Details

Time bar (total: 3.1s)

sample31.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 47.04159%

Results
8.0ms57×body640valid
7.0ms30×body320valid
6.0ms151×body80valid
2.0ms9×body1280valid
1.0ms9×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: 7.2b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(/ 1.0 (+ x 1.0))
1.6b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite62.0ms

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:
19.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms
(/ 1.0 (- x 1.0))
5.0ms
(/ 1.0 (+ x 1.0))
30.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series17.0ms

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

simplify47.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0496865
11681827
25001816

prune176.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1242126
Fresh000
Picked011
Done000
Total1243127

Merged error: 0.2b

Counts
127 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.2b
(* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))))
6.5b
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
17.2b
(/ (* (+ (/ 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)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
19×flip3-+ flip-+
18×add-exp-log frac-times add-cbrt-cube
11×associate-/r/ associate-/l/
10×frac-add
9×times-frac associate-*l/
8×add-sqr-sqrt distribute-lft-out add-log-exp
6×pow1 add-cube-cbrt associate-*r/ associate-*l*
5×prod-exp cbrt-unprod
4×cbrt-undiv associate-+r+ flip3-- div-exp flip--
3×distribute-rgt-in distribute-lft-in associate-*r*
2×+-commutative sub-neg sum-log
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 107
Calls
4 calls:
16.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
23.0ms
(* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))))
7.0ms
(+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0)))
42.0ms
(/ (* (+ (/ 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)))

series41.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ (/ 1.0 (+ x 1.0)) (/ 2.0 x))
16.0ms
(* (+ (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (+ 1.0 (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- x 1.0))))
8.0ms
(+ 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)))

simplify119.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07682120
143131693
250011683

prune280.0ms

Filtered
92 candidates to 119 candidates (-29.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1181119
Fresh011
Picked011
Done011
Total1184122

Merged error: 0.0b

Counts
122 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow x 3))
0.7b
(/ 1 (pow x 2))
2.6b
(/ (* (+ (/ 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)))
9.2b
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

rewrite182.0ms

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))
8.0ms
(/ 1 (pow x 2))
102.0ms
(/ (* (+ (/ 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)))
56.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

series15.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ 1 (pow x 3))
2.0ms
(/ 1 (pow x 2))
7.0ms
(/ (* (+ (/ 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)))

simplify54.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011502765
150012242

prune571.0ms

Filtered
122 candidates to 240 candidates (-96.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2382240
Fresh011
Picked101
Done022
Total2395244

Merged error: 0b

Counts
244 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow x 4))
0.3b
(/ 1 (pow x 3))
0.7b
(/ 1 (pow x 2))
9.2b
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
98×times-frac
93×*-un-lft-identity
85×add-sqr-sqrt
65×add-cube-cbrt
38×unpow-prod-down
31×add-exp-log
27×associate-/r*
18×div-exp
16×div-inv
14×cube-prod sqr-pow
13×distribute-lft-out--
11×distribute-lft-out
10×add-cbrt-cube
9×pow-to-exp rec-exp 1-exp pow-exp associate-/l* add-log-exp difference-of-squares
4×pow1 cube-mult unpow3 unpow2
3×cbrt-undiv pow-flip frac-2neg clear-num frac-sub inv-pow
2×diff-log
1×sub-neg flip3-- flip3-+ frac-add associate--l+ sum-log flip-- flip-+
Counts
4 → 222
Calls
4 calls:
5.0ms
(/ 1 (pow x 4))
5.0ms
(/ 1 (pow x 3))
5.0ms
(/ 1 (pow x 2))
56.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

series11.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ 1 (pow x 4))
3.0ms
(/ 1 (pow x 3))
2.0ms
(/ 1 (pow x 2))
3.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 4))) (/ 1 (pow x 3)))

simplify94.0ms

Algorithm
egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
05851338
129201073
250011048

prune223.0ms

Filtered
86 candidates to 234 candidates (-172.1%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New2340234
Fresh022
Picked011
Done022
Total2345239

Merged error: 0b

Counts
239 → 5

regimes90.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 9.9b

bsearch31.0ms

Steps
ItersRangePoint
10
0.00031157581617804726
8049369413.927381
142.4307990484766
9
-4028446.8497976456
-0.0065084385888304844
-1792.4066915638655

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05028
15228
25228

end0.0ms

sample790.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 47.04159%

Results
270.0ms1921×body640valid
158.0ms4181×body80valid
104.0ms573×body1280valid
89.0ms855×body320valid
33.0ms472×body160valid

Profiling

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