Average Error: 2.2 → 0.3
Time: 4.3s
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 r558080 = x;
        double r558081 = y;
        double r558082 = z;
        double r558083 = r558081 - r558082;
        double r558084 = t;
        double r558085 = r558084 - r558082;
        double r558086 = 1.0;
        double r558087 = r558085 + r558086;
        double r558088 = a;
        double r558089 = r558087 / r558088;
        double r558090 = r558083 / r558089;
        double r558091 = r558080 - r558090;
        return r558091;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r558092 = x;
        double r558093 = y;
        double r558094 = z;
        double r558095 = r558093 - r558094;
        double r558096 = t;
        double r558097 = r558096 - r558094;
        double r558098 = 1.0;
        double r558099 = r558097 + r558098;
        double r558100 = r558095 / r558099;
        double r558101 = a;
        double r558102 = r558100 * r558101;
        double r558103 = r558092 - r558102;
        return r558103;
}

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

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

Derivation

  1. Initial program 2.2

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

  3. Applied associate-/r/0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))))