Average Error: 6.1 → 2.1
Time: 7.2s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t} \]
↓
\[x + \frac{1}{\frac{\frac{t}{y}}{z - x}} \]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{1}{\frac{\frac{t}{y}}{z - x}}

(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t) :precision binary64 (+ x (/ 1.0 (/ (/ t y) (- z x)))))
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 + (1.0 / ((t / y) / (z - x)));
}

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

Original6.1
Target2.2
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right) \]

Derivation

  1. Initial program 6.1

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

  2. Applied clear-num_binary646.1

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

  3. Applied associate-/r*_binary642.1

    \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}} \]

  4. Final simplification2.1

    \[\leadsto x + \frac{1}{\frac{\frac{t}{y}}{z - x}} \]

Reproduce

herbie shell --seed 2022088 
(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)))