Average Error: 10.9 → 1.3
Time: 3.4s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{z - t}{z - a} \cdot y + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{z - t}{z - a} \cdot y + x
double f(double x, double y, double z, double t, double a) {
        double r581467 = x;
        double r581468 = y;
        double r581469 = z;
        double r581470 = t;
        double r581471 = r581469 - r581470;
        double r581472 = r581468 * r581471;
        double r581473 = a;
        double r581474 = r581469 - r581473;
        double r581475 = r581472 / r581474;
        double r581476 = r581467 + r581475;
        return r581476;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r581477 = z;
        double r581478 = t;
        double r581479 = r581477 - r581478;
        double r581480 = a;
        double r581481 = r581477 - r581480;
        double r581482 = r581479 / r581481;
        double r581483 = y;
        double r581484 = r581482 * r581483;
        double r581485 = x;
        double r581486 = r581484 + r581485;
        return r581486;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  2. Simplified2.9

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z - a}, z - t, x\right)}\]
  3. Using strategy rm

  4. Applied clear-num3.1

    \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{z - a}{y}}}, z - t, x\right)\]
  5. Using strategy rm

  6. Applied fma-udef3.1

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

  7. Simplified3.0

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

  9. Applied associate-/r/1.3

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

  10. Final simplification1.3

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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