Average Error: 7.2 → 1.1
Time: 17.1s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{t - z} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{t - z} \cdot \frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}
double f(double x, double y, double z, double t) {
        double r32263482 = x;
        double r32263483 = y;
        double r32263484 = z;
        double r32263485 = r32263483 - r32263484;
        double r32263486 = t;
        double r32263487 = r32263486 - r32263484;
        double r32263488 = r32263485 * r32263487;
        double r32263489 = r32263482 / r32263488;
        return r32263489;
}
↓
double f(double x, double y, double z, double t) {
        double r32263490 = x;
        double r32263491 = cbrt(r32263490);
        double r32263492 = y;
        double r32263493 = z;
        double r32263494 = r32263492 - r32263493;
        double r32263495 = cbrt(r32263494);
        double r32263496 = r32263491 / r32263495;
        double r32263497 = t;
        double r32263498 = r32263497 - r32263493;
        double r32263499 = r32263496 / r32263498;
        double r32263500 = r32263491 * r32263491;
        double r32263501 = r32263495 * r32263495;
        double r32263502 = r32263500 / r32263501;
        double r32263503 = r32263499 * r32263502;
        return r32263503;
}

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

Original7.2
Target8.0
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 7.2

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  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 div-inv2.2

    \[\leadsto \color{blue}{\frac{x}{y - z} \cdot \frac{1}{t - z}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt2.7

    \[\leadsto \frac{x}{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}} \cdot \frac{1}{t - z}\]

  8. Applied add-cube-cbrt2.9

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}} \cdot \frac{1}{t - z}\]

  9. Applied times-frac2.9

    \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}\right)} \cdot \frac{1}{t - z}\]

  10. Applied associate-*l*1.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}} \cdot \frac{1}{t - z}\right)}\]

  11. Simplified1.1

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

  12. Final simplification1.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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 (/ 1.0 (* (- y z) (- t z)))))

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