Average Error: 10.1 → 3.4
Time: 4.5s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\frac{x}{z} + y\right) - \frac{x \cdot y}{z}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\frac{x}{z} + y\right) - \frac{x \cdot y}{z}
double f(double x, double y, double z) {
        double r487500 = x;
        double r487501 = y;
        double r487502 = z;
        double r487503 = r487502 - r487500;
        double r487504 = r487501 * r487503;
        double r487505 = r487500 + r487504;
        double r487506 = r487505 / r487502;
        return r487506;
}
↓
double f(double x, double y, double z) {
        double r487507 = x;
        double r487508 = z;
        double r487509 = r487507 / r487508;
        double r487510 = y;
        double r487511 = r487509 + r487510;
        double r487512 = r487507 * r487510;
        double r487513 = r487512 / r487508;
        double r487514 = r487511 - r487513;
        return r487514;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.1
Target0.0
Herbie3.4
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.9243331055553158e+33 or 8.885584462050694e-36 < x

    1. Initial program 12.5

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

    2. Taylor expanded around 0 8.2

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

    4. Applied *-un-lft-identity8.2

      \[\leadsto \left(\frac{x}{z} + y\right) - \frac{x \cdot y}{\color{blue}{1 \cdot z}}\]

    5. Applied times-frac0.1

      \[\leadsto \left(\frac{x}{z} + y\right) - \color{blue}{\frac{x}{1} \cdot \frac{y}{z}}\]

    6. Simplified0.1

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

    if -1.9243331055553158e+33 < x < 8.885584462050694e-36

    1. Initial program 8.5

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

    2. Taylor expanded around 0 0.0

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

  4. Final simplification3.4

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))