Details

Time bar (total: 4.2s)

sample23.0ms

Algorithm
intervals
Results
7.0ms62×body640valid
4.0ms137×body80valid
2.0ms29×body320valid
2.0ms15×body1280valid
1.0ms13×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 7.4b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (+ x 1.0))
1.8b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
5.0ms
(/ 1.0 (- x 1.0))
16.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms
(/ 1.0 (+ x 1.0))
30.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1.0 (- x 1.0))
41.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
30.0ms
(/ 1.0 (+ x 1.0))
222.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0496865
11681827
25002816

prune221.0ms

Filtered
126 candidates to 92 candidates (73.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1233126
Fresh000
Picked011
Done000
Total1234127

Merged error: 0.5b

Counts
127 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.2b
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
4.7b
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
14.0b
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
16×add-exp-log add-cbrt-cube
13×flip3-+ flip-+
12×frac-times
11×associate-/r/ associate-/l/
10×add-log-exp
9×times-frac
8×frac-add distribute-lft-out
6×associate-*l/
4×pow1 cbrt-undiv add-sqr-sqrt add-cube-cbrt associate-+r+ flip3-- associate-*r/ div-exp prod-exp flip-- cbrt-unprod
3×+-commutative sum-log
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-2neg clear-num associate-/r* div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
16.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
16.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
7.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
46.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
46.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
134.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
312.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))

simplify83.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06271549
132301162
250021152

prune215.0ms

Filtered
100 candidates to 78 candidates (78.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh022
Picked011
Done011
Total995104

Merged error: 0.0b

Counts
104 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (pow x 3))
0.5b
(/ 1 (pow x 2))
1.2b
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 2.0 (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3))))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
10.8b
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×*-un-lft-identity
69×add-sqr-sqrt
49×add-cube-cbrt
43×add-exp-log
29×add-cbrt-cube
27×associate-*r/
26×unpow-prod-down
23×associate-/l/
21×frac-times associate-/r*
18×div-exp
16×div-inv
15×frac-sub
14×flip3-+ cube-prod frac-add flip-+
13×distribute-lft-out--
11×associate-/r/ distribute-lft-out
10×sqr-pow
9×flip3-- prod-exp flip-- cbrt-unprod add-log-exp difference-of-squares
8×cbrt-undiv
7×associate-/l*
6×pow-to-exp rec-exp 1-exp associate-*l/ pow-exp
4×pow1 cube-mult unpow3 unpow2
3×frac-2neg clear-num
2×pow-flip diff-log inv-pow
1×sub-neg associate--l+ sum-log
Counts
4 → 228
Calls
4 calls:
5.0ms
(/ 1 (pow x 3))
5.0ms
(/ 1 (pow x 2))
100.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 2.0 (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3))))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
57.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

series152.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1 (pow x 3))
16.0ms
(/ 1 (pow x 2))
82.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 2.0 (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3))))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
22.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

simplify64.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011502791
150012268

prune549.0ms

Filtered
240 candidates to 122 candidates (50.8%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2391240
Fresh022
Picked011
Done022
Total2396245

Merged error: 0b

Counts
245 → 6

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (pow x 4))
0.5b
(/ 1 (pow x 3))
1.2b
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 2.0 (- (+ (pow x (- 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3))))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
10.8b
(- (+ (pow x (- 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
65×add-sqr-sqrt
60×*-un-lft-identity
45×add-cube-cbrt
43×add-exp-log
32×associate-*r/
29×add-cbrt-cube
27×associate-/l/
26×unpow-prod-down
24×frac-times
20×frac-add associate-/r* frac-sub
18×div-exp
15×flip3-+ flip-+
14×cube-prod
11×associate-/r/
10×sqr-pow
9×flip3-- prod-exp flip-- cbrt-unprod add-log-exp difference-of-squares
8×cbrt-undiv div-inv
7×associate-/l*
6×pow-to-exp rec-exp 1-exp associate-*l/ pow-exp distribute-lft-out--
5×neg-sub0 pow-neg pow-sub
4×pow1 cube-mult unpow3 distribute-lft-out
3×frac-2neg clear-num
2×pow-flip diff-log inv-pow
1×sub-neg associate--l+ sum-log
Counts
4 → 222
Calls
4 calls:
5.0ms
(/ 1 (pow x 4))
5.0ms
(/ 1 (pow x 3))
74.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 2.0 (- (+ (pow x (- 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3))))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
31.0ms
(- (+ (pow x (- 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

series182.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1 (pow x 4))
36.0ms
(/ 1 (pow x 3))
92.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* 2.0 (- (+ (pow x (- 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3))))) (* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
27.0ms
(- (+ (pow x (- 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

simplify58.0ms

Algorithm
egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011502797
150022284

prune547.0ms

Filtered
234 candidates to 121 candidates (51.7%)
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New2340234
Fresh022
Picked011
Done033
Total2346240

Merged error: 0b

Counts
240 → 6

regimes81.0ms

Accuracy

94.5% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 9.6b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04542
14542

end0.0ms

sample587.0ms

Algorithm
intervals
Results
202.0ms1891×body640valid
117.0ms4147×body80valid
78.0ms564×body1280valid
75.0ms947×body320valid
24.0ms452×body160valid