Details

Time bar (total: 32.1s)

sample689.0ms

Algorithm
intervals
Results
472.0ms81×body1280valid
133.0ms71×body640valid
24.0ms26×body320valid
17.0ms72×body80valid
4.0ms6×body160valid

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03250
17450
219247
369947
4339047
done500147

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize51.0ms

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

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
152×add-sqr-sqrt
143×*-un-lft-identity
137×add-cube-cbrt
130×times-frac
105×prod-diff
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
13×associate-/l*
11×add-exp-log add-cbrt-cube div-inv
8×add-log-exp
6×pow1 fma-neg associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip-- distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos associate-/l/
Counts
4 → 250
Calls
4 calls:
13.0ms
(/ (/ (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 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
92.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
13.0ms
(- 3.0 (sqrt 5.0))
12.0ms
(- (cos x) (cos y))

series1.4s

Counts
4 → 10
Calls
4 calls:
1.2s
(/ (/ (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 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
101.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
76.0ms
(- (cos x) (cos y))

simplify964.0ms

Counts
260 → 260
Iterations

Useful iterations: done (937.0ms)

IterNodesCost
065811736
1157010876
done50009459

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize123.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 5.0)
1.0b
(cbrt 5.0)
2.0b
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
2.0b
(- (cos x) (cos y))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
9×prod-diff
6×cbrt-prod add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg
2×pow1/3
1×sub-neg flip3-- diff-log flip-- fma-udef diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 65
Calls
4 calls:
2.0ms
(cbrt 5.0)
2.0ms
(cbrt 5.0)
2.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
33.0ms
(- (cos x) (cos y))

series87.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 5.0)
0.0ms
(cbrt 5.0)
0.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
87.0ms
(- (cos x) (cos y))

simplify944.0ms

Counts
71 → 71
Iterations

Useful iterations: done (940.0ms)

IterNodesCost
01331015
1258902
2812720
done5000602

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 5.0)
1.0b
(cbrt 5.0)
2.0b
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
2.0b
(- (cos x) (cos y))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
9×prod-diff
6×cbrt-prod add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg
2×pow1/3
1×sub-neg flip3-- diff-log flip-- fma-udef diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 65
Calls
4 calls:
2.0ms
(cbrt 5.0)
2.0ms
(cbrt 5.0)
1.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
17.0ms
(- (cos x) (cos y))

series88.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 5.0)
0.0ms
(cbrt 5.0)
0.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (fabs (cbrt 5.0)))))
88.0ms
(- (cos x) (cos y))

simplify908.0ms

Counts
71 → 71
Iterations

Useful iterations: done (906.0ms)

IterNodesCost
01351024
1267892
2868720
done5000602

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
105×prod-diff
103×*-un-lft-identity
97×add-cube-cbrt
58×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
11×add-exp-log add-cbrt-cube
8×add-log-exp
7×div-inv
6×pow1 fma-neg associate-*r/ associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg associate-/r/ log1p-expm1-u
3×flip3-- flip3-+ flip-- flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative diff-cos
Counts
4 → 207
Calls
4 calls:
107.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
101.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
17.0ms
(- 3.0 (sqrt 5.0))
21.0ms
(- (cos x) (cos y))

series2.0s

Counts
4 → 10
Calls
4 calls:
1.8s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
124.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
70.0ms
(- (cos x) (cos y))

simplify951.0ms

Counts
217 → 217
Iterations

Useful iterations: done (941.0ms)

IterNodesCost
06028074
115617221
done50005700

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes356.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
034102
139102
done39102

end0.0ms

sample15.5s

Algorithm
intervals
Results
8.7s2747×body1280valid
3.7s1847×body640valid
1.2s2293×body80valid
1.1s744×body320valid
323.0ms369×body160valid