Details

Time bar (total: 16.4s)

sample191.0ms

Algorithm
intervals
Results
102.0ms88×body1280valid
36.0ms49×body640valid
13.0ms83×body80valid
13.0ms25×body320valid
4.0ms11×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
07430
119327
270427
3299427
4500127

prune18.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 2

localize35.0ms

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))) 3.0)
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))

rewrite42.0ms

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

series1.1s

Counts
4 → 10
Calls
4 calls:
962.0ms
(/ (/ (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)
87.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify85.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014067067
150025887

prune1.1s

Filtered
260 candidates to 139 candidates (53.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2519260
Fresh011
Picked101
Done000
Total25210262

Merged error: 0.0b

Counts
262 → 10

localize49.0ms

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))
1.7b
(- (cos x) (cos y))

rewrite65.0ms

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:
23.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))
14.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
5.0ms
(- (cos x) (cos y))

series365.0ms

Counts
4 → 10
Calls
4 calls:
224.0ms
(* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (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))
52.0ms
(- (cos x) (cos y))

simplify72.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014525955
150014771

prune983.0ms

Filtered
262 candidates to 132 candidates (50.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2620262
Fresh099
Picked011
Done000
Total26210272

Merged error: 0.0b

Counts
272 → 10

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 5.0)
1.0b
(* (cbrt 5.0) (cbrt 5.0))
1.7b
(- (cos x) (cos y))
2.0b
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

rewrite25.0ms

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:
1.0ms
(cbrt 5.0)
10.0ms
(* (cbrt 5.0) (cbrt 5.0))
9.0ms
(- (cos x) (cos y))
1.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

series56.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 5.0)
0.0ms
(* (cbrt 5.0) (cbrt 5.0))
56.0ms
(- (cos x) (cos y))
0.0ms
(fma (* (cbrt 3.0) (cbrt 3.0)) (cbrt 3.0) (- (* (sqrt (cbrt 5.0)) (sqrt (* (cbrt 5.0) (cbrt 5.0))))))

simplify176.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 3 (167.0ms)

IterNodesCost
0305825
1926680
24824648
35001639

prune774.0ms

Filtered
100 candidates to 66 candidates (66.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh178
Picked011
Done011
Total10010110

Merged error: 0.0b

Counts
110 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(expm1 (log1p (/ (/ (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)))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
1.7b
(- (cos x) (cos y))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
105×prod-diff
101×*-un-lft-identity
95×add-cube-cbrt
55×times-frac
41×distribute-rgt-in distribute-lft-in
14×sqrt-prod
8×add-log-exp
6×pow1 add-exp-log fma-neg associate-*r* associate-*l* add-cbrt-cube div-inv
5×difference-of-squares
4×expm1-log1p-u sub-neg log1p-expm1-u
3×flip3-- flip-- distribute-lft-out--
2×diff-log associate-*r/ unswap-sqr
1×expm1-log1p pow-prod-down prod-exp *-commutative cbrt-unprod diff-cos expm1-udef
Counts
4 → 189
Calls
4 calls:
1.0ms
(expm1 (log1p (/ (/ (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)))
14.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms
(- 3.0 (sqrt 5.0))
5.0ms
(- (cos x) (cos y))

series4.2s

Counts
4 → 10
Calls
4 calls:
4.0s
(expm1 (log1p (/ (/ (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)))
91.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify130.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
011484392
144753284
250013277

prune707.0ms

Filtered
199 candidates to 89 candidates (44.7%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1972199
Fresh167
Picked011
Done022
Total19811209

Merged error: 0b

Counts
209 → 11

regimes322.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04130
14130

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.2s2697×body1280valid
1.4s1869×body640valid
406.0ms762×body320valid
387.0ms2315×body80valid
125.0ms357×body160valid