Average Error: 6.3 → 2.1
Time: 7.9s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{t} \cdot \left(z - x\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{t} \cdot \left(z - x\right)
(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t) :precision binary64 (+ x (* (/ y t) (- 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 + ((y / t) * (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

Original6.3
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.3

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

  3. Applied add-cube-cbrt_binary646.8

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

  4. Applied associate-/r*_binary646.8

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

  5. Simplified3.0

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

  7. Applied clear-num_binary643.0

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

  8. Simplified2.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]
  9. Using strategy rm

  10. Applied div-inv_binary642.1

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

  11. Applied add-cube-cbrt_binary642.1

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

  12. Applied times-frac_binary642.3

    \[\leadsto x + \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{t}{y}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{z - x}}}\]

  13. Simplified2.2

    \[\leadsto x + \color{blue}{\frac{y}{t}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{z - x}}\]

  14. Simplified2.1

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

  15. Final simplification2.1

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

Reproduce

herbie shell --seed 2021174 
(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)))