Average Error: 7.9 → 1.2
Time: 4.6s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{t - z}}{\sqrt[3]{y - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{y - z}} \cdot \frac{\frac{\sqrt[3]{x}}{t - z}}{\sqrt[3]{y - z}}
double f(double x, double y, double z, double t) {
        double r755552 = x;
        double r755553 = y;
        double r755554 = z;
        double r755555 = r755553 - r755554;
        double r755556 = t;
        double r755557 = r755556 - r755554;
        double r755558 = r755555 * r755557;
        double r755559 = r755552 / r755558;
        return r755559;
}
↓
double f(double x, double y, double z, double t) {
        double r755560 = x;
        double r755561 = cbrt(r755560);
        double r755562 = r755561 * r755561;
        double r755563 = y;
        double r755564 = z;
        double r755565 = r755563 - r755564;
        double r755566 = cbrt(r755565);
        double r755567 = r755562 / r755566;
        double r755568 = r755567 / r755566;
        double r755569 = t;
        double r755570 = r755569 - r755564;
        double r755571 = r755561 / r755570;
        double r755572 = r755571 / r755566;
        double r755573 = r755568 * r755572;
        return r755573;
}

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

Original7.9
Target8.8
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.9

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

  3. Applied *-un-lft-identity7.9

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

  4. Applied times-frac2.2

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

  6. Applied pow12.2

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

  7. Applied pow12.2

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

  8. Applied pow-prod-down2.2

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

  9. Simplified2.1

    \[\leadsto {\color{blue}{\left(\frac{\frac{x}{t - z}}{y - z}\right)}}^{1}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt2.7

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

  12. Applied *-un-lft-identity2.7

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

  13. Applied add-cube-cbrt2.9

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

  14. Applied times-frac2.9

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

  15. Applied times-frac1.2

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

  16. Simplified1.2

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

  17. Final simplification1.2

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(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))))