Average Error: 7.2 → 2.1
Time: 15.3s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
↓
\[\frac{\left(x + y \cdot \frac{z}{t \cdot z - x}\right) - \frac{x}{t \cdot z - x}}{x + 1}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}
↓
\frac{\left(x + y \cdot \frac{z}{t \cdot z - x}\right) - \frac{x}{t \cdot z - x}}{x + 1}
double f(double x, double y, double z, double t) {
        double r473780 = x;
        double r473781 = y;
        double r473782 = z;
        double r473783 = r473781 * r473782;
        double r473784 = r473783 - r473780;
        double r473785 = t;
        double r473786 = r473785 * r473782;
        double r473787 = r473786 - r473780;
        double r473788 = r473784 / r473787;
        double r473789 = r473780 + r473788;
        double r473790 = 1.0;
        double r473791 = r473780 + r473790;
        double r473792 = r473789 / r473791;
        return r473792;
}
↓
double f(double x, double y, double z, double t) {
        double r473793 = x;
        double r473794 = y;
        double r473795 = z;
        double r473796 = t;
        double r473797 = r473796 * r473795;
        double r473798 = r473797 - r473793;
        double r473799 = r473795 / r473798;
        double r473800 = r473794 * r473799;
        double r473801 = r473793 + r473800;
        double r473802 = r473793 / r473798;
        double r473803 = r473801 - r473802;
        double r473804 = 1.0;
        double r473805 = r473793 + r473804;
        double r473806 = r473803 / r473805;
        return r473806;
}

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
Target0.3
Herbie2.1
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1}\]

Derivation

  1. Initial program 7.2

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1}\]
  2. Using strategy rm

  3. Applied div-sub7.2

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

  4. Applied associate-+r-7.2

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

  6. Applied *-un-lft-identity7.2

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

  7. Applied times-frac2.1

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

  8. Simplified2.1

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

  9. Final simplification2.1

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1)))