Details

Time bar (total: 4.7s)

sample52.0ms

Algorithm
intervals
Results
14.0ms201×body80valid
8.0ms24×body2560valid
6.0ms256×pre80true
4.0ms14×body1280valid
2.0ms7×body640valid
1.0ms8×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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

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)))))
14.1b
(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:
15.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.0ms
(+ (* (* 4.0 p) p) (* x x))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series208.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
34.0ms
(+ (* (* 4.0 p) p) (* x x))
72.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
52.0ms
(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

prune320.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.7b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1 fma-def sqrt-prod
4×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
2×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
4 → 68
Calls
4 calls:
26.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
25.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series276.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
72.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
67.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify116.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 4 (109.0ms)

IterNodesCost
0180588
1522546
21457544
33954542
45001526

prune370.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.7b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite74.0ms

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:
29.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
4.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
18.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
18.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))
82.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
59.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
67.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03591348
112631258
250011226

prune412.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize26.0ms

Local error

Found 4 expressions with local error:

7.7b
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))))
14.1b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.8b
(cbrt (+ (* (* 4.0 p) p) (* x x)))
14.8b
(cbrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
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
Counts
4 → 63
Calls
4 calls:
2.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))))
11.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

series620.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(+ 1.0 (* (/ 1 (sqrt (sqrt (+ (* (* 4.0 p) p) (* x x))))) (/ x (sqrt (* (fabs (cbrt (+ (* (* 4.0 p) p) (* x x)))) (sqrt (cbrt (+ (* (* 4.0 p) p) (* x x)))))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
153.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))
127.0ms
(cbrt (+ (* (* 4.0 p) p) (* x x)))

simplify43.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03671003
11369911
25002904

prune418.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.3b

regimes188.0ms

Accuracy

0% (1.3b remaining)

Error of 14.0b against oracle of 12.7b and baseline of 14.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03226
13226

end0.0ms

sample813.0ms

Algorithm
intervals
Results
207.0ms6089×body80valid
186.0ms795×body2560valid
105.0ms604×body1280valid
103.0ms8000×pre80true
42.0ms292×body640valid
15.0ms143×body320valid
5.0ms77×body160valid