Average Error: 1.3 → 1.3
Time: 21.5s
Precision: 64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[y \cdot \frac{z - t}{z - a} + x\]
x + y \cdot \frac{z - t}{z - a}
↓
y \cdot \frac{z - t}{z - a} + x
double f(double x, double y, double z, double t, double a) {
        double r25077206 = x;
        double r25077207 = y;
        double r25077208 = z;
        double r25077209 = t;
        double r25077210 = r25077208 - r25077209;
        double r25077211 = a;
        double r25077212 = r25077208 - r25077211;
        double r25077213 = r25077210 / r25077212;
        double r25077214 = r25077207 * r25077213;
        double r25077215 = r25077206 + r25077214;
        return r25077215;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r25077216 = y;
        double r25077217 = z;
        double r25077218 = t;
        double r25077219 = r25077217 - r25077218;
        double r25077220 = a;
        double r25077221 = r25077217 - r25077220;
        double r25077222 = r25077219 / r25077221;
        double r25077223 = r25077216 * r25077222;
        double r25077224 = x;
        double r25077225 = r25077223 + r25077224;
        return r25077225;
}

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
Target1.3
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

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

  4. Applied clear-num1.4

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

  6. Applied fma-udef1.4

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

  7. Simplified1.3

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

  9. Applied div-inv1.4

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

  10. Simplified1.3

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

  11. Final simplification1.3

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"

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

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