Average Error: 6.8 → 1.0
Time: 3.4s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(z - x\right)\right) + x\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \left(\frac{\sqrt[3]{y}}{\sqrt[3]{t}} \cdot \left(z - x\right)\right) + 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 ((((cbrt(y) * cbrt(y)) / (cbrt(t) * cbrt(t))) * ((cbrt(y) / cbrt(t)) * (z - x))) + 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

Original6.8
Target2.3
Herbie1.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.8

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

  2. Simplified2.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]
  3. Using strategy rm

  4. Applied fma-udef2.3

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

  6. Applied add-cube-cbrt2.8

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

  7. Applied add-cube-cbrt2.9

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

  8. Applied times-frac2.9

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

  9. Applied associate-*l*1.0

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

  10. Final simplification1.0

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

Reproduce

herbie shell --seed 2020091 +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)))