Average Error: 10.2 → 0.0
Time: 14.0s
Precision: 64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\left(\left(-y\right) + 1\right) \cdot \frac{x}{z} + y
double f(double x, double y, double z) {
        double r1060431 = x;
        double r1060432 = y;
        double r1060433 = z;
        double r1060434 = r1060433 - r1060431;
        double r1060435 = r1060432 * r1060434;
        double r1060436 = r1060431 + r1060435;
        double r1060437 = r1060436 / r1060433;
        return r1060437;
}
↓
double f(double x, double y, double z) {
        double r1060438 = y;
        double r1060439 = -r1060438;
        double r1060440 = 1.0;
        double r1060441 = r1060439 + r1060440;
        double r1060442 = x;
        double r1060443 = z;
        double r1060444 = r1060442 / r1060443;
        double r1060445 = r1060441 * r1060444;
        double r1060446 = r1060445 + r1060438;
        return r1060446;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.2
Target0.0
Herbie0.0
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Initial program 10.2

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

  2. Taylor expanded around 0 3.5

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

  4. Applied *-un-lft-identity3.5

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

  5. Applied *-un-lft-identity3.5

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

  6. Applied distribute-lft-out--3.5

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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))