Details

Time bar (total: 3.9s)

sample33.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 47.04159%

Results
12.0ms57×body1280valid
5.0ms151×body80valid
4.0ms28×body640valid
1.0ms14×body320valid
0.0ms6×body160valid

simplify22.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.8b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
40×times-frac
35×add-sqr-sqrt
18×distribute-lft-out--
14×distribute-lft-out
13×add-cube-cbrt
9×difference-of-squares
5×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-+ div-inv
Counts
2 → 71
Calls
2 calls:
7.0ms
(/ (+ x 1.0) (- x 1.0))
29.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series10.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(/ (+ x 1.0) (- x 1.0))
7.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify149.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0317591
11003565
24494559
35003559

prune122.0ms

Filtered
50 candidates to 77 candidates (-54.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New73477
Fresh000
Picked101
Done000
Total74478

Merged error: 0.1b

Counts
78 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
0.0b
(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b
(pow (/ x (+ x 1.0)) 3)
1.8b
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
1102×*-un-lft-identity
735×times-frac
560×add-sqr-sqrt
344×unpow-prod-down cube-prod
273×distribute-lft-out--
188×difference-of-squares
176×distribute-lft-out
124×add-cube-cbrt
77×associate-/l*
62×sqr-pow
31×associate-/r/
27×frac-add
16×frac-times associate-*r/
12×add-exp-log add-cbrt-cube
10×associate-*l/
9×flip3-+ flip-+
6×pow1 cube-div pow-unpow add-log-exp
5×difference-cubes div-inv
4×flip3-- pow-exp flip-- rem-cube-cbrt
3×cbrt-undiv div-exp associate-/r* associate-/l/
2×cube-mult pow-to-exp pow-pow unpow3 frac-sub
1×sub-neg frac-2neg diff-log div-sub clear-num
Counts
4 → 565
Calls
4 calls:
153.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
10.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
7.0ms
(pow (/ x (+ x 1.0)) 3)
102.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series57.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3)) (+ (* (/ (+ x 1.0) (- x 1.0)) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))) (* (/ x (+ x 1.0)) (/ x (+ x 1.0)))))
3.0ms
(pow (/ (+ x 1.0) (- x 1.0)) 3)
3.0ms
(pow (/ x (+ x 1.0)) 3)
15.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify183.0ms

Algorithm
egg-herbie
Counts
577 → 577
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0167717362
1500117123

prune1.3s

Filtered
203 candidates to 577 candidates (-184.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New5761577
Fresh033
Picked011
Done000
Total5765581

Merged error: 0.1b

Counts
581 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(* (sqrt (+ x 1.0)) (/ (sqrt (+ x 1.0)) (- x 1.0)))
0.1b
(/ (sqrt (+ x 1.0)) (- x 1.0))
5.9b
(- (/ x (+ x 1.0)) (* (sqrt (+ x 1.0)) (/ (sqrt (+ x 1.0)) (- x 1.0))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
92×add-sqr-sqrt
74×times-frac
57×sqrt-prod
45×add-cube-cbrt
41×associate-*r*
15×distribute-lft-out-- difference-of-squares
13×distribute-lft-out
12×sqrt-div
11×add-exp-log add-cbrt-cube
7×pow1 associate-*l* associate-/l*
6×flip3-+ flip-+ add-log-exp unswap-sqr
5×associate-/r* frac-sub
4×frac-times associate-*l/ associate-/r/
3×flip3-- flip--
2×cbrt-undiv associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative
Counts
4 → 168
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
20.0ms
(* (sqrt (+ x 1.0)) (/ (sqrt (+ x 1.0)) (- x 1.0)))
8.0ms
(/ (sqrt (+ x 1.0)) (- x 1.0))
9.0ms
(- (/ x (+ x 1.0)) (* (sqrt (+ x 1.0)) (/ (sqrt (+ x 1.0)) (- x 1.0))))

series23.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
3.0ms
(* (sqrt (+ x 1.0)) (/ (sqrt (+ x 1.0)) (- x 1.0)))
8.0ms
(/ (sqrt (+ x 1.0)) (- x 1.0))
8.0ms
(- (/ x (+ x 1.0)) (* (sqrt (+ x 1.0)) (/ (sqrt (+ x 1.0)) (- x 1.0))))

simplify83.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06891690
128431547
250011483

prune485.0ms

Filtered
112 candidates to 180 candidates (-60.7%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1800180
Fresh033
Picked011
Done011
Total1805185

Merged error: 0.1b

Counts
185 → 5

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(* x (+ 3.0 (* x 1.0)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
2×associate-*r/
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ add-log-exp unswap-sqr
Counts
1 → 22
Calls
1 calls:
5.0ms
(* x (+ 3.0 (* x 1.0)))

series6.0ms

Counts
1 → 3
Calls
1 calls:
6.0ms
(* x (+ 3.0 (* x 1.0)))

simplify103.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0144117
1680103
23770103
35002103

prune24.0ms

Filtered
16 candidates to 25 candidates (-56.3%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New25025
Fresh022
Picked011
Done022
Total25530

Merged error: 0.1b

Counts
30 → 5

regimes49.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 29.1b

bsearch30.0ms

Steps
ItersRangePoint
10
0.00031157581617804726
8049369413.927381
13481.081521407143
9
-4028446.8497976456
-0.0065084385888304844
-1.0084175906116333

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03919
13919

end0.0ms

sample757.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 47.04159%

Results
260.0ms1680×body1280valid
151.0ms1259×body640valid
129.0ms4126×body80valid
57.0ms642×body320valid
18.0ms293×body160valid

Profiling

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