Details

Time bar (total: 4.3s)

sample39.0ms

Algorithm
intervals
Results
7.0ms30×body2560valid
6.0ms182×body80valid
6.0ms256×pre80true
3.0ms23×body640valid
2.0ms14×body1280valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

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))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite140.0ms

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:
28.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
26.0ms
(+ (* (* 4.0 p) p) (* x x))
60.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
23.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
34.0ms
(+ (* (* 4.0 p) p) (* x x))
81.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
60.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify145.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (136.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune280.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.6b

localize12.0ms

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)))))
4.4b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
14×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×add-log-exp
7×pow1
5×unswap-sqr
4×expm1-log1p-u fma-def flip3-+ sqrt-div prod-exp flip-+ log1p-expm1-u
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 → 98
Calls
4 calls:
16.0ms
(+ (* (* 4.0 p) p) (* x x))
69.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
6.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(+ (* (* 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))))))
55.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0405866
11987780
25002742

prune288.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.6b

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))))))
10.2b
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
39×sqrt-prod
27×associate-*r*
23×add-sqr-sqrt
21×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×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def 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 → 97
Calls
4 calls:
148.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
6.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
22.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
76.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
53.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04011399
115781211
250021134

prune360.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.6b

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))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.4b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite122.0ms

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:
27.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
16.0ms
(+ (* (* 4.0 p) p) (* x x))
51.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
32.0ms
(+ (* (* 4.0 p) p) (* x x))
77.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
56.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify142.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 3 (134.0ms)

IterNodesCost
0296867
11081815
24584798
35001795

prune248.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 15.6b

regimes281.0ms

Accuracy

0% (0.2b remaining)

Error of 13.4b against oracle of 13.2b and baseline of 13.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0199
1199

end0.0ms

sample849.0ms

Algorithm
intervals
Results
207.0ms6014×body80valid
170.0ms814×body2560valid
103.0ms601×body1280valid
99.0ms8000×pre80true
50.0ms344×body640valid
15.0ms156×body320valid
5.0ms71×body160valid