Average Error: 7.7 → 1.1
Time: 17.0s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\frac{t - z}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\frac{t - z}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}
double f(double x, double y, double z, double t) {
        double r34520372 = x;
        double r34520373 = y;
        double r34520374 = z;
        double r34520375 = r34520373 - r34520374;
        double r34520376 = t;
        double r34520377 = r34520376 - r34520374;
        double r34520378 = r34520375 * r34520377;
        double r34520379 = r34520372 / r34520378;
        return r34520379;
}
↓
double f(double x, double y, double z, double t) {
        double r34520380 = x;
        double r34520381 = cbrt(r34520380);
        double r34520382 = r34520381 * r34520381;
        double r34520383 = y;
        double r34520384 = z;
        double r34520385 = r34520383 - r34520384;
        double r34520386 = cbrt(r34520385);
        double r34520387 = r34520386 * r34520386;
        double r34520388 = r34520382 / r34520387;
        double r34520389 = t;
        double r34520390 = r34520389 - r34520384;
        double r34520391 = r34520381 / r34520386;
        double r34520392 = r34520390 / r34520391;
        double r34520393 = r34520388 / r34520392;
        return r34520393;
}

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

Original7.7
Target8.4
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.7

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

  3. Applied associate-/r*2.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.7

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

  6. Applied add-cube-cbrt2.8

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

  7. Applied times-frac2.8

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

  8. Applied associate-/l*1.1

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

  9. Final simplification1.1

    \[\leadsto \frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\frac{t - z}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}\]

Reproduce

herbie shell --seed 2019163 
(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))))