Average Error: 1.8 → 0.2
Time: 9.4s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[a \cdot \left(\left(z - y\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) + x\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
a \cdot \left(\left(z - y\right) \cdot \frac{1}{\left(t - z\right) + 1}\right) + x
double f(double x, double y, double z, double t, double a) {
        double r593016 = x;
        double r593017 = y;
        double r593018 = z;
        double r593019 = r593017 - r593018;
        double r593020 = t;
        double r593021 = r593020 - r593018;
        double r593022 = 1.0;
        double r593023 = r593021 + r593022;
        double r593024 = a;
        double r593025 = r593023 / r593024;
        double r593026 = r593019 / r593025;
        double r593027 = r593016 - r593026;
        return r593027;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r593028 = a;
        double r593029 = z;
        double r593030 = y;
        double r593031 = r593029 - r593030;
        double r593032 = 1.0;
        double r593033 = t;
        double r593034 = r593033 - r593029;
        double r593035 = 1.0;
        double r593036 = r593034 + r593035;
        double r593037 = r593032 / r593036;
        double r593038 = r593031 * r593037;
        double r593039 = r593028 * r593038;
        double r593040 = x;
        double r593041 = r593039 + r593040;
        return r593041;
}

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

Original1.8
Target0.2
Herbie0.2
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 1.8

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

  2. Simplified0.2

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

  4. Applied fma-udef0.2

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

  6. Applied div-inv0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 +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))))