Details

Time bar (total: 38.3s)

sample433.0ms

Algorithm
intervals
Results
234.0ms80×body1280valid
89.0ms58×body640valid
38.0ms28×body320valid
23.0ms80×body80valid
7.0ms10×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
03250
17450
219247
369747
4290747
done500147

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.4b
(- (cos x) (cos y))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
133×add-sqr-sqrt
123×prod-diff
119×*-un-lft-identity
109×add-cube-cbrt
56×times-frac
52×distribute-rgt-in distribute-lft-in
14×sqrt-prod
12×associate-*r* associate-*l*
9×flip3-- flip--
8×pow1 add-exp-log add-cbrt-cube add-log-exp difference-of-squares
6×sub-neg fma-neg div-inv
5×distribute-lft-out--
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×unswap-sqr
2×diff-log pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
Counts
4 → 234
Calls
4 calls:
96.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms
(- 3.0 (sqrt 5.0))
18.0ms
(- (cos x) (cos y))

series346.0ms

Counts
4 → 10
Calls
4 calls:
154.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
110.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
82.0ms
(- (cos x) (cos y))

simplify2.3s

Counts
244 → 244
Iterations

Useful iterations: done (2.2s)

IterNodesCost
05387482
110736428
232314816
done50003982

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
0.3b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.4b
(- (cos x) (cos y))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
158×add-sqr-sqrt
146×*-un-lft-identity
138×add-cube-cbrt
131×times-frac
105×prod-diff
52×distribute-rgt-in distribute-lft-in
13×add-exp-log add-cbrt-cube associate-/l*
12×associate-*r* associate-*l*
11×div-inv
8×pow1 flip3-- flip--
6×add-log-exp difference-of-squares
5×sub-neg
4×expm1-log1p-u frac-times associate-*r/ sqrt-prod log1p-expm1-u distribute-lft-out--
3×cbrt-undiv fma-neg div-exp associate-/r* unswap-sqr
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
1×frac-2neg diff-log clear-num associate-/l/
Counts
4 → 268
Calls
4 calls:
12.0ms
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
98.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
108.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
19.0ms
(- (cos x) (cos y))

series2.5s

Counts
4 → 12
Calls
4 calls:
2.1s
(/ (/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) 3.0) (fma (cos y) (/ (/ (- (* 3.0 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
160.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
149.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
81.0ms
(- (cos x) (cos y))

simplify2.7s

Counts
280 → 280
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
068713457
1148512539
2454710707
done500010707

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos x))
0.3b
(cbrt (cos x))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.1b
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
79×*-un-lft-identity
78×prod-diff
77×add-cube-cbrt
55×times-frac
41×distribute-rgt-in distribute-lft-in
6×pow1 add-exp-log cbrt-prod associate-*r* associate-*l* add-cbrt-cube div-inv
4×expm1-log1p-u sqrt-prod log1p-expm1-u add-log-exp
2×sub-neg pow1/3 associate-*r/ difference-of-squares unswap-sqr
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef distribute-lft-out--
Counts
4 → 147
Calls
4 calls:
2.0ms
(cbrt (cos x))
3.0ms
(cbrt (cos x))
120.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series700.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(cbrt (cos x))
163.0ms
(cbrt (cos x))
168.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
234.0ms
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify1.8s

Counts
159 → 159
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03425022
16354525
217933172
done50012500

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
2.1b
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
2.0ms
(cbrt 16.0)
2.0ms
(cbrt 16.0)
2.0ms
(cbrt 16.0)
1.0ms
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

series285.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
284.0ms
(fma (* (cbrt (cos x)) (cbrt (cos x))) (cbrt (cos x)) (- (cos y)))

simplify2.8s

Counts
55 → 55
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
079638
1144577
2308461
3837394
43023388
done5001388

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes335.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04285
15085
done5085

end0.0ms

sample15.1s

Algorithm
intervals
Results
8.4s2636×body1280valid
4.3s1918×body640valid
964.0ms780×body320valid
773.0ms2375×body80valid
394.0ms291×body160valid