Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]
↓
\[\left(t + 0.125 \cdot x\right) - 0.5 \cdot \left(z \cdot y\right)\]
\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t
↓
\left(t + 0.125 \cdot x\right) - 0.5 \cdot \left(z \cdot y\right)
double f(double x, double y, double z, double t) {
        double r780032 = 1.0;
        double r780033 = 8.0;
        double r780034 = r780032 / r780033;
        double r780035 = x;
        double r780036 = r780034 * r780035;
        double r780037 = y;
        double r780038 = z;
        double r780039 = r780037 * r780038;
        double r780040 = 2.0;
        double r780041 = r780039 / r780040;
        double r780042 = r780036 - r780041;
        double r780043 = t;
        double r780044 = r780042 + r780043;
        return r780044;
}
↓
double f(double x, double y, double z, double t) {
        double r780045 = t;
        double r780046 = 0.125;
        double r780047 = x;
        double r780048 = r780046 * r780047;
        double r780049 = r780045 + r780048;
        double r780050 = 0.5;
        double r780051 = z;
        double r780052 = y;
        double r780053 = r780051 * r780052;
        double r780054 = r780050 * r780053;
        double r780055 = r780049 - r780054;
        return r780055;
}

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

Original0.0
Target0.0
Herbie0.0
\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y\]

Derivation

  1. Initial program 0.0

    \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(0.125 \cdot x + t\right) - 0.5 \cdot \left(z \cdot y\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\left(t + 0.125 \cdot x\right) - 0.5 \cdot \left(z \cdot y\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(t + 0.125 \cdot x\right) - 0.5 \cdot \left(z \cdot y\right)\]

Reproduce

herbie shell --seed 2020034 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8) t) (* (/ z 2) y))

  (+ (- (* (/ 1 8) x) (/ (* y z) 2)) t))