Average Error: 6.2 → 1.6
Time: 3.4s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{t}}{\sqrt[3]{z - x}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}} \cdot \frac{\sqrt[3]{y}}{\frac{\sqrt[3]{t}}{\sqrt[3]{z - x}}}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (((double) (((double) cbrt(y)) * ((double) cbrt(y)))) / ((double) (((double) (((double) cbrt(t)) * ((double) cbrt(t)))) / ((double) (((double) cbrt(((double) (z - x)))) * ((double) cbrt(((double) (z - x)))))))))) * ((double) (((double) cbrt(y)) / ((double) (((double) cbrt(t)) / ((double) cbrt(((double) (z - x))))))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.2
Target2.0
Herbie1.6
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.2

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

  3. Applied associate-/l*6.0

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

  5. Applied add-cube-cbrt6.4

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

  6. Applied add-cube-cbrt6.6

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

  7. Applied times-frac6.6

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

  8. Applied add-cube-cbrt6.6

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

  9. Applied times-frac1.6

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

  10. Final simplification1.6

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

Reproduce

herbie shell --seed 2020153 
(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)) (* (neg z) (/ y t))))

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