Details

Time bar (total: 3.4s)

analyze780.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%48.6%51.4%0
0%48.6%51.4%1
24.3%24.3%51.4%2
24.3%24.3%51.4%3
30.4%18.2%51.4%4
30.4%18.2%51.4%5
33.4%15.2%51.4%6
33.4%15.2%51.4%7
34.6%14.1%51.4%8
34.8%13.9%51.4%9
35.4%13.2%51.4%10
35.6%13.1%51.4%11
35.9%12.7%51.4%12
36%12.6%51.4%13
36.2%12.4%51.4%14

sample44.0ms

Algorithm
intervals
Results
10.0ms192×body80valid
9.0ms27×body2560valid
7.0ms256×pre80true
6.0ms23×body1280valid
2.0ms9×body640valid
1.0ms4×body320valid
0.0ms1×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03817
13817

prune6.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 14.5b

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))))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
17.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

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))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series36.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
11.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify31.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
049941385
149941385

prune195.0ms

Filtered
71 candidates to 91 candidates (-28.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New791291
Fresh000
Picked101
Done000
Total801292

Merged error: 14.3b

Counts
92 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
0.2b
(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
3.9b
(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
17.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×sqrt-div associate-/r* add-log-exp
5×unswap-sqr
4×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip associate-*l* associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 122
Calls
4 calls:
8.0ms
(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
14.0ms
(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
5.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

series39.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))
11.0ms
(* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
12.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
7.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify63.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049321899
149321899

prune210.0ms

Filtered
81 candidates to 134 candidates (-65.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1313134
Fresh3811
Picked101
Done000
Total13511146

Merged error: 14.3b

Counts
146 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
17.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
17.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
17.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-+ add-cbrt-cube flip-+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×+-commutative sum-log
Counts
4 → 56
Calls
4 calls:
4.0ms
(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
6.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

series38.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
7.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
9.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify29.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
05159810

prune201.0ms

Filtered
57 candidates to 68 candidates (-19.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New68068
Fresh01010
Picked011
Done000
Total681179

Merged error: 14.3b

Counts
79 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.5b
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
17.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
17.8b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
39×sqrt-prod
27×associate-*r*
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
11×pow1
10×sqrt-div
9×add-exp-log add-cbrt-cube
6×add-log-exp
4×flip3-+ flip-+
3×associate-*r/ pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×+-commutative frac-times associate-*l* associate-*l/ sum-log *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
25.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
3.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
6.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x))))))
12.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
7.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
9.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
049661616
149661616

prune189.0ms

Filtered
72 candidates to 98 candidates (-36.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New97198
Fresh189
Picked011
Done011
Total9811109

Merged error: 14.3b

Counts
109 → 11

regimes138.0ms

Accuracy

0% (0.8b remaining)

Error of 13.2b against oracle of 12.4b and baseline of 13.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02649
12649

end0.0ms

sample1.1s

Algorithm
intervals
Results
319.0ms6096×body80valid
264.0ms830×body2560valid
157.0ms592×body1280valid
140.0ms8000×pre80true
57.0ms283×body640valid
19.0ms124×body320valid
8.0ms75×body160valid

Profiling

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