Average Error: 11.5 → 2.0
Time: 11.5s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[x \cdot \frac{y - z}{t - z}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
x \cdot \frac{y - z}{t - z}
double f(double x, double y, double z, double t) {
        double r23462755 = x;
        double r23462756 = y;
        double r23462757 = z;
        double r23462758 = r23462756 - r23462757;
        double r23462759 = r23462755 * r23462758;
        double r23462760 = t;
        double r23462761 = r23462760 - r23462757;
        double r23462762 = r23462759 / r23462761;
        return r23462762;
}
↓
double f(double x, double y, double z, double t) {
        double r23462763 = x;
        double r23462764 = y;
        double r23462765 = z;
        double r23462766 = r23462764 - r23462765;
        double r23462767 = t;
        double r23462768 = r23462767 - r23462765;
        double r23462769 = r23462766 / r23462768;
        double r23462770 = r23462763 * r23462769;
        return r23462770;
}

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

Original11.5
Target2.0
Herbie2.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.5

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

  3. Applied *-un-lft-identity11.5

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

  4. Applied times-frac2.0

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

  5. Simplified2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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