Details

Time bar (total: 19.8s)

sample187.0ms

Algorithm
intervals
Results
90.0ms79×body1280valid
45.0ms67×body640valid
16.0ms22×body320valid
10.0ms77×body80valid
3.0ms11×body160valid

simplify632.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
03250
17450
218747
359347
4197147
done500047

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.5b
(- (cos x) (cos y))

rewrite130.0ms

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:
64.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
40.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series278.0ms

Counts
4 → 10
Calls
4 calls:
136.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
90.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
52.0ms
(- (cos x) (cos y))

simplify498.0ms

Counts
301 → 301
Iterations

Useful iterations: done (483.0ms)

IterNodesCost
073212252
1173510935
done500010884

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 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
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.5b
(- (cos x) (cos y))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
209×add-sqr-sqrt
199×*-un-lft-identity
193×add-cube-cbrt
185×times-frac
165×prod-diff
82×distribute-rgt-in distribute-lft-in
17×div-inv
16×add-exp-log add-cbrt-cube
13×associate-/l*
12×associate-*r*
11×pow1
10×associate-*r/
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg difference-of-squares
4×expm1-log1p-u frac-times pow-prod-down prod-exp sqrt-prod cbrt-unprod log1p-expm1-u
3×cbrt-undiv fma-neg div-exp associate-/r* distribute-lft-out--
2×associate-*l/ *-commutative unswap-sqr
1×frac-2neg diff-log clear-num diff-cos associate-/l/
Counts
4 → 325
Calls
4 calls:
8.0ms
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 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)))
62.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
40.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- (cos x) (cos y))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 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)))
137.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
97.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
53.0ms
(- (cos x) (cos y))

simplify619.0ms

Counts
337 → 337
Iterations

Useful iterations: done (600.0ms)

IterNodesCost
088018227
1214817028
done500016985

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (cos x) (cos y))
4.9b
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))
4.9b
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))
4.9b
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div associate-*r/
19×flip3-- flip--
13×add-sqr-sqrt *-un-lft-identity
12×frac-times
11×add-cube-cbrt
9×prod-diff
6×associate-*l/ add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cbrt-prod fma-neg pow1/3
1×sub-neg diff-log diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 86
Calls
4 calls:
4.0ms
(- (cos x) (cos y))
41.0ms
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))
39.0ms
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))
41.0ms
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))

series931.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (cos x) (cos y))
291.0ms
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))
288.0ms
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))
293.0ms
(cbrt (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))))

simplify479.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (131.0ms)

IterNodesCost
01782769
14392538
213992341
done50022341

prune978.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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)) (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0))
0.3b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.5b
(- (cos x) (cos y))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
209×add-sqr-sqrt
199×*-un-lft-identity
193×add-cube-cbrt
185×times-frac
165×prod-diff
82×distribute-rgt-in distribute-lft-in
17×div-inv
16×add-exp-log add-cbrt-cube
13×associate-/r*
12×associate-*r*
11×pow1
10×associate-*r/
8×flip3-- flip--
7×associate-*l*
6×add-log-exp
5×sub-neg difference-of-squares
4×expm1-log1p-u frac-times pow-prod-down prod-exp sqrt-prod cbrt-unprod log1p-expm1-u
3×cbrt-undiv fma-neg div-exp associate-/l* distribute-lft-out--
2×associate-*l/ *-commutative unswap-sqr
1×frac-2neg diff-log clear-num associate-/r/ diff-cos
Counts
4 → 325
Calls
4 calls:
5.0ms
(/ (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)) (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0))
66.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
37.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- (cos x) (cos y))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.5s
(/ (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)) (/ (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) 3.0))
135.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
54.0ms
(- (cos x) (cos y))

simplify621.0ms

Counts
337 → 337
Iterations

Useful iterations: done (595.0ms)

IterNodesCost
087318235
1211817024
done500116973

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes270.0ms

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
03288
13588
done3588

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.1s2767×body1280valid
1.3s1856×body640valid
364.0ms730×body320valid
330.0ms2330×body80valid
110.0ms317×body160valid