Average Error: 11.9 → 2.4
Time: 3.8s
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 code(double x, double y, double z, double t) {
	return ((x * (y - z)) / (t - z));
}
↓
double code(double x, double y, double z, double t) {
	return (x / ((t - z) / (y - z)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

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Results

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Target

Original11.9
Target2.4
Herbie2.4
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.9

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

  3. Applied associate-/l*2.4

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

  4. Final simplification2.4

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

Reproduce

herbie shell --seed 2020091 
(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)))