Average Error: 6.7 → 3.0
Time: 6.0s
Precision: 64
\[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.646136584525686015243781694282027335309 \cdot 10^{138} \lor \neg \left(z \le 8.697575599925424886021160018753896601857 \cdot 10^{81}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \end{array}\]
\frac{x \cdot 2}{y \cdot z - t \cdot z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.646136584525686015243781694282027335309 \cdot 10^{138} \lor \neg \left(z \le 8.697575599925424886021160018753896601857 \cdot 10^{81}\right):\\
\;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r617590 = x;
        double r617591 = 2.0;
        double r617592 = r617590 * r617591;
        double r617593 = y;
        double r617594 = z;
        double r617595 = r617593 * r617594;
        double r617596 = t;
        double r617597 = r617596 * r617594;
        double r617598 = r617595 - r617597;
        double r617599 = r617592 / r617598;
        return r617599;
}
↓
double f(double x, double y, double z, double t) {
        double r617600 = z;
        double r617601 = -5.646136584525686e+138;
        bool r617602 = r617600 <= r617601;
        double r617603 = 8.697575599925425e+81;
        bool r617604 = r617600 <= r617603;
        double r617605 = !r617604;
        bool r617606 = r617602 || r617605;
        double r617607 = x;
        double r617608 = 2.0;
        double r617609 = r617607 * r617608;
        double r617610 = r617609 / r617600;
        double r617611 = y;
        double r617612 = t;
        double r617613 = r617611 - r617612;
        double r617614 = r617610 / r617613;
        double r617615 = r617600 * r617613;
        double r617616 = r617609 / r617615;
        double r617617 = r617606 ? r617614 : r617616;
        return r617617;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.7
Target2.2
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt -2.559141628295061113708240820439530037456 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \mathbf{elif}\;\frac{x \cdot 2}{y \cdot z - t \cdot z} \lt 1.045027827330125861587720199944080049996 \cdot 10^{-269}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot 2}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - t\right) \cdot z} \cdot 2\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.646136584525686e+138 or 8.697575599925425e+81 < z

    1. Initial program 13.3

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified10.5

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}}\]
    3. Using strategy rm

    4. Applied associate-/r*2.7

      \[\leadsto \color{blue}{\frac{\frac{x \cdot 2}{z}}{y - t}}\]

    if -5.646136584525686e+138 < z < 8.697575599925425e+81

    1. Initial program 3.3

      \[\frac{x \cdot 2}{y \cdot z - t \cdot z}\]

    2. Simplified3.1

      \[\leadsto \color{blue}{\frac{x \cdot 2}{z \cdot \left(y - t\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.646136584525686015243781694282027335309 \cdot 10^{138} \lor \neg \left(z \le 8.697575599925424886021160018753896601857 \cdot 10^{81}\right):\\ \;\;\;\;\frac{\frac{x \cdot 2}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{z \cdot \left(y - t\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.Projection:infinitePerspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (if (< (/ (* x 2) (- (* y z) (* t z))) -2.559141628295061e-13) (* (/ x (* (- y t) z)) 2) (if (< (/ (* x 2) (- (* y z) (* t z))) 1.0450278273301259e-269) (/ (* (/ x z) 2) (- y t)) (* (/ x (* (- y t) z)) 2)))

  (/ (* x 2) (- (* y z) (* t z))))