Average Error: 6.6 → 1.7
Time: 4.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \left(y \cdot \left(\sqrt[3]{z - x} \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)\right) \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \left(y \cdot \left(\sqrt[3]{z - x} \cdot \frac{\sqrt[3]{z - x}}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)\right) \cdot \frac{\sqrt[3]{z - x}}{\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 (- z x)) (/ (cbrt (- z x)) (* (cbrt t) (cbrt t)))))
   (/ (cbrt (- z x)) (cbrt t)))))
double code(double x, double y, double z, double t) {
	return ((double) (x + (((double) (y * ((double) (z - x)))) / t)));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * ((double) (((double) cbrt(((double) (z - x)))) * (((double) cbrt(((double) (z - x)))) / ((double) (((double) cbrt(t)) * ((double) cbrt(t))))))))) * (((double) cbrt(((double) (z - x)))) / ((double) 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

Original6.6
Target1.9
Herbie1.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

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

  2. Simplified6.7

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

  4. Applied add-cube-cbrt7.1

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

  5. Applied add-cube-cbrt7.2

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

  6. Applied times-frac7.2

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

  7. Applied associate-*r*1.7

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

  8. Simplified1.7

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

  9. Final simplification1.7

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

Reproduce

herbie shell --seed 2020198 
(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)))