Details

Time bar (total: 5.2s)

sample32.0ms

Algorithm
intervals
Results
7.0ms201×body80valid
5.0ms22×body2560valid
3.0ms256×pre80true
3.0ms18×body1280valid
2.0ms11×body640valid
0.0ms4×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.1b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×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×expm1-log1p-u fma-def flip3-+ sqrt-div flip-+ log1p-expm1-u
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 → 91
Calls
4 calls:
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms
(+ (* (* 4.0 p) p) (* x x))
29.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
33.0ms
(+ (* (* 4.0 p) p) (* x x))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify149.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (140.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune314.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.1b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.1b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1
5×log-pow
4×add-exp-log expm1-log1p-u log-prod exp-prod fma-def add-cbrt-cube log1p-expm1-u
3×flip3-+ sqrt-prod flip-+
2×+-commutative sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp exp-sum
Counts
4 → 67
Calls
4 calls:
8.0ms
(+ (* (* 4.0 p) p) (* x x))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
99.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* (* 4.0 p) p) (* x x))
80.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify89.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0249589
1926533
23159528
35001524

prune317.0ms

Filtered
79 candidates to 65 candidates (82.3%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.4b
(/ (pow x 2) (fma (* 4.0 p) p (* x x)))
14.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
89×*-un-lft-identity
87×add-cube-cbrt
80×times-frac
72×prod-diff
34×sqrt-prod
12×unpow-prod-down
10×sqrt-div
9×add-exp-log
8×associate-/l*
6×pow1 associate-/r/ add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u div-inv unpow2 sqr-pow
3×fma-neg div-exp associate-/r* difference-of-squares
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log pow-exp clear-num flip-- distribute-lft-out--
Counts
4 → 178
Calls
4 calls:
33.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.0ms
(/ (pow x 2) (fma (* 4.0 p) p (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(/ (pow x 2) (fma (* 4.0 p) p (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify93.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
07604872
128763417
250023214

prune803.0ms

Filtered
190 candidates to 105 candidates (55.3%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×sqrt-div
4×add-exp-log cbrt-prod expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3 distribute-lft-out
Counts
4 → 67
Calls
4 calls:
27.0ms
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
359.0ms
(cbrt (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify112.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0209650
1546618
21536614
34272614
45001614

prune392.0ms

Filtered
79 candidates to 71 candidates (89.9%)
Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 11.8b

regimes343.0ms

Accuracy

0% (0.2b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03127
13127

end0.0ms

sample830.0ms

Algorithm
intervals
Results
213.0ms6079×body80valid
186.0ms790×body2560valid
113.0ms622×body1280valid
102.0ms8000×pre80true
42.0ms301×body640valid
14.0ms140×body320valid
5.0ms68×body160valid