Details

Time bar (total: 12.4s)

sample179.0ms

Algorithm
intervals
Results
90.0ms82×body1280valid
40.0ms60×body640valid
12.0ms26×body320valid
12.0ms79×body80valid
3.0ms9×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07430
118230
265730
3272730
4500130

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize39.0ms

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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.5b
(- (cos x) (cos y))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
30×flip3-- flip--
28×frac-times associate-*r/
25×add-sqr-sqrt
16×*-un-lft-identity
15×pow1 add-exp-log add-cbrt-cube
14×associate-*l/
12×associate-*r*
8×add-cube-cbrt add-log-exp
7×associate-*l* pow-prod-down prod-exp cbrt-unprod
6×sub-neg difference-of-squares
5×sqrt-prod
4×distribute-rgt-in distribute-lft-in distribute-lft-out--
2×diff-log *-commutative diff-cos unswap-sqr
1×times-frac
Counts
4 → 115
Calls
4 calls:
285.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
51.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
6.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series367.0ms

Counts
4 → 10
Calls
4 calls:
221.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
55.0ms
(- (cos x) (cos y))

simplify115.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08441973
144131829
250011829

prune740.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

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)))
0.3b
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.5b
(- (cos x) (cos y))

rewrite449.0ms

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:
98.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
288.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
51.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
7.0ms
(- (cos x) (cos y))

series509.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
225.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
94.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
53.0ms
(- (cos x) (cos y))

simplify131.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08482481
149312282
250022282

prune929.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(+ (* (cos y) (cos y)) (* (cos x) (cos y)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.2b
(- (pow (cos x) 3) (pow (cos y) 3))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
22×*-un-lft-identity
18×difference-of-squares
15×unpow-prod-down cube-prod
10×add-cube-cbrt
9×sqr-pow
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* distribute-lft-out--
4×sqrt-prod
3×sub-neg pow-unpow
2×distribute-rgt-in flip3-- distribute-lft-in associate-*r/ cos-mult flip-- unswap-sqr
1×difference-cubes +-commutative cube-mult pow-to-exp sqr-cos associate-+l+ distribute-rgt-out pow-pow flip3-+ times-frac diff-log unpow3 pow-prod-down frac-add pow-exp prod-exp sum-log *-commutative cbrt-unprod flip-+ rem-cube-cbrt
Counts
4 → 102
Calls
4 calls:
3.0ms
(pow (cos x) 3)
13.0ms
(+ (* (cos y) (cos y)) (* (cos x) (cos y)))
52.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
24.0ms
(- (pow (cos x) 3) (pow (cos y) 3))

series274.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(pow (cos x) 3)
67.0ms
(+ (* (cos y) (cos y)) (* (cos x) (cos y)))
92.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
88.0ms
(- (pow (cos x) 3) (pow (cos y) 3))

simplify68.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0513889
12096824
25001804

prune783.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(+ 1/2 (+ (* 1/2 (cos (* 2 y))) (* (cos x) (cos y))))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
2.2b
(- (pow (cos x) 3) (pow (cos y) 3))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
24×*-un-lft-identity
18×difference-of-squares
15×unpow-prod-down cube-prod
11×add-log-exp
10×add-cube-cbrt
9×sqr-pow
7×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* distribute-lft-out--
4×sqrt-prod
3×sub-neg pow-unpow sum-log
2×distribute-rgt-in flip3-- distribute-lft-in associate-*r/ flip-- unswap-sqr
1×difference-cubes +-commutative cube-mult pow-to-exp associate-+r+ pow-pow flip3-+ times-frac diff-log unpow3 pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 102
Calls
4 calls:
3.0ms
(pow (cos x) 3)
18.0ms
(+ 1/2 (+ (* 1/2 (cos (* 2 y))) (* (cos x) (cos y))))
52.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
23.0ms
(- (pow (cos x) 3) (pow (cos y) 3))

series273.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
72.0ms
(+ 1/2 (+ (* 1/2 (cos (* 2 y))) (* (cos x) (cos y))))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
80.0ms
(- (pow (cos x) 3) (pow (cos y) 3))

simplify66.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0493916
11988862
25001842

prune787.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

regimes146.0ms

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
07170
17170

end0.0ms

sample5.8s

Algorithm
intervals
Results
3.1s2776×body1280valid
1.5s1846×body640valid
371.0ms753×body320valid
323.0ms2260×body80valid
118.0ms365×body160valid