Details

Time bar (total: 36.6s)

sample408.0ms

Algorithm
intervals
Results
158.0ms85×body1280valid
136.0ms63×body640valid
51.0ms63×body80valid
28.0ms33×body320valid
6.0ms12×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03250
17450
219247
369747
4290747
done500147

prune49.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize52.0ms

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

rewrite197.0ms

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:
27.0ms
(/ (/ (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)))
104.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
18.0ms
(- 3.0 (sqrt 5.0))
19.0ms
(- (cos x) (cos y))

series1.8s

Counts
4 → 10
Calls
4 calls:
1.5s
(/ (/ (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)))
135.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
103.0ms
(- (cos x) (cos y))

simplify2.9s

Counts
260 → 260
Iterations

Useful iterations: done (2.9s)

IterNodesCost
065811736
1139410851
238959139
done50009131

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt (sin y)) 3)
0.7b
(pow (cbrt (sin y)) 3)
1.0b
(- 3.0 (sqrt 5.0))
2.0b
(- (cos x) (cos y))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×*-un-lft-identity
34×add-cube-cbrt
27×prod-diff
12×cbrt-prod unpow-prod-down cube-prod
10×sqrt-prod
8×add-log-exp
6×pow1 add-exp-log pow-unpow fma-neg
4×expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u
3×difference-of-squares
2×cube-mult pow-to-exp sub-neg flip3-- pow1/3 diff-log unpow3 pow-exp flip-- distribute-lft-out-- rem-cube-cbrt sqr-pow
1×diff-cos
Counts
4 → 131
Calls
4 calls:
19.0ms
(pow (cbrt (sin y)) 3)
9.0ms
(pow (cbrt (sin y)) 3)
20.0ms
(- 3.0 (sqrt 5.0))
14.0ms
(- (cos x) (cos y))

series486.0ms

Counts
4 → 10
Calls
4 calls:
201.0ms
(pow (cbrt (sin y)) 3)
185.0ms
(pow (cbrt (sin y)) 3)
0.0ms
(- 3.0 (sqrt 5.0))
99.0ms
(- (cos x) (cos y))

simplify1.3s

Counts
141 → 141
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02241834
14841273
211271046
done5001915

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize88.0ms

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))

rewrite24.0ms

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))

series110.0ms

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)))))
110.0ms
(- (cos x) (cos y))

simplify2.1s

Counts
71 → 71
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01331015
1250899
2543720
31895602
done5000584

prune966.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (sin x) (/ (sin y) 16.0)))
0.6b
(cbrt (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.0b
(- (cos x) (cos y))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×*-un-lft-identity
27×prod-diff
26×add-cube-cbrt
12×cbrt-prod
10×sqrt-prod
8×add-log-exp
7×difference-of-squares
6×fma-neg
4×pow1 add-exp-log expm1-log1p-u cbrt-div flip3-- add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out--
2×sub-neg times-frac pow1/3 diff-log
1×diff-cos
Counts
4 → 103
Calls
4 calls:
18.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
12.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
10.0ms
(- 3.0 (sqrt 5.0))
26.0ms
(- (cos x) (cos y))

series554.0ms

Counts
4 → 10
Calls
4 calls:
218.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
249.0ms
(cbrt (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
87.0ms
(- (cos x) (cos y))

simplify2.5s

Counts
113 → 113
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02241835
14581488
29671268
327141137
done50001058

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes488.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03879
14579
done4579

end0.0ms

sample16.4s

Algorithm
intervals
Results
8.0s2741×body1280valid
5.3s1829×body640valid
1.1s786×body320valid
827.0ms2309×body80valid
659.0ms335×body160valid