Details

Time bar (total: 4.8s)

sample43.0ms

Algorithm
intervals
Results
10.0ms194×body80valid
9.0ms29×body2560valid
5.0ms20×body1280valid
5.0ms256×pre80true
2.0ms8×body640valid
1.0ms5×body320valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.1b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv
Counts
4 → 80
Calls
4 calls:
14.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(+ (* (* 4.0 p) p) (* x x))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
34.0ms
(+ (* (* 4.0 p) p) (* x x))
63.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify161.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295847
11045801
24347787
35003787

prune254.0ms

Filtered
92 candidates to 68 candidates (73.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New821092
Fresh000
Picked101
Done000
Total831093

Merged error: 12.9b

Counts
93 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(* (sqrt 0.5) (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
30×sqrt-prod
29×*-un-lft-identity
25×add-cube-cbrt
18×times-frac
10×pow1
8×add-exp-log sqrt-div add-cbrt-cube
7×associate-*r*
6×associate-*l* associate-/r*
4×sqrt-pow1 flip3-+ pow1/2 flip-+ add-log-exp unswap-sqr
3×pow-prod-down associate-/l*
2×rem-sqrt-square associate-*r/ associate-/r/ distribute-lft-out
1×cbrt-undiv frac-2neg sqrt-unprod div-exp prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 105
Calls
4 calls:
12.0ms
(sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
17.0ms
(* (sqrt 0.5) (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series658.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
293.0ms
(* (sqrt 0.5) (sqrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify87.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
03111194
19971146
229481129
350021128

prune483.0ms

Filtered
117 candidates to 83 candidates (70.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1170117
Fresh099
Picked011
Done000
Total11710127

Merged error: 12.9b

Counts
127 → 10

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)))))
2.9b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.1b
(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))))
15.0ms
(* 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)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
58.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
62.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify55.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03671195
116491076
250011014

prune252.0ms

Filtered
134 candidates to 78 candidates (58.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1313134
Fresh268
Picked101
Done011
Total13410144

Merged error: 12.9b

Counts
144 → 10

localize16.0ms

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))))))
7.3b
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.1b
(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:
26.0ms
(* (* 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)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series244.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
76.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
03861301
115091123
250011062

prune259.0ms

Filtered
98 candidates to 72 candidates (73.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New95398
Fresh268
Picked011
Done011
Total9711108

Merged error: 12.9b

Counts
108 → 11

regimes218.0ms

Accuracy

0% (0.5b remaining)

Error of 13.7b against oracle of 13.2b and baseline of 13.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

sample1.1s

Algorithm
intervals
Results
299.0ms6007×body80valid
252.0ms828×body2560valid
153.0ms629×body1280valid
130.0ms8000×pre80true
63.0ms306×body640valid
23.0ms148×body320valid
8.0ms82×body160valid

Profiling

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