Average Error: 11.6 → 2.0
Time: 3.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x}{\frac{t - z}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x}{\frac{t - z}{y - z}}
double f(double x, double y, double z, double t) {
        double r618113 = x;
        double r618114 = y;
        double r618115 = z;
        double r618116 = r618114 - r618115;
        double r618117 = r618113 * r618116;
        double r618118 = t;
        double r618119 = r618118 - r618115;
        double r618120 = r618117 / r618119;
        return r618120;
}
↓
double f(double x, double y, double z, double t) {
        double r618121 = x;
        double r618122 = t;
        double r618123 = z;
        double r618124 = r618122 - r618123;
        double r618125 = y;
        double r618126 = r618125 - r618123;
        double r618127 = r618124 / r618126;
        double r618128 = r618121 / r618127;
        return r618128;
}

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

Original11.6
Target2.0
Herbie2.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.6

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

  3. Applied associate-/l*2.0

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

  4. Final simplification2.0

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

Reproduce

herbie shell --seed 2020027 +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)))