Details

Time bar (total: 11.9s)

sample188.0ms

Algorithm
intervals
Results
94.0ms88×body1280valid
46.0ms61×body640valid
11.0ms78×body80valid
10.0ms16×body160valid
6.0ms13×body320valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
07430
119327
270427
3299427
4500127

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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))
1.9b
(- (cos x) (cos y))

rewrite111.0ms

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)))
74.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
14.0ms
(- 3.0 (sqrt 5.0))
8.0ms
(- (cos x) (cos y))

series975.0ms

Counts
4 → 10
Calls
4 calls:
842.0ms
(/ (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)))
85.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
48.0ms
(- (cos x) (cos y))

simplify127.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
011604965
144023841
250013834

prune867.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.0b
(cbrt 16.0)
1.9b
(- (cos x) (cos y))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
9×cbrt-prod prod-diff
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg pow1/3
1×sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 68
Calls
4 calls:
4.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
8.0ms
(- (cos x) (cos y))

series57.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
57.0ms
(- (cos x) (cos y))

simplify115.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0255549
1748444
23867426
35001416

prune584.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 16.0)
1.9b
(- (cos x) (cos y))
1.9b
(- (cos x) (cos y))
1.9b
(- (cos x) (cos y))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
27×prod-diff
26×add-cube-cbrt
10×add-log-exp
9×fma-neg
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cbrt-prod sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
1×pow1/3
Counts
4 → 100
Calls
4 calls:
1.0ms
(cbrt 16.0)
13.0ms
(- (cos x) (cos y))
8.0ms
(- (cos x) (cos y))
8.0ms
(- (cos x) (cos y))

series152.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(cbrt 16.0)
48.0ms
(- (cos x) (cos y))
56.0ms
(- (cos x) (cos y))
48.0ms
(- (cos x) (cos y))

simplify87.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0175922
1481631
22340601
35001535

prune818.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize33.0ms

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))
1.9b
(- (cos x) (cos y))

rewrite208.0ms

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:
108.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
60.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
11.0ms
(- 3.0 (sqrt 5.0))
9.0ms
(- (cos x) (cos y))

series271.0ms

Counts
4 → 10
Calls
4 calls:
134.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
87.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
49.0ms
(- (cos x) (cos y))

simplify88.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
017307731
150016094

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes215.0ms

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
05450
15850
25850

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.2s2896×body1280valid
1.3s1781×body640valid
367.0ms743×body320valid
314.0ms2222×body80valid
112.0ms358×body160valid