Average Error: 6.5 → 6.0
Time: 6.1s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{\frac{t}{z - x}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{\frac{t}{z - x}}
double f(double x, double y, double z, double t) {
        double r291024 = x;
        double r291025 = y;
        double r291026 = z;
        double r291027 = r291026 - r291024;
        double r291028 = r291025 * r291027;
        double r291029 = t;
        double r291030 = r291028 / r291029;
        double r291031 = r291024 + r291030;
        return r291031;
}
↓
double f(double x, double y, double z, double t) {
        double r291032 = x;
        double r291033 = y;
        double r291034 = t;
        double r291035 = z;
        double r291036 = r291035 - r291032;
        double r291037 = r291034 / r291036;
        double r291038 = r291033 / r291037;
        double r291039 = r291032 + r291038;
        return r291039;
}

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

Original6.5
Target2.0
Herbie6.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 1.812525037796768e+293 < (+ x (/ (* y (- z x)) t))

    1. Initial program 55.5

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

    3. Applied associate-/l*3.3

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

    if -inf.0 < (+ x (/ (* y (- z x)) t)) < 1.812525037796768e+293

    1. Initial program 0.7

      \[x + \frac{y \cdot \left(z - x\right)}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.0

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

Reproduce

herbie shell --seed 2019304 
(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)))