Details

Time bar (total: 4.7s)

sample52.0ms

Algorithm
intervals
Results
16.0ms186×body80valid
8.0ms28×body2560valid
6.0ms256×pre80overflowed
6.0ms27×body1280valid
2.0ms12×body640valid
0.0ms2×body160valid
0.0ms1×body320valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize12.0ms

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))
0.5b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×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×flip3-+ sqrt-div flip-+
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 → 79
Calls
4 calls:
13.0ms
(/ 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)))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
35.0ms
(+ (* (* 4.0 p) p) (* x x))
74.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify154.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune259.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 4.0 p) p) (* x x))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.2b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp
7×pow1
5×unswap-sqr
4×flip3-+ sqrt-div prod-exp flip-+
3×associate-*l*
2×+-commutative div-exp sum-log associate-/r/ cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
35.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* (* 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))))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0387817
11913734
25002700

prune292.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.7b
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
30×add-sqr-sqrt *-un-lft-identity
28×add-cube-cbrt
27×times-frac
9×associate-/r*
8×sqrt-div
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×flip3-+ flip-+
3×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 → 95
Calls
4 calls:
14.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
132.0ms
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
77.0ms
(+ 1.0 (/ (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
54.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify126.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03341259
110701153
238901119
350021119

prune371.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 15.2b

localize28.0ms

Local error

Found 4 expressions with local error:

10.7b
(+ 1.0 (/ (* (/ (cbrt x) (/ (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt x))) (/ (cbrt x) (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
15.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity sqrt-prod
7×pow1 add-cube-cbrt
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 distribute-lft-out
Counts
4 → 57
Calls
4 calls:
24.0ms
(+ 1.0 (/ (* (/ (cbrt x) (/ (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt x))) (/ (cbrt x) (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(+ 1.0 (/ (* (/ (cbrt x) (/ (fabs (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (cbrt x))) (/ (cbrt x) (sqrt (cbrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))) (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))))
51.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify136.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (126.0ms)

IterNodesCost
0261968
1891894
24375894
35002891

prune355.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 15.2b

regimes157.0ms

Accuracy

0% (1.1b remaining)

Error of 14.1b against oracle of 13.0b and baseline of 14.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03246
13246

end0.0ms

sample1.2s

Algorithm
intervals
Results
400.0ms6041×body80valid
229.0ms827×body2560valid
173.0ms8000×pre80overflowed
138.0ms587×body1280valid
61.0ms326×body640valid
20.0ms138×body320valid
8.0ms81×body160valid