Average Error: 1.9 → 0.2
Time: 24.0s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{\left(t - z\right) + 1} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r36832041 = x;
        double r36832042 = y;
        double r36832043 = z;
        double r36832044 = r36832042 - r36832043;
        double r36832045 = t;
        double r36832046 = r36832045 - r36832043;
        double r36832047 = 1.0;
        double r36832048 = r36832046 + r36832047;
        double r36832049 = a;
        double r36832050 = r36832048 / r36832049;
        double r36832051 = r36832044 / r36832050;
        double r36832052 = r36832041 - r36832051;
        return r36832052;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r36832053 = x;
        double r36832054 = y;
        double r36832055 = z;
        double r36832056 = r36832054 - r36832055;
        double r36832057 = t;
        double r36832058 = r36832057 - r36832055;
        double r36832059 = 1.0;
        double r36832060 = r36832058 + r36832059;
        double r36832061 = r36832056 / r36832060;
        double r36832062 = a;
        double r36832063 = r36832061 * r36832062;
        double r36832064 = r36832053 - r36832063;
        return r36832064;
}

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

Original1.9
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.9

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

  3. Applied associate-/r/0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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))))