Details

Time bar (total: 43.0s)

sample391.0ms

Algorithm
intervals
Results
171.0ms87×body1280valid
133.0ms51×body640valid
24.0ms28×body320valid
20.0ms82×body80valid
5.0ms8×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
03250
17450
219247
369747
4290747
done500147

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize59.0ms

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))
3.1b
(- (cos x) (cos y))

rewrite163.0ms

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:
23.0ms
(/ (/ (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)))
81.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
27.0ms
(- (cos x) (cos y))

series1.6s

Counts
4 → 10
Calls
4 calls:
1.4s
(/ (/ (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)))
123.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
84.0ms
(- (cos x) (cos y))

simplify2.4s

Counts
260 → 260
Iterations

Useful iterations: done (2.4s)

IterNodesCost
065811736
1139410851
238959139
done50009131

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
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 3.0) 5.0) (+ 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)))
3.1b
(- (cos x) (cos y))

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
158×add-sqr-sqrt
146×*-un-lft-identity
138×add-cube-cbrt
131×times-frac
105×prod-diff
52×distribute-rgt-in distribute-lft-in
13×add-exp-log add-cbrt-cube associate-/l*
12×associate-*r* associate-*l*
11×div-inv
8×pow1 flip3-- flip--
6×add-log-exp difference-of-squares
5×sub-neg
4×expm1-log1p-u frac-times associate-*r/ sqrt-prod log1p-expm1-u distribute-lft-out--
3×cbrt-undiv fma-neg div-exp associate-/r* unswap-sqr
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
1×frac-2neg diff-log clear-num associate-/l/
Counts
4 → 268
Calls
4 calls:
119.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
142.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
17.0ms
(- (cos x) (cos y))

series2.5s

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
2.1s
(/ (/ (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 3.0) 5.0) (+ 3.0 (sqrt 5.0))) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
146.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
91.0ms
(- (cos x) (cos y))

simplify2.8s

Counts
280 → 280
Iterations

Useful iterations: done (2.7s)

IterNodesCost
068713457
1148612539
2455310707
done500010705

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
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 (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)) 3.0))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.1b
(- (cos x) (cos y))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
106×*-un-lft-identity
105×prod-diff
98×add-cube-cbrt
59×times-frac
52×distribute-rgt-in distribute-lft-in
13×add-exp-log add-cbrt-cube
12×associate-*r* associate-*l*
8×pow1 flip3-- flip--
7×div-inv
6×add-log-exp difference-of-squares
5×sub-neg
4×expm1-log1p-u frac-times associate-*r/ sqrt-prod log1p-expm1-u distribute-lft-out--
3×fma-neg prod-exp cbrt-unprod associate-/l* unswap-sqr
2×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative diff-cos
1×frac-2neg diff-log clear-num associate-/r*
Counts
4 → 219
Calls
4 calls:
95.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
16.0ms
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (* (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)) 3.0))
104.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms
(- (cos x) (cos y))

series2.8s

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
2.4s
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (* (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)) 3.0))
141.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
102.0ms
(- (cos x) (cos y))

simplify2.4s

Counts
231 → 231
Iterations

Useful iterations: done (2.4s)

IterNodesCost
05868748
112647876
241446046
done50006039

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 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))
3.1b
(- (cos x) (cos y))

rewrite149.0ms

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
15×add-exp-log
14×sqrt-prod
13×associate-/l*
11×add-cbrt-cube div-inv
8×add-log-exp
6×pow1 fma-neg div-exp associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cbrt-undiv flip3-- associate-/r* flip-- distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×rec-exp frac-2neg 1-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos associate-/l/
Counts
4 → 252
Calls
4 calls:
19.0ms
(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
82.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
9.0ms
(- 3.0 (sqrt 5.0))
26.0ms
(- (cos x) (cos y))

series787.0ms

Counts
4 → 10
Calls
4 calls:
523.0ms
(/ (/ 1 3.0) (fma (cos y) (/ (- 3.0 (sqrt 5.0)) 2.0) (fma (cos x) (/ (- (sqrt 5.0) 1.0) 2.0) 1.0)))
163.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
100.0ms
(- (cos x) (cos y))

simplify2.6s

Counts
262 → 262
Iterations

Useful iterations: done (2.6s)

IterNodesCost
06148935
112437984
231296392
done50015646

prune1.5s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes236.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03253
13553
done3553

end0.0ms

sample14.7s

Algorithm
intervals
Results
7.8s2705×body1280valid
4.1s1806×body640valid
975.0ms2375×body80valid
770.0ms765×body320valid
667.0ms349×body160valid