Average Error: 2.1 → 0.3
Time: 4.9s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \left(\left(y - z\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \left(\left(y - z\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) \cdot a
double f(double x, double y, double z, double t, double a) {
        double r599398 = x;
        double r599399 = y;
        double r599400 = z;
        double r599401 = r599399 - r599400;
        double r599402 = t;
        double r599403 = r599402 - r599400;
        double r599404 = 1.0;
        double r599405 = r599403 + r599404;
        double r599406 = a;
        double r599407 = r599405 / r599406;
        double r599408 = r599401 / r599407;
        double r599409 = r599398 - r599408;
        return r599409;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r599410 = x;
        double r599411 = y;
        double r599412 = z;
        double r599413 = r599411 - r599412;
        double r599414 = 1.0;
        double r599415 = t;
        double r599416 = r599415 - r599412;
        double r599417 = 1.0;
        double r599418 = r599416 + r599417;
        double r599419 = r599414 / r599418;
        double r599420 = r599413 * r599419;
        double r599421 = a;
        double r599422 = r599420 * r599421;
        double r599423 = r599410 - r599422;
        return r599423;
}

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. Using strategy rm

  3. Applied div-inv2.2

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

  4. Applied associate-/r*0.3

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

  6. Applied div-inv0.3

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

  8. Applied div-inv0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1) a))))