Average Error: 2.2 → 0.3
Time: 11.6s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[a \cdot \frac{z - y}{\left(t - z\right) + 1} + x\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
a \cdot \frac{z - y}{\left(t - z\right) + 1} + x
double f(double x, double y, double z, double t, double a) {
        double r638120 = x;
        double r638121 = y;
        double r638122 = z;
        double r638123 = r638121 - r638122;
        double r638124 = t;
        double r638125 = r638124 - r638122;
        double r638126 = 1.0;
        double r638127 = r638125 + r638126;
        double r638128 = a;
        double r638129 = r638127 / r638128;
        double r638130 = r638123 / r638129;
        double r638131 = r638120 - r638130;
        return r638131;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r638132 = a;
        double r638133 = z;
        double r638134 = y;
        double r638135 = r638133 - r638134;
        double r638136 = t;
        double r638137 = r638136 - r638133;
        double r638138 = 1.0;
        double r638139 = r638137 + r638138;
        double r638140 = r638135 / r638139;
        double r638141 = r638132 * r638140;
        double r638142 = x;
        double r638143 = r638141 + r638142;
        return r638143;
}

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. Simplified0.3

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

  4. Applied fma-udef0.3

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

  5. Final simplification0.3

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

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))))