Details

Time bar (total: 3.4s)

sample122.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 63.231787%

Results
21.0ms215×body80valid
9.0ms18×body2560valid
6.0ms256×pre80true
6.0ms14×body1280valid
1.0ms4×body640valid
0.0ms2×body320valid
0.0ms3×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 8.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
5.0ms
(+ (* (* 4.0 p) p) (* x x))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series35.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
11.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify141.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0278822
11014772
24232757
35001757

prune262.0ms

Filtered
67 candidates to 91 candidates (-35.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New82991
Fresh000
Picked101
Done000
Total83992

Merged error: 8.5b

Counts
92 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.6b
(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
2.5b
(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
17.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
36×add-sqr-sqrt times-frac
35×add-cube-cbrt
26×log-pow
24×exp-prod sqrt-prod
7×pow1
6×add-exp-log log-prod sqrt-div associate-/r* add-cbrt-cube
5×add-log-exp
4×flip3-+ associate-/r/ flip-+
3×associate-+r+ associate-/l*
2×div-inv distribute-lft-out
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log
Counts
4 → 108
Calls
4 calls:
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms
(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms
(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series39.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms
(+ 1.0 (log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms
(log (exp (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify68.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
03081094
18031021
222681001
35002998

prune233.0ms

Filtered
88 candidates to 120 candidates (-36.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1200120
Fresh088
Picked011
Done000
Total1209129

Merged error: 8.5b

Counts
129 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 94
Calls
4 calls:
11.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series55.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03841288
113071207
250011169

prune290.0ms

Filtered
77 candidates to 106 candidates (-37.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1024106
Fresh167
Picked101
Done101
Total10510115

Merged error: 8.5b

Counts
115 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
17.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 94
Calls
4 calls:
9.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03841288
113071207
250011169

prune288.0ms

Filtered
77 candidates to 106 candidates (-37.7%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1006106
Fresh369
Picked011
Done000
Total10313116

Merged error: 8.5b

Counts
116 → 13

regimes274.0ms

Accuracy

0% (1.1b remaining)

Error of 14.1b against oracle of 13.0b and baseline of 14.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02920
12920

end0.0ms

sample1.3s

Algorithm
intervals
sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 63.231787%

Results
328.0ms6047×body80valid
270.0ms808×body2560valid
157.0ms600×body1280valid
149.0ms8000×pre80true
64.0ms311×body640valid
24.0ms155×body320valid
8.0ms79×body160valid

Profiling

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