Average Error: 2.1 → 0.3
Time: 9.9s
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 r612962 = x;
        double r612963 = y;
        double r612964 = z;
        double r612965 = r612963 - r612964;
        double r612966 = t;
        double r612967 = r612966 - r612964;
        double r612968 = 1.0;
        double r612969 = r612967 + r612968;
        double r612970 = a;
        double r612971 = r612969 / r612970;
        double r612972 = r612965 / r612971;
        double r612973 = r612962 - r612972;
        return r612973;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r612974 = x;
        double r612975 = y;
        double r612976 = z;
        double r612977 = r612975 - r612976;
        double r612978 = 1.0;
        double r612979 = t;
        double r612980 = r612979 - r612976;
        double r612981 = 1.0;
        double r612982 = r612980 + r612981;
        double r612983 = r612978 / r612982;
        double r612984 = r612977 * r612983;
        double r612985 = a;
        double r612986 = r612984 * r612985;
        double r612987 = r612974 - r612986;
        return r612987;
}

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 +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))))