Details

Time bar (total: 5.9s)

sample1.3s

Algorithm
intervals
sampling

Space saved by range analysis: 51.36237%

Space saved by search: 51.36237%

Guaranteed chance to sample good point: 0%

Results
13.0ms197×body80valid
10.0ms22×body2560valid
5.0ms256×pre80true
5.0ms17×body1280valid
2.0ms9×body640valid
2.0ms9×body320valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.9b

Counts
2 → 1

localize18.0ms

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))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite35.0ms

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))))
16.0ms
(+ 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))
9.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify144.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278822
11014772
24232757
35001757

prune205.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New811091
Fresh000
Picked101
Done000
Total821092

Merged error: 12.6b

Counts
92 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.5b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(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:
30.0ms
(/ 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)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03841288
113071207
250011169

prune291.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1024106
Fresh279
Picked101
Done000
Total10511116

Merged error: 12.6b

Counts
116 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

8.5b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (pow (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.8b
(cbrt (pow (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
72×cbrt-prod
60×sqrt-prod
54×times-frac
47×add-sqr-sqrt
45×add-cube-cbrt *-un-lft-identity
33×unpow-prod-down cube-prod
12×sqrt-div
6×pow1 add-log-exp
5×flip3-+ flip-+
4×add-exp-log associate-/r/ add-cbrt-cube
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
1×+-commutative cube-div cube-mult cbrt-div pow1/3 unpow3 sum-log rem-cbrt-cube sqr-pow
Counts
4 → 123
Calls
4 calls:
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (pow (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(cbrt (pow (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))

series64.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt (pow (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
34.0ms
(cbrt (pow (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))

simplify75.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07441942
130471818
250011729

prune299.0ms

Filtered
71 candidates to 135 candidates (-90.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1314135
Fresh2810
Picked101
Done000
Total13412146

Merged error: 12.6b

Counts
146 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.5b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.6b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.6b
(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:
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)))

series62.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03841288
113071207
250011169

prune295.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1024106
Fresh2911
Picked101
Done000
Total10513118

Merged error: 12.6b

Counts
118 → 13

regimes384.0ms

Accuracy

0% (1.5b remaining)

Error of 14.3b against oracle of 12.7b and baseline of 14.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03435
13435

end0.0ms

sample2.4s

Algorithm
intervals
sampling

Space saved by range analysis: 51.36237%

Space saved by search: 51.36237%

Guaranteed chance to sample good point: 0%

Results
310.0ms6080×body80valid
248.0ms798×body2560valid
165.0ms626×body1280valid
141.0ms8000×pre80true
59.0ms278×body640valid
22.0ms147×body320valid
7.0ms71×body160valid

Profiling

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