Details

Time bar (total: 5.5s)

sample57.0ms

Algorithm
intervals
Results
16.0ms191×body80valid
11.0ms26×body2560valid
7.0ms21×body1280valid
6.0ms256×pre80true
2.0ms9×body640valid
2.0ms9×body320valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

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)))))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite59.0ms

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:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
12.0ms
(/ x (sqrt (+ (* (* 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)))

series220.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(+ (* (* 4.0 p) p) (* x x))
52.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify144.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune316.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.2b
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
31×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv distribute-lft-out
Counts
4 → 106
Calls
4 calls:
13.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
115.0ms
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (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)))

series319.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
73.0ms
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify130.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
03511329
111361212
241911179
350011174

prune411.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
31×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 105
Calls
4 calls:
13.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (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)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify80.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
03591348
112631258
250011226

prune423.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.7b

localize18.0ms

Local error

Found 4 expressions with local error:

7.8b
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
16.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
17.4b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
17.4b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u cbrt-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×fma-def sqrt-prod
2×pow1/3 sqrt-div
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
4 → 64
Calls
4 calls:
65.0ms
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
9.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x))))))))
51.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
129.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
124.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify113.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03411002
11165915
24573903
35001903

prune393.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.7b

regimes153.0ms

Accuracy

0% (1.6b remaining)

Error of 14.8b against oracle of 13.2b and baseline of 14.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03027
13027

end0.0ms

sample1.5s

Algorithm
intervals
Results
502.0ms5979×body80valid
349.0ms875×body2560valid
189.0ms571×body1280valid
169.0ms8000×pre80true
86.0ms329×body640valid
35.0ms160×body320valid
12.0ms86×body160valid