Details

Time bar (total: 4.2s)

sample36.0ms

Algorithm
intervals
Results
7.0ms31×body2560valid
6.0ms172×body80valid
5.0ms26×body1280valid
4.0ms256×pre80true
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify9.0ms

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: 17.3b

localize16.0ms

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))))
1.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

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:
6.0ms
(+ (* (* 4.0 p) p) (* x x))
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (* (* 4.0 p) p) (* x x))
53.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify150.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune278.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.9b

localize14.0ms

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)))))
4.8b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite59.0ms

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))
37.0ms
(* 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)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* (* 4.0 p) p) (* x x))
58.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
74.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0387817
11913734
25002700

prune292.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.6b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.6b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite157.0ms

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:
13.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
28.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
104.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
72.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
79.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify67.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0269900
1805835
22267823
35002822

prune336.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.9b

localize32.0ms

Local error

Found 4 expressions with local error:

3.3b
(* (/ 1 (+ (* (* 4.0 p) p) (* x x))) (pow x 2))
4.7b
(+ (pow 1.0 3) (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.9b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
27×add-exp-log
21×*-un-lft-identity
17×times-frac
15×add-cube-cbrt associate-*l*
12×prod-exp unswap-sqr
9×add-cbrt-cube
8×associate-*r*
6×pow1 unpow-prod-down div-exp sqrt-prod add-log-exp
4×pow-to-exp flip3-+ sqrt-div pow-exp flip-+ unpow2 sqr-pow
3×rec-exp 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative associate-*l/ sum-log sum-cubes *-commutative div-inv distribute-lft-out
Counts
4 → 101
Calls
4 calls:
34.0ms
(* (/ 1 (+ (* (* 4.0 p) p) (* x x))) (pow x 2))
12.0ms
(+ (pow 1.0 3) (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* (/ 1 (+ (* (* 4.0 p) p) (* x x))) (pow x 2))
82.0ms
(+ (pow 1.0 3) (pow (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))) 3))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify93.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
04431056
12050935
25001911

prune465.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.9b

regimes215.0ms

Accuracy

0% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 13.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05054
15054

end0.0ms

sample822.0ms

Algorithm
intervals
Results
213.0ms6084×body80valid
175.0ms798×body2560valid
109.0ms608×body1280valid
106.0ms8000×pre80true
41.0ms298×body640valid
18.0ms130×body320valid
6.0ms82×body160valid