Details

Time bar (total: 4.3s)

sample34.0ms

Algorithm
intervals
Results
7.0ms193×body80valid
6.0ms31×body1280valid
4.0ms256×pre80true
4.0ms17×body2560valid
1.0ms7×body640valid
0.0ms4×body320valid
0.0ms4×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: 14.5b

localize15.0ms

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))))
1.2b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
16.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite54.0ms

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))))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(+ (* (* 4.0 p) p) (* x x))
53.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
76.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify147.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278822
11014772
24246757
35001757

prune282.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 14.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
1.2b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
1.2b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite146.0ms

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:
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
24.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
97.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
76.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify69.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 3 (60.0ms)

IterNodesCost
0269900
1805835
22267823
35002822

prune364.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.1b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
16.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
40×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
26×sqrt-prod
24×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×pow1
6×sqrt-div associate-/r* add-log-exp
5×unswap-sqr
4×flip3-+ div-exp prod-exp associate-/r/ flip-+
3×pow-flip associate-*l* associate-/l*
2×cbrt-undiv rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 122
Calls
4 calls:
13.0ms
(/ 1 (sqrt (+ (* (* 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))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))
55.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
80.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
61.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03671199
116421080
250011018

prune345.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.4b
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
16.7b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
39×sqrt-prod
27×associate-*r*
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
11×pow1
10×sqrt-div
9×add-exp-log add-cbrt-cube
6×add-log-exp
4×flip3-+ flip-+
3×associate-*r/ pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×+-commutative frac-times associate-*l* associate-*l/ sum-log *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
75.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
2.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
79.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03861299
115091123
250011062

prune349.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

regimes254.0ms

Accuracy

0% (0.2b remaining)

Error of 13.6b against oracle of 13.4b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02111
12111

end0.0ms

sample874.0ms

Algorithm
intervals
Results
214.0ms5989×body80valid
191.0ms807×body2560valid
118.0ms647×body1280valid
116.0ms8000×pre80true
53.0ms323×body640valid
17.0ms161×body320valid
5.0ms73×body160valid