Details

Time bar (total: 4.5s)

sample43.0ms

Algorithm
intervals
Results
10.0ms189×body80valid
8.0ms26×body2560valid
5.0ms20×body1280valid
5.0ms256×pre80true
3.0ms15×body640valid
1.0ms4×body320valid
0.0ms2×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune2.0ms

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: 14.8b

Counts
2 → 1

localize14.0ms

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
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
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 distribute-lft-out
Counts
4 → 81
Calls
4 calls:
12.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 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)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
281.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
51.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify76.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0280888
1816840
22500828
35001827

prune242.0ms

Filtered
93 candidates to 71 candidates (76.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New811293
Fresh000
Picked101
Done000
Total821294

Merged error: 14.6b

Counts
94 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.4b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
23×add-sqr-sqrt
22×add-cube-cbrt
18×times-frac
15×sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log-pow
4×log-prod exp-prod sqrt-div
3×flip3-+ flip-+ associate-/l*
2×associate-/r/ distribute-lft-out
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp exp-sum clear-num sum-log div-inv
Counts
4 → 85
Calls
4 calls:
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
77.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify73.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0269900
1805835
22267823
35002822

prune273.0ms

Filtered
97 candidates to 72 candidates (74.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New95297
Fresh01111
Picked101
Done000
Total9613109

Merged error: 14.6b

Counts
109 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.1b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
10×pow1
9×add-cbrt-cube
6×sqrt-div add-log-exp
5×unswap-sqr
4×flip3-+ prod-exp flip-+
3×sqrt-pow1 associate-*r/ associate-*l*
2×pow1/2 div-exp pow-prod-down associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp 1-exp sum-log un-div-inv *-commutative div-inv
Counts
4 → 88
Calls
4 calls:
4.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 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)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
52.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0390900
11684818
25001784

prune233.0ms

Filtered
100 candidates to 71 candidates (71.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New964100
Fresh6612
Picked101
Done000
Total10310113

Merged error: 14.6b

Counts
113 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.1b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
23×*-un-lft-identity
22×times-frac
21×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×exp-prod sqrt-div prod-exp
3×log-prod flip3-+ associate-*l* flip-+
2×div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ rem-log-exp pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 91
Calls
4 calls:
15.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* 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)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
283.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
71.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0399963
11665851
25002816

prune261.0ms

Filtered
103 candidates to 76 candidates (73.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New958103
Fresh369
Picked101
Done000
Total9914113

Merged error: 14.6b

Counts
113 → 14

regimes182.0ms

Accuracy

0% (0.6b remaining)

Error of 13.6b against oracle of 13.0b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02814
12814

end0.0ms

sample1.1s

Algorithm
intervals
Results
299.0ms6019×body80valid
252.0ms827×body2560valid
150.0ms593×body1280valid
144.0ms8000×pre80true
60.0ms311×body640valid
24.0ms167×body320valid
8.0ms83×body160valid

Profiling

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