Average Error: 12.1 → 2.0
Time: 3.1s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x}{1 \cdot \frac{t - z}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x}{1 \cdot \frac{t - z}{y - z}}
double f(double x, double y, double z, double t) {
        double r1138789 = x;
        double r1138790 = y;
        double r1138791 = z;
        double r1138792 = r1138790 - r1138791;
        double r1138793 = r1138789 * r1138792;
        double r1138794 = t;
        double r1138795 = r1138794 - r1138791;
        double r1138796 = r1138793 / r1138795;
        return r1138796;
}
↓
double f(double x, double y, double z, double t) {
        double r1138797 = x;
        double r1138798 = 1.0;
        double r1138799 = t;
        double r1138800 = z;
        double r1138801 = r1138799 - r1138800;
        double r1138802 = y;
        double r1138803 = r1138802 - r1138800;
        double r1138804 = r1138801 / r1138803;
        double r1138805 = r1138798 * r1138804;
        double r1138806 = r1138797 / r1138805;
        return r1138806;
}

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

Original12.1
Target2.0
Herbie2.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 12.1

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

  3. Applied associate-/l*2.0

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

  5. Applied *-un-lft-identity2.0

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

  6. Applied *-un-lft-identity2.0

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

  7. Applied times-frac2.0

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

  8. Simplified2.0

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

  9. Final simplification2.0

    \[\leadsto \frac{x}{1 \cdot \frac{t - z}{y - z}}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (/ x (/ (- t z) (- y z)))

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