Average Error: 0.1 → 0.1
Time: 4.3s
Precision: binary64
\[[x, y] = \mathsf{sort}([x, y]) \\]
\[\frac{\left(x + y\right) - z}{t \cdot 2} \]
↓
\[\frac{y + \left(x - z\right)}{t \cdot 2} \]
\frac{\left(x + y\right) - z}{t \cdot 2}
↓
\frac{y + \left(x - z\right)}{t \cdot 2}

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))
↓
(FPCore (x y z t) :precision binary64 (/ (+ y (- x z)) (* t 2.0)))
double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}
↓
double code(double x, double y, double z, double t) {
	return (y + (x - z)) / (t * 2.0);
}

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

Derivation

  1. Initial program 0.1

    \[\frac{\left(x + y\right) - z}{t \cdot 2} \]

  2. Applied add-cube-cbrt_binary640.5

    \[\leadsto \frac{\left(x + y\right) - \color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{t \cdot 2} \]

  3. Applied add-cube-cbrt_binary641.3

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) \cdot \sqrt[3]{x + y}} - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}{t \cdot 2} \]

  4. Applied prod-diff_binary641.3

    \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}, \sqrt[3]{x + y}, -\sqrt[3]{z} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \mathsf{fma}\left(-\sqrt[3]{z}, \sqrt[3]{z} \cdot \sqrt[3]{z}, \sqrt[3]{z} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)}}{t \cdot 2} \]

  5. Simplified0.1

    \[\leadsto \frac{\color{blue}{\left(y + \left(x - z\right)\right)} + \mathsf{fma}\left(-\sqrt[3]{z}, \sqrt[3]{z} \cdot \sqrt[3]{z}, \sqrt[3]{z} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)}{t \cdot 2} \]

  6. Simplified0.1

    \[\leadsto \frac{\left(y + \left(x - z\right)\right) + \color{blue}{0}}{t \cdot 2} \]

  7. Final simplification0.1

    \[\leadsto \frac{y + \left(x - z\right)}{t \cdot 2} \]

Reproduce

herbie shell --seed 2022076 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))