Details

Time bar (total: 4.3s)

sample23.0ms

Algorithm
intervals
Results
6.0ms47×body1280valid
4.0ms43×body640valid
4.0ms142×body80valid
1.0ms17×body320valid
0.0ms7×body160valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

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: 27.1b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
7.0ms
(/ (+ x 1.0) (- x 1.0))
32.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series206.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ x (+ x 1.0))
42.0ms
(/ (+ x 1.0) (- x 1.0))
129.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0392760
11379726
25001716

prune204.0ms

Filtered
113 candidates to 76 candidates (67.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1085113
Fresh000
Picked101
Done000
Total1095114

Merged error: 0.0b

Counts
114 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.2b
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
103×*-un-lft-identity
67×add-sqr-sqrt
60×times-frac
37×add-cube-cbrt
18×distribute-lft-out
15×associate-/r* distribute-lft-out-- difference-of-squares
12×cbrt-div associate-/l*
10×add-exp-log add-cbrt-cube
7×frac-sub
6×associate-/r/ associate-/l/ add-log-exp
5×frac-times associate-*l/
4×pow1 flip3-- flip--
3×cbrt-undiv frac-2neg flip3-+ associate-*r/ div-exp clear-num flip-+ div-inv
1×sub-neg diff-log
Counts
4 → 154
Calls
4 calls:
8.0ms
(/ (+ x 1.0) (- x 1.0))
7.0ms
(/ (+ x 1.0) (- x 1.0))
7.0ms
(/ (+ x 1.0) (- x 1.0))
10.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ (+ x 1.0) (- x 1.0))
37.0ms
(/ (+ x 1.0) (- x 1.0))
44.0ms
(/ (+ x 1.0) (- x 1.0))
163.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03901462
112681330
250011304

prune314.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1642166
Fresh134
Picked011
Done000
Total1656171

Merged error: 0.0b

Counts
171 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x 1.0) (- x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.1b
(+ (* (neg (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
103×*-un-lft-identity
72×cbrt-div
67×add-sqr-sqrt
66×frac-times associate-*l/
60×times-frac
45×frac-add
42×distribute-neg-frac
37×add-cube-cbrt
36×associate-*r/
18×distribute-lft-out
15×associate-/r* distribute-lft-out-- difference-of-squares
12×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r/ associate-/l/ add-log-exp
4×pow1 flip3-+ flip-+
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
1×+-commutative sum-log
Counts
4 → 191
Calls
4 calls:
7.0ms
(/ (+ x 1.0) (- x 1.0))
8.0ms
(/ (+ x 1.0) (- x 1.0))
7.0ms
(/ (+ x 1.0) (- x 1.0))
14.0ms
(+ (* (neg (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

series374.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ (+ x 1.0) (- x 1.0))
38.0ms
(/ (+ x 1.0) (- x 1.0))
44.0ms
(/ (+ x 1.0) (- x 1.0))
248.0ms
(+ (* (neg (* (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (cbrt (/ (+ x 1.0) (- x 1.0))))) (/ (+ x 1.0) (- x 1.0))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0))))

simplify107.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
09692948
136992762
250012716

prune440.0ms

Filtered
203 candidates to 120 candidates (59.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2021203
Fresh044
Picked011
Done011
Total2027209

Merged error: 0.0b

Counts
209 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
5.6b
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
8.0b
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
14.2b
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
287×add-sqr-sqrt
258×*-un-lft-identity
201×times-frac
144×difference-of-squares
108×unpow-prod-down cube-prod
106×associate-*l*
72×sqr-pow
66×add-cube-cbrt
51×distribute-lft-out
45×distribute-lft-out--
25×associate-/r*
11×add-exp-log add-cbrt-cube add-log-exp
9×difference-cubes
6×pow1 flip3-+ flip-+
5×frac-sub
4×frac-times associate-*r/ associate-/r/ associate-/l*
3×flip3-- associate-*r* sum-log flip--
2×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ associate--r+ unswap-sqr
1×+-commutative sub-neg associate-+r+ frac-2neg diff-log pow-prod-down clear-num *-commutative
Counts
4 → 308
Calls
4 calls:
9.0ms
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
17.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
10.0ms
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
34.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
51.0ms
(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
171.0ms
(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
73.0ms
(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify68.0ms

Algorithm
egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011833932
150013801

prune573.0ms

Filtered
320 candidates to 168 candidates (52.5%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New3200320
Fresh044
Picked011
Done022
Total3207327

Merged error: 0.0b

Counts
327 → 7

regimes46.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.5b

bsearch97.0ms

Steps
ItersRangePoint
9
7137.79058365099
1345801877840.7417
9381.346170100443
9
-16048011.320361046
-5.155753157609302
-8846.441191001562

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04851
15651
25951
36251
46251

end0.0ms

sample829.0ms

Algorithm
intervals
Results
408.0ms1715×body1280valid
134.0ms1307×body640valid
119.0ms4082×body80valid
45.0ms589×body320valid
18.0ms307×body160valid

Profiling

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