Details

Time bar (total: 21.4s)

sample197.0ms

Algorithm
intervals
Results
99.0ms88×body1280valid
50.0ms61×body640valid
14.0ms28×body320valid
10.0ms69×body80valid
3.0ms10×body160valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
03250
17450
218747
358747
4193547
done500047

prune21.0ms

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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (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:
67.0ms
(* (* (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:
132.0ms
(* (* (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))
59.0ms
(- (cos x) (cos y))

simplify649.0ms

Counts
301 → 301
Iterations

Useful iterations: done (633.0ms)

IterNodesCost
073212252
1168810920
done500210000

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.7b
(- (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-/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:
6.0ms
(/ (/ (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)))
66.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
38.0ms
(* (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)))
136.0ms
(* (* (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)))
58.0ms
(- (cos x) (cos y))

simplify985.0ms

Counts
337 → 337
Iterations

Useful iterations: done (956.0ms)

IterNodesCost
088018227
1209317028
done500116985

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(log1p (expm1 (- (cos x) (cos y))))
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)))
1.7b
(- (cos x) (cos y))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
165×prod-diff
157×*-un-lft-identity
151×add-cube-cbrt
110×times-frac
82×distribute-rgt-in distribute-lft-in
12×associate-*r* div-inv
11×pow1 add-exp-log add-cbrt-cube
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×fma-neg distribute-lft-out--
2×associate-*l/ *-commutative unswap-sqr
1×log1p-udef diff-log log1p-expm1 diff-cos
Counts
4 → 264
Calls
4 calls:
0.0ms
(log1p (expm1 (- (cos x) (cos y))))
68.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
39.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- (cos x) (cos y))

series362.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(log1p (expm1 (- (cos x) (cos y))))
132.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
87.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
52.0ms
(- (cos x) (cos y))

simplify723.0ms

Counts
276 → 276
Iterations

Useful iterations: done (708.0ms)

IterNodesCost
066111664
1153910518
done50009607

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

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) (/ (/ 1 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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.7b
(- (cos x) (cos y))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
215×add-sqr-sqrt
194×*-un-lft-identity
187×add-cube-cbrt
181×times-frac
165×prod-diff
82×distribute-rgt-in distribute-lft-in
55×associate-*r*
26×add-exp-log
20×add-cbrt-cube
16×div-inv
13×pow1
11×associate-*r/
10×associate-*l*
9×prod-exp
8×flip3-- flip--
7×cbrt-unprod
6×div-exp add-log-exp unswap-sqr
5×sub-neg pow-prod-down difference-of-squares
4×expm1-log1p-u frac-times sqrt-prod log1p-expm1-u
3×cbrt-undiv fma-neg *-commutative distribute-lft-out--
2×associate-*l/
1×rec-exp diff-log 1-exp diff-cos
Counts
4 → 323
Calls
4 calls:
20.0ms
(* (fma (- (cos x) (cos y)) (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) 2.0) (/ (/ 1 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))))
66.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
38.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(- (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) (/ (/ 1 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))))
138.0ms
(* (* (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)))
52.0ms
(- (cos x) (cos y))

simplify845.0ms

Counts
335 → 335
Iterations

Useful iterations: done (820.0ms)

IterNodesCost
088916533
1219515205
done500015112

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes192.0ms

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
04173
14973
done4973

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.2s2801×body1280valid
1.4s1817×body640valid
379.0ms726×body320valid
354.0ms2321×body80valid
113.0ms335×body160valid