Details

Time bar (total: 2.7s)

sample36.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.993896%

Results
8.0ms54×body1280valid
5.0ms142×body80valid
4.0ms35×body640valid
1.0ms16×body320valid
1.0ms9×body160valid

simplify18.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.3b

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)))

rewrite46.0ms

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))
30.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series12.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(/ x (+ x 1.0))
3.0ms
(/ (+ x 1.0) (- x 1.0))
7.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0392760
11379726
25001716

prune187.0ms

Filtered
76 candidates to 113 candidates (-48.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1076113
Fresh000
Picked101
Done000
Total1086114

Merged error: 0.1b

Counts
114 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
329×*-un-lft-identity
212×times-frac
173×add-sqr-sqrt
99×add-cube-cbrt
72×swap-sqr
62×distribute-lft-out
44×associate-*r* associate-*l*
37×distribute-lft-out--
30×add-exp-log add-cbrt-cube
26×difference-of-squares
18×pow1 associate-/r/
9×cbrt-undiv div-exp frac-sub div-inv
8×frac-times associate-*r/ associate-*l/ prod-exp cbrt-unprod unswap-sqr
6×flip3-- flip-- add-log-exp
5×flip3-+ associate-/r* flip-+
4×associate-/l*
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up associate-/l/
1×sub-neg frac-2neg diff-log clear-num
Counts
4 → 283
Calls
4 calls:
7.0ms
(/ (+ x 1.0) (- x 1.0))
18.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
24.0ms
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
11.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series19.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (+ x 1.0) (- x 1.0))
3.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.0ms
(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
11.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify62.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011252873
150012657

prune544.0ms

Filtered
160 candidates to 295 candidates (-84.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2932295
Fresh145
Picked011
Done000
Total2947301

Merged error: 0.0b

Counts
301 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ 1 (- x 1.0))
0.1b
(* (+ x 1.0) (/ 1 (- x 1.0)))
5.3b
(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
54×add-sqr-sqrt
44×times-frac
33×add-cube-cbrt
21×associate-*r*
19×add-exp-log
13×add-cbrt-cube
9×associate-/r*
7×pow1 distribute-lft-out-- difference-of-squares
6×associate-/r/ frac-sub associate-/l* add-log-exp
5×flip3-+ div-exp flip-+ distribute-lft-out
4×frac-times associate-*l* associate-*l/ prod-exp
3×cbrt-undiv flip3-- flip-- div-inv unswap-sqr
2×rec-exp frac-2neg 1-exp associate-*r/ clear-num un-div-inv cbrt-unprod
1×sub-neg pow-flip diff-log pow-prod-down *-commutative inv-pow
Counts
4 → 141
Calls
4 calls:
4.0ms
(/ x (+ x 1.0))
5.0ms
(/ 1 (- x 1.0))
14.0ms
(* (+ x 1.0) (/ 1 (- x 1.0)))
9.0ms
(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series14.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ x (+ x 1.0))
2.0ms
(/ 1 (- x 1.0))
3.0ms
(* (+ x 1.0) (/ 1 (- x 1.0)))
7.0ms
(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify73.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0576948
12837860
25001818

prune176.0ms

Filtered
98 candidates to 153 candidates (-56.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1521153
Fresh055
Picked011
Done011
Total1528160

Merged error: 0.0b

Counts
160 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.2b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
16.5b
(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
40×cbrt-div
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
20×frac-times flip3-+ flip-+
17×frac-sub
14×add-cube-cbrt associate-*l/
11×pow1
9×swap-sqr
8×pow1/3 distribute-lft-out
7×associate-*r/ associate-*r* associate-*l*
6×add-exp-log add-log-exp
4×add-cbrt-cube unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log prod-exp *-commutative flip-- cbrt-unprod
Counts
4 → 110
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
9.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
11.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

series25.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ x 1.0))
6.0ms
(cbrt (+ x 1.0))
6.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
7.0ms
(- (/ x (+ x 1.0)) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ (cbrt (+ x 1.0)) (- x 1.0))))

simplify76.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06851563
124361476
250011428

prune241.0ms

Filtered
81 candidates to 122 candidates (-50.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1211122
Fresh145
Picked101
Done022
Total1237130

Merged error: 0.0b

Counts
130 → 7

regimes58.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch46.0ms

Steps
ItersRangePoint
9
10.561152600940856
114979947.1237121
13297.252132290163
7
-14993.128773526949
-80.64400264069371
-13297.41441786825

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03515
13515

end0.0ms

sample800.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 99.993896%

Results
281.0ms1779×body1280valid
164.0ms1276×body640valid
135.0ms4082×body80valid
53.0ms578×body320valid
20.0ms285×body160valid

Profiling

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