Average Error: 2.0 → 0.4
Time: 19.3s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
↓
\[x - \frac{1}{\frac{1.0 + \left(t - z\right)}{y - z}} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}
↓
x - \frac{1}{\frac{1.0 + \left(t - z\right)}{y - z}} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r29247201 = x;
        double r29247202 = y;
        double r29247203 = z;
        double r29247204 = r29247202 - r29247203;
        double r29247205 = t;
        double r29247206 = r29247205 - r29247203;
        double r29247207 = 1.0;
        double r29247208 = r29247206 + r29247207;
        double r29247209 = a;
        double r29247210 = r29247208 / r29247209;
        double r29247211 = r29247204 / r29247210;
        double r29247212 = r29247201 - r29247211;
        return r29247212;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r29247213 = x;
        double r29247214 = 1.0;
        double r29247215 = 1.0;
        double r29247216 = t;
        double r29247217 = z;
        double r29247218 = r29247216 - r29247217;
        double r29247219 = r29247215 + r29247218;
        double r29247220 = y;
        double r29247221 = r29247220 - r29247217;
        double r29247222 = r29247219 / r29247221;
        double r29247223 = r29247214 / r29247222;
        double r29247224 = a;
        double r29247225 = r29247223 * r29247224;
        double r29247226 = r29247213 - r29247225;
        return r29247226;
}

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

Original2.0
Target0.3
Herbie0.4
\[x - \frac{y - z}{\left(t - z\right) + 1.0} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1.0}{a}}\]
  2. Using strategy rm

  3. Applied associate-/r/0.3

    \[\leadsto x - \color{blue}{\frac{y - z}{\left(t - z\right) + 1.0} \cdot a}\]
  4. Using strategy rm

  5. Applied clear-num0.4

    \[\leadsto x - \color{blue}{\frac{1}{\frac{\left(t - z\right) + 1.0}{y - z}}} \cdot a\]

  6. Final simplification0.4

    \[\leadsto x - \frac{1}{\frac{1.0 + \left(t - z\right)}{y - z}} \cdot a\]

Reproduce

herbie shell --seed 2019164 
(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))))