Average Error: 7.4 → 1.7
Time: 20.1s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z}\right)\right)\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}} \cdot \left(\frac{\sqrt[3]{\sqrt[3]{x}}}{\sqrt[3]{t - z}} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z}\right)\right)
double f(double x, double y, double z, double t) {
        double r39817314 = x;
        double r39817315 = y;
        double r39817316 = z;
        double r39817317 = r39817315 - r39817316;
        double r39817318 = t;
        double r39817319 = r39817318 - r39817316;
        double r39817320 = r39817317 * r39817319;
        double r39817321 = r39817314 / r39817320;
        return r39817321;
}
↓
double f(double x, double y, double z, double t) {
        double r39817322 = x;
        double r39817323 = cbrt(r39817322);
        double r39817324 = cbrt(r39817323);
        double r39817325 = t;
        double r39817326 = z;
        double r39817327 = r39817325 - r39817326;
        double r39817328 = cbrt(r39817327);
        double r39817329 = r39817324 / r39817328;
        double r39817330 = r39817323 * r39817323;
        double r39817331 = y;
        double r39817332 = r39817331 - r39817326;
        double r39817333 = r39817330 / r39817332;
        double r39817334 = r39817329 * r39817333;
        double r39817335 = r39817329 * r39817334;
        double r39817336 = r39817329 * r39817335;
        return r39817336;
}

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

Original7.4
Target7.8
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.4

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

  3. Applied add-cube-cbrt7.9

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

  4. Applied times-frac1.6

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt1.8

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

  7. Applied add-cube-cbrt1.9

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

  8. Applied times-frac1.9

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

  9. Applied associate-*r*1.7

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

  10. Simplified1.7

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

  11. Final simplification1.7

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z)))))

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