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
0.0ms
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series449.0ms

Counts
4 → 10
Calls
4 calls:
147.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
141.0ms
(cbrt (- (sin y) (/ (sin x) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
161.0ms
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify757.0ms

Counts
94 → 94
Iterations

Useful iterations: done (754.0ms)

IterNodesCost
01771559
13491325
27561087
32065970
done5000967

prune613.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03575
13875
done3875

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.1s2675×body1280valid
1.4s1850×body640valid
442.0ms823×body320valid
346.0ms2318×body80valid
114.0ms334×body160valid