Average Error: 6.5 → 2.0
Time: 3.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{t} \cdot \left(\frac{x}{-1} - \frac{z}{-1}\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{t} \cdot \left(\frac{x}{-1} - \frac{z}{-1}\right)
(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (+ x (* (/ y t) (- (/ x -1.0) (/ z -1.0)))))
double code(double x, double y, double z, double t) {
	return x + ((y * (z - x)) / t);
}
↓
double code(double x, double y, double z, double t) {
	return x + ((y / t) * ((x / -1.0) - (z / -1.0)));
}

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

Target

Original6.5
Target2.0
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.5

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

  3. Applied add-cube-cbrt_binary64_124987.0

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

  4. Applied times-frac_binary64_124693.0

    \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}}\]

  5. Taylor expanded around -inf 6.5

    \[\leadsto x + \color{blue}{\left(\frac{x \cdot y}{t \cdot {\left(\sqrt[3]{-1}\right)}^{3}} - \frac{z \cdot y}{t \cdot {\left(\sqrt[3]{-1}\right)}^{3}}\right)}\]

  6. Simplified2.0

    \[\leadsto x + \color{blue}{\frac{y}{t} \cdot \left(\frac{x}{-1} - \frac{z}{-1}\right)}\]

  7. Final simplification2.0

    \[\leadsto x + \frac{y}{t} \cdot \left(\frac{x}{-1} - \frac{z}{-1}\right)\]

Reproduce

herbie shell --seed 2020280 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))