Details

Time bar (total: 2.8s)

sample48.0ms

Algorithm
intervals
Results
10.0ms194×body80valid
7.0ms11×body640valid
7.0ms23×body2560valid
5.0ms19×body1280valid
4.0ms256×pre80true
1.0ms6×body320valid
0.0ms3×body160valid

simplify4.0ms

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: 13.1b

Counts
2 → 1

localize11.0ms

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))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.9b
(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))))
11.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
9.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify65.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049131479
149131479

prune196.0ms

Filtered
74 candidates to 93 candidates (-25.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New831093
Fresh000
Picked101
Done000
Total841094

Merged error: 12.8b

Counts
94 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

3.9b
(+ 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)))))))
15.9b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite20.0ms

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:
3.0ms
(+ 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)))))))
5.0ms
(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)))

series37.0ms

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)))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04976810
14976810

prune211.0ms

Filtered
58 candidates to 68 candidates (-17.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New66268
Fresh099
Picked101
Done000
Total671178

Merged error: 12.8b

Counts
78 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* p p))
0.3b
(* (sqrt 0.5) (sqrt (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
15.9b
(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×pow1 *-un-lft-identity sqrt-prod
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt
9×associate-*l*
8×associate-*r*
6×pow-prod-down add-log-exp
5×unswap-sqr
4×sqrt-div prod-exp cbrt-unprod
3×sqrt-pow1 flip3-+ pow1/2 flip-+
2×associate-*r/ *-commutative distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-unprod sum-log
Counts
4 → 79
Calls
4 calls:
5.0ms
(* 4.0 (* p p))
16.0ms
(* (sqrt 0.5) (sqrt (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))))
7.0ms
(sqrt (+ (* 4.0 (* p p)) (* x x)))

series54.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 4.0 (* p p))
32.0ms
(* (sqrt 0.5) (sqrt (+ 1.0 (/ 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)))

simplify52.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049551256
149551256

prune172.0ms

Filtered
64 candidates to 91 candidates (-42.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New91091
Fresh01010
Picked011
Done000
Total9111102

Merged error: 12.8b

Counts
102 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

15.9b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b
(sqrt (+ (* 4.0 (* p p)) (* x x)))
16.7b
(cbrt (+ (* 4.0 (* p p)) (* x x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 58
Calls
4 calls:
7.0ms
(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)))
5.0ms
(cbrt (+ (* 4.0 (* p p)) (* x x)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(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)))
21.0ms
(cbrt (+ (* 4.0 (* p p)) (* x x)))

simplify33.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
04933862
14933862

prune229.0ms

Filtered
58 candidates to 70 candidates (-20.7%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New70070
Fresh099
Picked011
Done011
Total701181

Merged error: 12.8b

Counts
81 → 11

regimes146.0ms

Accuracy

0% (0.5b remaining)

Error of 13.5b against oracle of 13.0b and baseline of 13.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01918
11918

end0.0ms

sample1.2s

Algorithm
intervals
Results
316.0ms6034×body80valid
259.0ms819×body2560valid
152.0ms599×body1280valid
133.0ms8000×pre80true
63.0ms321×body640valid
23.0ms157×body320valid
7.0ms70×body160valid

Profiling

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