Average Error: 1.3 → 1.3
Time: 4.2s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\frac{1}{\frac{\frac{z - a}{z - t}}{y}} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
\frac{1}{\frac{\frac{z - a}{z - t}}{y}} + x
double f(double x, double y, double z, double t, double a) {
        double r581030 = x;
        double r581031 = y;
        double r581032 = z;
        double r581033 = t;
        double r581034 = r581032 - r581033;
        double r581035 = a;
        double r581036 = r581032 - r581035;
        double r581037 = r581034 / r581036;
        double r581038 = r581031 * r581037;
        double r581039 = r581030 + r581038;
        return r581039;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r581040 = 1.0;
        double r581041 = z;
        double r581042 = a;
        double r581043 = r581041 - r581042;
        double r581044 = t;
        double r581045 = r581041 - r581044;
        double r581046 = r581043 / r581045;
        double r581047 = y;
        double r581048 = r581046 / r581047;
        double r581049 = r581040 / r581048;
        double r581050 = x;
        double r581051 = r581049 + r581050;
        return r581051;
}

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

Original1.3
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 1.3

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

  2. Simplified1.3

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

  4. Applied clear-num1.4

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

  6. Applied fma-udef1.4

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

  7. Simplified1.2

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

  9. Applied clear-num1.3

    \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z - a}{z - t}}{y}}} + x\]

  10. Final simplification1.3

    \[\leadsto \frac{1}{\frac{\frac{z - a}{z - t}}{y}} + x\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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