Average Error: 2.1 → 0.3
Time: 19.7s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[\frac{\frac{z}{\left(1 + t\right) - z}}{\frac{1}{a}} - \left(\frac{\frac{y}{\left(t - z\right) + 1}}{\frac{1}{a}} - x\right)\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
\frac{\frac{z}{\left(1 + t\right) - z}}{\frac{1}{a}} - \left(\frac{\frac{y}{\left(t - z\right) + 1}}{\frac{1}{a}} - x\right)
double f(double x, double y, double z, double t, double a) {
        double r484329 = x;
        double r484330 = y;
        double r484331 = z;
        double r484332 = r484330 - r484331;
        double r484333 = t;
        double r484334 = r484333 - r484331;
        double r484335 = 1.0;
        double r484336 = r484334 + r484335;
        double r484337 = a;
        double r484338 = r484336 / r484337;
        double r484339 = r484332 / r484338;
        double r484340 = r484329 - r484339;
        return r484340;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r484341 = z;
        double r484342 = 1.0;
        double r484343 = t;
        double r484344 = r484342 + r484343;
        double r484345 = r484344 - r484341;
        double r484346 = r484341 / r484345;
        double r484347 = 1.0;
        double r484348 = a;
        double r484349 = r484347 / r484348;
        double r484350 = r484346 / r484349;
        double r484351 = y;
        double r484352 = r484343 - r484341;
        double r484353 = r484352 + r484342;
        double r484354 = r484351 / r484353;
        double r484355 = r484354 / r484349;
        double r484356 = x;
        double r484357 = r484355 - r484356;
        double r484358 = r484350 - r484357;
        return r484358;
}

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

Original2.1
Target0.2
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.1

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

  2. Simplified2.1

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

  4. Applied div-inv2.2

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

  5. Applied associate-/r*0.3

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

  6. Simplified0.3

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

  8. Applied div-sub0.3

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

  9. Applied div-sub0.3

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

  10. Applied associate-+l-0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))