Details

Time bar (total: 3.0s)

sample34.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0.021362%

Guaranteed chance to sample good point: 99.984738%

Results
9.0ms63×body640valid
5.0ms143×body80valid
3.0ms26×body320valid
2.0ms13×body1280valid
1.0ms11×body160valid

simplify15.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 8.4b

Counts
2 → 1

localize8.0ms

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))
1.6b
(+ (- (/ 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))
15.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms
(/ 1.0 (+ x 1.0))
32.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series17.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ 1.0 (- x 1.0))
3.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.0ms
(/ 1.0 (+ x 1.0))
10.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0496865
11681827
25001816

prune194.0ms

Filtered
92 candidates to 126 candidates (-37.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1233126
Fresh000
Picked101
Done000
Total1243127

Merged error: 0.2b

Counts
127 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
0.0b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
15.6b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*l/
22×flip3-- flip--
16×frac-times frac-add
13×add-sqr-sqrt
12×flip3-+ flip-+
11×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
10×associate-*r*
8×associate-*r/ add-log-exp
7×add-cube-cbrt sub-neg
6×distribute-rgt-in distribute-lft-in
4×associate-+l+ associate-*l* pow-prod-down prod-exp cbrt-unprod
2×*-commutative distribute-lft-out-- difference-of-squares
1×+-commutative diff-log sum-log unswap-sqr
Counts
4 → 107
Calls
4 calls:
8.0ms
(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
3.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
11.0ms
(* (* (+ x 1.0) x) (- x 1.0))
10.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series16.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0))
3.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
8.0ms
(* (* (+ x 1.0) x) (- x 1.0))
1.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify122.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07951594
144561513
250021513

prune252.0ms

Filtered
87 candidates to 119 candidates (-36.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1190119
Fresh022
Picked011
Done000
Total1193122

Merged error: 0.2b

Counts
122 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.1b
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
6.6b
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
19.5b
(/ (* (+ (/ 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)))

rewrite80.0ms

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:
15.0ms
(+ (/ 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)))
38.0ms
(/ (* (+ (/ 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)))

series28.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
3.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
7.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
14.0ms
(/ (* (+ (/ 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 (67.0ms)

IterNodesCost
06271549
132301162
250021152

prune216.0ms

Filtered
78 candidates to 100 candidates (-28.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh011
Picked011
Done011
Total994103

Merged error: 0.0b

Counts
103 → 4

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow x 3))
0.4b
(/ 1 (pow x 4))
1.0b
(/ (* (+ (/ 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)))
10.4b
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
75×times-frac
68×add-sqr-sqrt
48×add-cube-cbrt
43×add-exp-log
29×add-cbrt-cube
27×associate-*r/
26×unpow-prod-down
23×associate-/l/
21×frac-times
20×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
3×frac-2neg clear-num
2×pow-flip diff-log inv-pow
1×sub-neg associate--l+ sum-log
Counts
4 → 224
Calls
4 calls:
5.0ms
(/ 1 (pow x 3))
5.0ms
(/ 1 (pow x 4))
95.0ms
(/ (* (+ (/ 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)))
53.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

series16.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ 1 (pow x 3))
3.0ms
(/ 1 (pow x 4))
6.0ms
(/ (* (+ (/ 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)))
3.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

simplify53.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011482759
150022255

prune582.0ms

Filtered
120 candidates to 236 candidates (-96.7%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2342236
Fresh011
Picked011
Done022
Total2346240

Merged error: 0b

Counts
240 → 6

regimes55.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 25.7b

bsearch55.0ms

Steps
ItersRangePoint
11
2.6250463493313255e-08
2.340944862551434e+16
140820.49055888815
10
-160790015148248.7
-21869.37453130546
-606408.6583681721

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06036
16236
26236

end0.0ms

sample807.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0.021362%

Guaranteed chance to sample good point: 99.984738%

Results
266.0ms1864×body640valid
157.0ms4158×body80valid
100.0ms552×body1280valid
97.0ms926×body320valid
36.0ms500×body160valid

Profiling

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