Average Error: 10.7 → 1.3
Time: 4.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\frac{\frac{z - t}{z - a}}{\frac{1}{y}} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\frac{\frac{z - t}{z - a}}{\frac{1}{y}} + x
double f(double x, double y, double z, double t, double a) {
        double r502128 = x;
        double r502129 = y;
        double r502130 = z;
        double r502131 = t;
        double r502132 = r502130 - r502131;
        double r502133 = r502129 * r502132;
        double r502134 = a;
        double r502135 = r502130 - r502134;
        double r502136 = r502133 / r502135;
        double r502137 = r502128 + r502136;
        return r502137;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r502138 = z;
        double r502139 = t;
        double r502140 = r502138 - r502139;
        double r502141 = a;
        double r502142 = r502138 - r502141;
        double r502143 = r502140 / r502142;
        double r502144 = 1.0;
        double r502145 = y;
        double r502146 = r502144 / r502145;
        double r502147 = r502143 / r502146;
        double r502148 = x;
        double r502149 = r502147 + r502148;
        return r502149;
}

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

Original10.7
Target1.1
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.7

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

  2. Simplified3.0

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

  4. Applied clear-num3.3

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

  6. Applied fma-udef3.3

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

  7. Simplified3.1

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

  9. Applied div-inv3.1

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

  10. Applied associate-/r*1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2020089 +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))))