Average Error: 6.2 → 1.0
Time: 2.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{\sqrt[3]{z - x}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\sqrt[3]{z - x} \cdot \sqrt[3]{z - x}}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{\sqrt[3]{z - x}}{\frac{\sqrt[3]{t}}{\sqrt[3]{y}}}
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(((double) (z - x)))) * ((double) cbrt(((double) (z - x)))))) / ((double) (((double) (((double) cbrt(t)) * ((double) cbrt(t)))) / ((double) (((double) cbrt(y)) * ((double) cbrt(y)))))))) * ((double) (((double) cbrt(((double) (z - x)))) / ((double) (((double) cbrt(t)) / ((double) cbrt(y))))))))));
}

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

Derivation

  1. Initial program 6.2

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

  3. Applied *-commutative6.2

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

  4. Applied associate-/l*2.0

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

  6. Applied add-cube-cbrt2.5

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

  7. Applied add-cube-cbrt2.6

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

  8. Applied times-frac2.6

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

  9. Applied add-cube-cbrt2.7

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

  10. Applied times-frac1.0

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

  11. Final simplification1.0

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(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)))