Details

Time bar (total: 11.4s)

sample178.0ms

Algorithm
intervals
Results
87.0ms80×body1280valid
43.0ms64×body640valid
11.0ms24×body320valid
10.0ms75×body80valid
4.0ms13×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
07430
119327
270427
3299427
4500127

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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) (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))
2.3b
(- (cos x) (cos y))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
118×add-sqr-sqrt
109×*-un-lft-identity
105×prod-diff
103×add-cube-cbrt
64×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
8×add-exp-log add-cbrt-cube add-log-exp
7×div-inv
6×pow1 fma-neg associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×flip3-- associate-/r* flip-- associate-/l* distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos
Counts
4 → 207
Calls
4 calls:
5.0ms
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (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)))
63.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series960.0ms

Counts
4 → 10
Calls
4 calls:
818.0ms
(/ (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (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)))
87.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
54.0ms
(- (cos x) (cos y))

simplify134.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
011604965
144023841
250013834

prune811.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.0b
(- 3.0 (sqrt 5.0))
2.3b
(- (cos x) (cos y))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×*-un-lft-identity
27×prod-diff
26×add-cube-cbrt
10×sqrt-prod
8×add-log-exp
6×cbrt-prod fma-neg
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×difference-of-squares
2×sub-neg flip3-- pow1/3 diff-log flip-- distribute-lft-out--
1×diff-cos
Counts
4 → 93
Calls
4 calls:
1.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series53.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(- 3.0 (sqrt 5.0))
52.0ms
(- (cos x) (cos y))

simplify41.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0398959
11187722
25001703

prune728.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
2.6b
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u cos-mult add-cbrt-cube log1p-expm1-u
3×pow1/3
2×sqr-cos
1×sub-neg flip3-- fma-neg diff-log prod-diff associate--l+ frac-sub flip-- associate--r+ sub-div difference-of-squares
Counts
4 → 60
Calls
4 calls:
1.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
17.0ms
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

series70.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
70.0ms
(- (* (cos x) (cos x)) (* (cos y) (cos y)))

simplify83.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0198356
1694308
22474292
35001291

prune919.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.3b
(- (cos x) (cos y))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
184×add-sqr-sqrt
183×prod-diff
172×*-un-lft-identity
164×add-cube-cbrt
110×times-frac
82×distribute-rgt-in distribute-lft-in
14×sqrt-prod
12×associate-*r* div-inv
11×pow1 add-exp-log add-cbrt-cube
10×associate-*r/
9×flip3-- flip--
8×add-log-exp
7×associate-*l* difference-of-squares
6×sub-neg fma-neg
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod log1p-expm1-u distribute-lft-out--
2×diff-log associate-*l/ *-commutative unswap-sqr
1×diff-cos
Counts
4 → 291
Calls
4 calls:
110.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
61.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
8.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series262.0ms

Counts
4 → 10
Calls
4 calls:
124.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
84.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
54.0ms
(- (cos x) (cos y))

simplify91.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
017307731
150016094

prune972.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06251
16451
26451

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.0s2698×body1280valid
1.3s1869×body640valid
364.0ms759×body320valid
321.0ms2319×body80valid
116.0ms355×body160valid