Average Error: 10.5 → 1.3
Time: 19.1s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r25881205 = x;
        double r25881206 = y;
        double r25881207 = z;
        double r25881208 = t;
        double r25881209 = r25881207 - r25881208;
        double r25881210 = r25881206 * r25881209;
        double r25881211 = a;
        double r25881212 = r25881207 - r25881211;
        double r25881213 = r25881210 / r25881212;
        double r25881214 = r25881205 + r25881213;
        return r25881214;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25881215 = x;
        double r25881216 = y;
        double r25881217 = z;
        double r25881218 = a;
        double r25881219 = r25881217 - r25881218;
        double r25881220 = t;
        double r25881221 = r25881217 - r25881220;
        double r25881222 = r25881219 / r25881221;
        double r25881223 = r25881216 / r25881222;
        double r25881224 = r25881215 + r25881223;
        return r25881224;
}

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

Original10.5
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.5

    \[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
  2. Using strategy rm

  3. Applied associate-/l*1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

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

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