Average Error: 11.8 → 2.3
Time: 4.2s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[x \cdot \frac{y - z}{t - z}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
x \cdot \frac{y - z}{t - z}
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * ((double) (y - z)))) / ((double) (t - z))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x * ((double) (((double) (y - z)) / ((double) (t - z))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Target

Original11.8
Target2.3
Herbie2.3
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.8

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

  2. Simplified2.3

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

  3. Final simplification2.3

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

Reproduce

herbie shell --seed 2020181 
(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)))