Average Error: 11.7 → 2.1
Time: 2.8s
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 r562201 = x;
        double r562202 = y;
        double r562203 = z;
        double r562204 = r562202 - r562203;
        double r562205 = r562201 * r562204;
        double r562206 = t;
        double r562207 = r562206 - r562203;
        double r562208 = r562205 / r562207;
        return r562208;
}
↓
double f(double x, double y, double z, double t) {
        double r562209 = x;
        double r562210 = t;
        double r562211 = z;
        double r562212 = r562210 - r562211;
        double r562213 = y;
        double r562214 = r562213 - r562211;
        double r562215 = r562212 / r562214;
        double r562216 = r562209 / r562215;
        return r562216;
}

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

Original11.7
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.7

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

  3. Applied associate-/l*2.1

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

  4. Final simplification2.1

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

Reproduce

herbie shell --seed 2020001 +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)))