Details

Time bar (total: 12.0s)

sample161.0ms

Algorithm
intervals
Results
80.0ms71×body1280valid
29.0ms43×body640valid
15.0ms33×body320valid
14.0ms100×body80valid
3.0ms9×body160valid

simplify69.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
07430
119327
270427
3299427
4500127

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite58.0ms

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:
2.0ms
(/ (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)))
37.0ms
(* (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:
906.0ms
(/ (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)))
94.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
61.0ms
(- (cos x) (cos y))

simplify127.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
011604965
144023841
250013834

prune831.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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)))
0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite123.0ms

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:
61.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
35.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms
(- 3.0 (sqrt 5.0))
7.0ms
(- (cos x) (cos y))

series293.0ms

Counts
4 → 10
Calls
4 calls:
142.0ms
(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
92.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
59.0ms
(- (cos x) (cos y))

simplify89.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
017307731
150016094

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

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))))))
2.8b
(- (cos x) (cos y))

rewrite16.0ms

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))

series54.0ms

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))))))
54.0ms
(- (cos x) (cos y))

simplify41.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0325834
11016680
25001657

prune846.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.5b
(pow (- (cos x) (cos y)) 3)
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
117×add-sqr-sqrt
108×*-un-lft-identity
105×prod-diff
98×add-cube-cbrt
55×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
8×add-log-exp
7×pow1 add-exp-log add-cbrt-cube difference-of-squares
6×unpow-prod-down fma-neg cube-prod associate-*r* associate-*l* div-inv
5×distribute-lft-out--
4×expm1-log1p-u sub-neg flip3-- flip-- log1p-expm1-u
3×pow-unpow diff-cos
2×cube-div diff-log associate-*r/ unswap-sqr
1×cube-mult pow-to-exp pow-pow unpow3 pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod rem-cube-cbrt sqr-pow
Counts
4 → 211
Calls
4 calls:
35.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(pow (- (cos x) (cos y)) 3)
4.0ms
(- 3.0 (sqrt 5.0))
4.0ms
(- (cos x) (cos y))

series226.0ms

Counts
4 → 10
Calls
4 calls:
96.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
73.0ms
(pow (- (cos x) (cos y)) 3)
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify115.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
010173888
140942839
250022832

prune839.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes220.0ms

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

sample5.5s

Algorithm
intervals
Results
3.1s2758×body1280valid
1.3s1748×body640valid
392.0ms773×body320valid
346.0ms2327×body80valid
140.0ms394×body160valid