Average Error: 25.1 → 15.3
Time: 2.2m
Precision: 64
Internal Precision: 320
\[\frac{1 - y}{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}\]
\[\begin{array}{l} \mathbf{if}\;y \le -3.322168255576266 \cdot 10^{+46}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 - y}{\sqrt{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}}}{\sqrt{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}}\\ \end{array}\]

Error

Bits error versus y

Bits error versus p

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes
  2. if y < -3.322168255576266e+46

    1. Initial program 37.7

      \[\frac{1 - y}{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}\]
    2. Taylor expanded around -inf 0.8

      \[\leadsto \color{blue}{1}\]

    if -3.322168255576266e+46 < y

    1. Initial program 20.4

      \[\frac{1 - y}{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt20.4

      \[\leadsto \frac{1 - y}{\sqrt{\color{blue}{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}} \cdot \sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}}}\]
    4. Applied sqrt-prod20.6

      \[\leadsto \frac{1 - y}{\color{blue}{\sqrt{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}} \cdot \sqrt{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}}}\]
    5. Applied associate-/r*20.6

      \[\leadsto \color{blue}{\frac{\frac{1 - y}{\sqrt{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}}}{\sqrt{\sqrt{\frac{p}{y} + {\left(1 - y\right)}^{2}}}}}\]
  3. Recombined 2 regimes into one program.

Runtime

Time bar (total: 2.2m)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (y p)
  :name "(1-y)/sqrt(p/y +(1-y)^2)"
  (/ (- 1 y) (sqrt (+ (/ p y) (pow (- 1 y) 2)))))