Average Error: 7.5 → 2.2
Time: 10.5s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \frac{\frac{x}{t - z}}{y - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \frac{\frac{x}{t - z}}{y - z}
double f(double x, double y, double z, double t) {
        double r849457 = x;
        double r849458 = y;
        double r849459 = z;
        double r849460 = r849458 - r849459;
        double r849461 = t;
        double r849462 = r849461 - r849459;
        double r849463 = r849460 * r849462;
        double r849464 = r849457 / r849463;
        return r849464;
}
↓
double f(double x, double y, double z, double t) {
        double r849465 = 1.0;
        double r849466 = cbrt(r849465);
        double r849467 = r849466 * r849466;
        double r849468 = x;
        double r849469 = t;
        double r849470 = z;
        double r849471 = r849469 - r849470;
        double r849472 = r849468 / r849471;
        double r849473 = y;
        double r849474 = r849473 - r849470;
        double r849475 = r849472 / r849474;
        double r849476 = r849467 * r849475;
        return r849476;
}

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

Original7.5
Target8.4
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.5

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

  3. Applied *-un-lft-identity7.5

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

  4. Applied times-frac2.2

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

  6. Applied *-un-lft-identity2.2

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

  7. Applied add-cube-cbrt2.2

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

  8. Applied times-frac2.2

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

  9. Applied associate-*l*2.2

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

  10. Simplified2.2

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

  11. Final simplification2.2

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

Reproduce

herbie shell --seed 2020047 +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))))