Average Error: 10.4 → 1.4
Time: 16.1s
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 r420505 = x;
        double r420506 = y;
        double r420507 = z;
        double r420508 = t;
        double r420509 = r420507 - r420508;
        double r420510 = r420506 * r420509;
        double r420511 = a;
        double r420512 = r420507 - r420511;
        double r420513 = r420510 / r420512;
        double r420514 = r420505 + r420513;
        return r420514;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r420515 = z;
        double r420516 = t;
        double r420517 = r420515 - r420516;
        double r420518 = a;
        double r420519 = r420515 - r420518;
        double r420520 = r420517 / r420519;
        double r420521 = y;
        double r420522 = r420520 * r420521;
        double r420523 = x;
        double r420524 = r420522 + r420523;
        return r420524;
}

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

Original10.4
Target1.4
Herbie1.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.4

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

  2. Simplified3.0

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

  4. Applied clear-num3.2

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

  6. Applied fma-udef3.2

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

  7. Simplified2.9

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

  9. Applied associate-/r/1.4

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

  10. Final simplification1.4

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

Reproduce

herbie shell --seed 2019325 +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))))