Average Error: 12.0 → 2.2
Time: 12.7s
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 r411639 = x;
        double r411640 = y;
        double r411641 = z;
        double r411642 = r411640 - r411641;
        double r411643 = r411639 * r411642;
        double r411644 = t;
        double r411645 = r411644 - r411641;
        double r411646 = r411643 / r411645;
        return r411646;
}
↓
double f(double x, double y, double z, double t) {
        double r411647 = x;
        double r411648 = t;
        double r411649 = z;
        double r411650 = r411648 - r411649;
        double r411651 = y;
        double r411652 = r411651 - r411649;
        double r411653 = r411650 / r411652;
        double r411654 = r411647 / r411653;
        return r411654;
}

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

Original12.0
Target2.2
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 12.0

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

  3. Applied associate-/l*2.2

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

  4. Final simplification2.2

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

Reproduce

herbie shell --seed 2019303 +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)))