Details

Time bar (total: 12.9s)

sample183.0ms

Algorithm
intervals
Results
92.0ms84×body1280valid
43.0ms55×body640valid
12.0ms24×body320valid
11.0ms78×body80valid
5.0ms15×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
07430
119327
270427
3299427
4500127

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.4b
(- (cos x) (cos y))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
133×add-sqr-sqrt
123×prod-diff
119×*-un-lft-identity
109×add-cube-cbrt
56×times-frac
52×distribute-rgt-in distribute-lft-in
14×sqrt-prod
12×associate-*r* associate-*l*
9×flip3-- flip--
8×pow1 add-exp-log add-cbrt-cube add-log-exp difference-of-squares
6×sub-neg fma-neg div-inv
5×distribute-lft-out--
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×unswap-sqr
2×diff-log pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod diff-cos
Counts
4 → 234
Calls
4 calls:
37.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
38.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series246.0ms

Counts
4 → 10
Calls
4 calls:
99.0ms
(* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y)))
89.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify132.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
010794683
143433463
250013456

prune859.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (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))
2.5b
(+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos y))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
100×*-un-lft-identity
96×add-cube-cbrt prod-diff
64×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
8×add-exp-log associate-*l/ add-cbrt-cube add-log-exp
7×div-inv
6×pow1 flip3-- associate-*r* associate-*l* flip--
4×expm1-log1p-u frac-add log1p-expm1-u difference-of-squares
3×sub-neg fma-neg associate-/r* associate-/l*
2×associate-*r/ distribute-rgt-neg-out distribute-lft-out-- unswap-sqr
1×cbrt-undiv +-commutative fma-def frac-2neg flip3-+ diff-log div-exp unsub-neg pow-prod-down prod-exp clear-num sum-log *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 199
Calls
4 calls:
3.0ms
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (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)))
57.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
14.0ms
(+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos y))))

series1.3s

Counts
4 → 10
Calls
4 calls:
1.0s
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (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))
186.0ms
(+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos y))))

simplify66.0ms

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012995456
150014285

prune924.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
2.5b
(+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos y))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×associate-*l/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u flip3-- frac-add add-cbrt-cube flip-- log1p-expm1-u
3×pow1/3
2×distribute-rgt-neg-out
1×+-commutative fma-def flip3-+ unsub-neg sum-log flip-+ distribute-lft-out
Counts
4 → 60
Calls
4 calls:
0.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
14.0ms
(+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos y))))

series192.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
192.0ms
(+ (* (- (sin y) (/ (sin x) 16.0)) (cos x)) (* (- (sin y) (/ (sin x) 16.0)) (- (cos y))))

simplify50.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0396835
11540734
25001726

prune886.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.4b
(- (cos x) (cos y))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
123×prod-diff
116×*-un-lft-identity
108×add-cube-cbrt
55×times-frac
52×distribute-rgt-in distribute-lft-in
30×flip3-- flip--
28×frac-times associate-*r/
15×pow1 add-exp-log add-cbrt-cube
14×associate-*l/ sqrt-prod
12×associate-*r*
8×add-log-exp
7×associate-*l* pow-prod-down prod-exp cbrt-unprod
6×sub-neg fma-neg div-inv difference-of-squares
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
2×diff-log *-commutative diff-cos unswap-sqr
Counts
4 → 252
Calls
4 calls:
167.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
35.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series369.0ms

Counts
4 → 10
Calls
4 calls:
225.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
52.0ms
(- (cos x) (cos y))

simplify80.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
014525955
150014771

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes236.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04434
14434

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.2s2762×body1280valid
1.4s1862×body640valid
380.0ms732×body320valid
347.0ms2291×body80valid
116.0ms353×body160valid