Details

Time bar (total: 13.2s)

sample190.0ms

Algorithm
intervals
Results
104.0ms94×body1280valid
44.0ms66×body640valid
10.0ms22×body320valid
9.0ms70×body80valid
1.0ms4×body160valid

simplify55.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
07430
119327
270427
3299427
4500127
done500127

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize38.0ms

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) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.3b
(- (cos x) (cos y))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
109×*-un-lft-identity
105×prod-diff
103×add-cube-cbrt
64×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
8×add-exp-log add-cbrt-cube add-log-exp
7×div-inv
6×pow1 fma-neg associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×flip3-- associate-/r* flip-- associate-/l* distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos
Counts
4 → 207
Calls
4 calls:
5.0ms
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
62.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series1.0s

Counts
4 → 10
Calls
4 calls:
898.0ms
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
58.0ms
(- (cos x) (cos y))

simplify128.0ms

Counts
217 → 217
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
011604965
144023841
250013834
done50013834

prune844.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

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))
2.3b
(- (cos x) (cos y))

rewrite205.0ms

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:
109.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
61.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series498.0ms

Counts
4 → 10
Calls
4 calls:
339.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
98.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
61.0ms
(- (cos x) (cos y))

simplify87.0ms

Counts
301 → 301
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
017307731
150016094
done50016094

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 5.0)
1.0b
(* (cbrt 5.0) (cbrt 5.0))
2.0b
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))
2.3b
(- (cos x) (cos y))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×cbrt-prod
11×pow1
9×prod-diff
7×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
3×fma-neg
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log prod-exp *-commutative flip-- cbrt-unprod fma-udef diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 94
Calls
4 calls:
1.0ms
(cbrt 5.0)
11.0ms
(* (cbrt 5.0) (cbrt 5.0))
0.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))
10.0ms
(- (cos x) (cos y))

series55.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 5.0)
0.0ms
(* (cbrt 5.0) (cbrt 5.0))
0.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))
55.0ms
(- (cos x) (cos y))

simplify41.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0325834
11016680
25001657
done5001657

prune847.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.3b
(- (cos x) (cos y))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
110×*-un-lft-identity
105×prod-diff
103×add-cube-cbrt
66×times-frac
41×distribute-rgt-in distribute-lft-in
19×associate-*r*
15×add-exp-log
14×sqrt-prod
11×add-cbrt-cube
9×associate-*l*
8×pow1 add-log-exp
7×div-inv
6×fma-neg
5×prod-exp difference-of-squares unswap-sqr
4×expm1-log1p-u sub-neg log1p-expm1-u
3×flip3-- associate-*r/ flip-- cbrt-unprod distribute-lft-out--
2×diff-log div-exp pow-prod-down *-commutative
1×cbrt-undiv rec-exp 1-exp un-div-inv diff-cos
Counts
4 → 216
Calls
4 calls:
14.0ms
(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))
63.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series1.0s

Counts
4 → 10
Calls
4 calls:
889.0ms
(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))))
92.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
55.0ms
(- (cos x) (cos y))

simplify137.0ms

Counts
226 → 226
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012485063
148903859
250013859
done50013859

prune784.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes253.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06251
16451
26451
done6451

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.1s2766×body1280valid
1.3s1872×body640valid
366.0ms761×body320valid
319.0ms2284×body80valid
105.0ms317×body160valid