Average Error: 2.1 → 6.1
Time: 6.6s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[t - \left(\frac{t \cdot x}{y} - \frac{x \cdot z}{y}\right)\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
t - \left(\frac{t \cdot x}{y} - \frac{x \cdot z}{y}\right)
double f(double x, double y, double z, double t) {
        double r296179 = x;
        double r296180 = y;
        double r296181 = r296179 / r296180;
        double r296182 = z;
        double r296183 = t;
        double r296184 = r296182 - r296183;
        double r296185 = r296181 * r296184;
        double r296186 = r296185 + r296183;
        return r296186;
}
↓
double f(double x, double y, double z, double t) {
        double r296187 = t;
        double r296188 = x;
        double r296189 = r296187 * r296188;
        double r296190 = y;
        double r296191 = r296189 / r296190;
        double r296192 = z;
        double r296193 = r296188 * r296192;
        double r296194 = r296193 / r296190;
        double r296195 = r296191 - r296194;
        double r296196 = r296187 - r296195;
        return r296196;
}

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

Original2.1
Target2.2
Herbie6.1
\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Initial program 2.1

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

  3. Applied add-cube-cbrt2.6

    \[\leadsto \frac{x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot \left(z - t\right) + t\]

  4. Applied add-cube-cbrt2.7

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(z - t\right) + t\]

  5. Applied times-frac2.7

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right)} \cdot \left(z - t\right) + t\]

  6. Applied associate-*l*1.0

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}} \cdot \left(z - t\right)\right)} + t\]

  7. Final simplification6.1

    \[\leadsto t - \left(\frac{t \cdot x}{y} - \frac{x \cdot z}{y}\right)\]

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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