Details

Time bar (total: 12.6s)

sample192.0ms

Algorithm
intervals
Results
109.0ms100×body1280valid
33.0ms47×body640valid
14.0ms21×body320valid
10.0ms71×body80valid
5.0ms17×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07430
118230
265730
3272730
4500130

prune8.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize53.0ms

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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.6b
(- (cos x) (cos y))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
16×*-un-lft-identity
12×associate-*r*
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
8×add-cube-cbrt add-log-exp
7×associate-*l* difference-of-squares
6×sub-neg
5×sqrt-prod
4×distribute-rgt-in frac-times distribute-lft-in pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
2×times-frac diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 94
Calls
4 calls:
58.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
28.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- (cos x) (cos y))

series314.0ms

Counts
4 → 10
Calls
4 calls:
174.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
86.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
54.0ms
(- (cos x) (cos y))

simplify64.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
06221094
126431002
250031002

prune555.0ms

Filtered
104 candidates to 70 candidates (67.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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))) (- (cos x) (cos y)))
0.3b
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.6b
(- (cos x) (cos y))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
36×associate-*r/
35×flip3-- flip--
32×frac-times
27×add-sqr-sqrt
20×pow1 add-exp-log add-cbrt-cube
18×associate-*r*
17×*-un-lft-identity
16×associate-*l/
10×pow-prod-down prod-exp cbrt-unprod
9×add-cube-cbrt
8×associate-*l*
7×sub-neg
6×distribute-rgt-in distribute-lft-in add-log-exp difference-of-squares
4×sqrt-prod distribute-lft-out--
3×*-commutative
2×times-frac diff-cos unswap-sqr
1×diff-log
Counts
4 → 133
Calls
4 calls:
166.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
53.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
30.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- (cos x) (cos y))

series484.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
130.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
86.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
50.0ms
(- (cos x) (cos y))

simplify122.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08482481
149312282
250022282

prune906.0ms

Filtered
145 candidates to 101 candidates (69.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) (+ (sin x) (/ (sin y) 16.0)))
0.3b
(* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.4b
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
1.6b
(- (cos x) (cos y))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
88×associate-*r/
87×frac-times
56×flip3-- flip--
53×associate-/l/
50×associate-*l/
39×frac-sub sin-mult
25×add-exp-log add-cbrt-cube
21×add-sqr-sqrt
18×*-un-lft-identity
11×pow1
10×add-cube-cbrt associate-*r* prod-exp cbrt-unprod
7×associate-*l*
6×add-log-exp
5×sub-neg times-frac
4×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp pow-prod-down associate-/r* sqrt-prod difference-of-squares
2×associate-/r/ *-commutative distribute-lft-out distribute-lft-out-- unswap-sqr
1×frac-2neg flip3-+ diff-log clear-num flip-+ div-inv diff-cos associate-/l*
Counts
4 → 171
Calls
4 calls:
129.0ms
(/ (* (* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) (+ (sin x) (/ (sin y) 16.0)))
50.0ms
(* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
19.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
3.0ms
(- (cos x) (cos y))

series826.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (* (* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y))) (+ (sin x) (/ (sin y) 16.0)))
347.0ms
(* (* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
106.0ms
(* (sqrt 2.0) (- (* (sin x) (sin x)) (* (/ (sin y) 16.0) (/ (sin y) 16.0))))
56.0ms
(- (cos x) (cos y))

simplify57.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012773813
150013583

prune1.5s

Filtered
183 candidates to 145 candidates (79.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

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)))
0.6b
(cbrt (+ (sin x) (/ (sin y) 16.0)))
1.6b
(- (cos x) (cos y))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×cbrt-prod
9×add-sqr-sqrt
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 57
Calls
4 calls:
6.0ms
(cbrt (+ (sin x) (/ (sin y) 16.0)))
6.0ms
(cbrt (+ (sin x) (/ (sin y) 16.0)))
7.0ms
(cbrt (+ (sin x) (/ (sin y) 16.0)))
3.0ms
(- (cos x) (cos y))

series434.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(cbrt (+ (sin x) (/ (sin y) 16.0)))
128.0ms
(cbrt (+ (sin x) (/ (sin y) 16.0)))
125.0ms
(cbrt (+ (sin x) (/ (sin y) 16.0)))
58.0ms
(- (cos x) (cos y))

simplify53.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0230622
1546582
21568575
35001569

prune540.0ms

Filtered
69 candidates to 55 candidates (79.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes184.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05557
15557

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.2s2812×body1280valid
1.3s1770×body640valid
367.0ms740×body320valid
342.0ms2350×body80valid
104.0ms328×body160valid