Details

Time bar (total: 3.4s)

sample38.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 50%

Guaranteed chance to sample good point: 100%

Results
15.0ms69×body640valid
7.0ms38×body1280valid
5.0ms123×body80valid
3.0ms23×body320valid
0.0ms3×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 20.4b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
1.3b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
31.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series33.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ 1.0 (sqrt x))
15.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
06101151
123011116
250011086

prune264.0ms

Filtered
100 candidates to 145 candidates (-45.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New13312145
Fresh000
Picked101
Done000
Total13412146

Merged error: 20.0b

Counts
146 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.3b
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.6b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
1.3b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
234×times-frac
223×add-sqr-sqrt
181×*-un-lft-identity
139×add-cube-cbrt
132×sqrt-prod
67×swap-sqr
49×associate-*r* associate-*l*
30×add-exp-log add-cbrt-cube
18×pow1 distribute-lft-out unswap-sqr
9×cbrt-undiv div-exp frac-sub div-inv
8×frac-times sqrt-div associate-*r/ associate-*l/ prod-exp associate-/r/ cbrt-unprod
6×associate-/r* add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×sub-neg flip3-- frac-2neg diff-log clear-num flip-- difference-of-squares
Counts
4 → 292
Calls
4 calls:
4.0ms
(/ 1.0 (sqrt x))
25.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
19.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
9.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series19.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1.0 (sqrt x))
2.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
3.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
6.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011933186
150022825

prune696.0ms

Filtered
171 candidates to 304 candidates (-77.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2986304
Fresh8311
Picked101
Done000
Total3079316

Merged error: 5.5b

Counts
316 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b
(/ 1.0 (sqrt x))
1.0b
(- (+ x 1.0) x)

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity
296×times-frac
124×sqrt-prod
117×distribute-lft-out
108×add-sqr-sqrt
106×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*l/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
9×prod-exp cbrt-unprod add-log-exp
4×pow1
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 248
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
50.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
4.0ms
(/ 1.0 (sqrt x))
6.0ms
(- (+ x 1.0) x)

series50.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
35.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
8.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (+ x 1.0) x)

simplify69.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014944115
150013785

prune463.0ms

Filtered
144 candidates to 260 candidates (-80.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2564260
Fresh448
Picked101
Done000
Total2618269

Merged error: 5.5b

Counts
269 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
1.0b
(- (+ x 1.0) x)
5.3b
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* (+ x 1.0) x))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
57×times-frac
44×add-sqr-sqrt
42×add-cube-cbrt
40×sqrt-prod
19×distribute-lft-out
14×associate-*l*
13×add-exp-log associate-/r* add-cbrt-cube
11×associate-*l/
9×pow1 add-log-exp
8×flip3-+ flip-+
6×frac-times associate-/l*
4×div-inv
3×pow-prod-down frac-add prod-exp cbrt-unprod
2×cbrt-undiv frac-2neg sqrt-div diff-log associate-*r/ div-exp clear-num associate-/r/ distribute-lft-out--
1×sub-neg flip3-- associate-*r* associate--l+ sum-log *-commutative flip-- difference-of-squares
Counts
4 → 141
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
6.0ms
(- (+ x 1.0) x)
39.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* (+ x 1.0) x))

series32.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (+ x 1.0) x)
18.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* (+ x 1.0) x))

simplify93.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08061277
138041193
250021165

prune254.0ms

Filtered
105 candidates to 153 candidates (-45.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1521153
Fresh077
Picked101
Done000
Total1538161

Merged error: 5.4b

Counts
161 → 8

regimes49.0ms

Accuracy

0% (0.2b remaining)

Error of 5.7b against oracle of 5.5b and baseline of 5.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01812
11812

end0.0ms

sample893.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 50%

Guaranteed chance to sample good point: 100%

Results
284.0ms1846×body640valid
220.0ms1150×body1280valid
167.0ms4137×body80valid
63.0ms572×body320valid
22.0ms295×body160valid

Profiling

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