Average Error: 6.8 → 2.1
Time: 4.1s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{t} \cdot \left(z - x\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{t} \cdot \left(z - x\right)
double f(double x, double y, double z, double t) {
        double r233032 = x;
        double r233033 = y;
        double r233034 = z;
        double r233035 = r233034 - r233032;
        double r233036 = r233033 * r233035;
        double r233037 = t;
        double r233038 = r233036 / r233037;
        double r233039 = r233032 + r233038;
        return r233039;
}
↓
double f(double x, double y, double z, double t) {
        double r233040 = x;
        double r233041 = y;
        double r233042 = t;
        double r233043 = r233041 / r233042;
        double r233044 = z;
        double r233045 = r233044 - r233040;
        double r233046 = r233043 * r233045;
        double r233047 = r233040 + r233046;
        return r233047;
}

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
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.9907489930006894e-129 or 4.674838803392881e-172 < x

    1. Initial program 7.3

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

    3. Applied associate-/l*6.3

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

    5. Applied associate-/r/0.9

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

    if -3.9907489930006894e-129 < x < 4.674838803392881e-172

    1. Initial program 5.5

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

    3. Applied associate-/l*4.9

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

    5. Applied div-inv4.9

      \[\leadsto x + \frac{y}{\color{blue}{t \cdot \frac{1}{z - x}}}\]

    6. Taylor expanded around 0 5.5

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

    7. Simplified4.9

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

  4. Final simplification2.1

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

Reproduce

herbie shell --seed 2019308 
(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)))