Average Error: 2.2 → 0.2
Time: 20.8s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[\frac{a}{\frac{\left(t - z\right) + 1}{z - y}} + x\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
\frac{a}{\frac{\left(t - z\right) + 1}{z - y}} + x
double f(double x, double y, double z, double t, double a) {
        double r463091 = x;
        double r463092 = y;
        double r463093 = z;
        double r463094 = r463092 - r463093;
        double r463095 = t;
        double r463096 = r463095 - r463093;
        double r463097 = 1.0;
        double r463098 = r463096 + r463097;
        double r463099 = a;
        double r463100 = r463098 / r463099;
        double r463101 = r463094 / r463100;
        double r463102 = r463091 - r463101;
        return r463102;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r463103 = a;
        double r463104 = t;
        double r463105 = z;
        double r463106 = r463104 - r463105;
        double r463107 = 1.0;
        double r463108 = r463106 + r463107;
        double r463109 = y;
        double r463110 = r463105 - r463109;
        double r463111 = r463108 / r463110;
        double r463112 = r463103 / r463111;
        double r463113 = x;
        double r463114 = r463112 + r463113;
        return r463114;
}

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

Derivation

  1. Initial program 2.2

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

  2. Simplified0.2

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

  4. Applied clear-num0.2

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

  6. Applied fma-udef0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 +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))))