Details

Time bar (total: 12.8s)

sample194.0ms

Algorithm
intervals
Results
96.0ms83×body1280valid
53.0ms67×body640valid
13.0ms26×body320valid
10.0ms72×body80valid
3.0ms8×body160valid

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

localize31.0ms

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) (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))) 3.0)
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.4b
(- (cos x) (cos y))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
152×add-sqr-sqrt
143×*-un-lft-identity
137×add-cube-cbrt
130×times-frac
105×prod-diff
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
13×associate-/l*
11×add-exp-log add-cbrt-cube div-inv
8×add-log-exp
6×pow1 fma-neg associate-*r* associate-*l*
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip-- distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×frac-2neg pow-prod-down prod-exp clear-num *-commutative cbrt-unprod diff-cos associate-/l/
Counts
4 → 250
Calls
4 calls:
6.0ms
(/ (/ (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))) 3.0)
39.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series1.1s

Counts
4 → 10
Calls
4 calls:
974.0ms
(/ (/ (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))) 3.0)
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
59.0ms
(- (cos x) (cos y))

simplify83.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014067067
150025887

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

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) (/ (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))) 3.0))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.4b
(- (cos x) (cos y))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
158×add-sqr-sqrt
138×*-un-lft-identity
131×add-cube-cbrt
126×times-frac
105×prod-diff
49×associate-*r*
41×distribute-rgt-in distribute-lft-in
21×add-exp-log
15×add-cbrt-cube
14×sqrt-prod
10×div-inv
9×associate-*l*
8×pow1 add-log-exp
6×fma-neg div-exp prod-exp unswap-sqr
5×difference-of-squares
4×expm1-log1p-u sub-neg cbrt-unprod log1p-expm1-u
3×cbrt-undiv flip3-- associate-*r/ flip-- distribute-lft-out--
2×diff-log pow-prod-down *-commutative
1×rec-exp 1-exp diff-cos
Counts
4 → 248
Calls
4 calls:
19.0ms
(* (fma (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (* (- (sin y) (/ (sin x) 16.0)) (- (cos x) (cos y))) 2.0) (/ (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))) 3.0))
36.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
7.0ms
(- (cos x) (cos y))

series1.2s

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) (cos y))) 2.0) (/ (/ 1 (fma (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y) (fma (/ (- (sqrt 5.0) 1.0) 2.0) (cos x) 1.0))) 3.0))
92.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
51.0ms
(- (cos x) (cos y))

simplify74.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015026211
150015037

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

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))
2.4b
(- (cos x) (cos y))

rewrite12.0ms

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:
0.0ms
(cbrt 16.0)
1.0ms
(cbrt 16.0)
5.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series58.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 16.0)
0.0ms
(cbrt 16.0)
0.0ms
(- 3.0 (sqrt 5.0))
58.0ms
(- (cos x) (cos y))

simplify44.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0398944
11193707
25002682

prune858.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 5.0)
1.0b
(* (cbrt 5.0) (cbrt 5.0))
2.0b
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))
2.4b
(- (cos x) (cos y))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×cbrt-prod
11×pow1
9×prod-diff
7×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
3×fma-neg
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log prod-exp *-commutative flip-- cbrt-unprod fma-udef diff-cos distribute-lft-out-- difference-of-squares
Counts
4 → 94
Calls
4 calls:
0.0ms
(cbrt 5.0)
6.0ms
(* (cbrt 5.0) (cbrt 5.0))
0.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))
4.0ms
(- (cos x) (cos y))

series58.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 5.0)
0.0ms
(* (cbrt 5.0) (cbrt 5.0))
0.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))
58.0ms
(- (cos x) (cos y))

simplify153.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 3 (145.0ms)

IterNodesCost
0305825
1926680
24824648
35001639

prune697.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes136.0ms

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
06356
16556
26556

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.1s2706×body1280valid
1.4s1832×body640valid
386.0ms746×body320valid
364.0ms2387×body80valid
116.0ms329×body160valid