Average Error: 7.4 → 0.4
Time: 55.3s
Precision: 64
\[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
↓
\[\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1.0} - \frac{\frac{x}{t \cdot z - x}}{x + 1.0}\]
\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}
↓
\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1.0} - \frac{\frac{x}{t \cdot z - x}}{x + 1.0}
double f(double x, double y, double z, double t) {
        double r24272755 = x;
        double r24272756 = y;
        double r24272757 = z;
        double r24272758 = r24272756 * r24272757;
        double r24272759 = r24272758 - r24272755;
        double r24272760 = t;
        double r24272761 = r24272760 * r24272757;
        double r24272762 = r24272761 - r24272755;
        double r24272763 = r24272759 / r24272762;
        double r24272764 = r24272755 + r24272763;
        double r24272765 = 1.0;
        double r24272766 = r24272755 + r24272765;
        double r24272767 = r24272764 / r24272766;
        return r24272767;
}
↓
double f(double x, double y, double z, double t) {
        double r24272768 = x;
        double r24272769 = y;
        double r24272770 = t;
        double r24272771 = z;
        double r24272772 = r24272768 / r24272771;
        double r24272773 = r24272770 - r24272772;
        double r24272774 = r24272769 / r24272773;
        double r24272775 = r24272768 + r24272774;
        double r24272776 = 1.0;
        double r24272777 = r24272768 + r24272776;
        double r24272778 = r24272775 / r24272777;
        double r24272779 = r24272770 * r24272771;
        double r24272780 = r24272779 - r24272768;
        double r24272781 = r24272768 / r24272780;
        double r24272782 = r24272781 / r24272777;
        double r24272783 = r24272778 - r24272782;
        return r24272783;
}

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
Target0.4
Herbie0.4
\[\frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1.0}\]

Derivation

  1. Initial program 7.4

    \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1.0}\]
  2. Using strategy rm

  3. Applied div-sub7.4

    \[\leadsto \frac{x + \color{blue}{\left(\frac{y \cdot z}{t \cdot z - x} - \frac{x}{t \cdot z - x}\right)}}{x + 1.0}\]

  4. Applied associate-+r-7.4

    \[\leadsto \frac{\color{blue}{\left(x + \frac{y \cdot z}{t \cdot z - x}\right) - \frac{x}{t \cdot z - x}}}{x + 1.0}\]

  5. Applied div-sub7.4

    \[\leadsto \color{blue}{\frac{x + \frac{y \cdot z}{t \cdot z - x}}{x + 1.0} - \frac{\frac{x}{t \cdot z - x}}{x + 1.0}}\]
  6. Using strategy rm

  7. Applied associate-/l*2.3

    \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t \cdot z - x}{z}}}}{x + 1.0} - \frac{\frac{x}{t \cdot z - x}}{x + 1.0}\]

  8. Taylor expanded around 0 0.4

    \[\leadsto \frac{x + \frac{y}{\color{blue}{t - \frac{x}{z}}}}{x + 1.0} - \frac{\frac{x}{t \cdot z - x}}{x + 1.0}\]

  9. Final simplification0.4

    \[\leadsto \frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1.0} - \frac{\frac{x}{t \cdot z - x}}{x + 1.0}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))