Average Error: 4.5 → 1.9
Time: 3.3s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t} \]
↓
\[x + \frac{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(z - x\right)}{\sqrt[3]{t}} \]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(z - x\right)}{\sqrt[3]{t}}

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

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

Original4.5
Target5.9
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right) \]

Derivation

  1. Initial program 4.5

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

  2. Applied add-cube-cbrt_binary644.8

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

  3. Applied associate-/r*_binary644.8

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

  4. Simplified1.9

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

  5. Final simplification1.9

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

Reproduce

herbie shell --seed 2022068 
(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)))