Average Error: 7.4 → 1.9
Time: 4.8s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\sqrt[3]{x} \cdot \left(\left(\sqrt{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}} \cdot \sqrt{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}\right) \cdot \sqrt[3]{\sqrt[3]{x}}\right)}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\sqrt[3]{x} \cdot \left(\left(\sqrt{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}} \cdot \sqrt{\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}}\right) \cdot \sqrt[3]{\sqrt[3]{x}}\right)}{y - z} \cdot \frac{\sqrt[3]{x}}{t - z}
double f(double x, double y, double z, double t) {
        double r977401 = x;
        double r977402 = y;
        double r977403 = z;
        double r977404 = r977402 - r977403;
        double r977405 = t;
        double r977406 = r977405 - r977403;
        double r977407 = r977404 * r977406;
        double r977408 = r977401 / r977407;
        return r977408;
}
↓
double f(double x, double y, double z, double t) {
        double r977409 = x;
        double r977410 = cbrt(r977409);
        double r977411 = r977410 * r977410;
        double r977412 = cbrt(r977411);
        double r977413 = sqrt(r977412);
        double r977414 = r977413 * r977413;
        double r977415 = cbrt(r977410);
        double r977416 = r977414 * r977415;
        double r977417 = r977410 * r977416;
        double r977418 = y;
        double r977419 = z;
        double r977420 = r977418 - r977419;
        double r977421 = r977417 / r977420;
        double r977422 = t;
        double r977423 = r977422 - r977419;
        double r977424 = r977410 / r977423;
        double r977425 = r977421 * r977424;
        return r977425;
}

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
Target8.1
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

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-frac1.8

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

  6. Applied add-cube-cbrt1.8

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

  7. Applied cbrt-prod1.9

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

  9. Applied add-sqr-sqrt1.9

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

  10. Final simplification1.9

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

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :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))))