Average Error: 2.1 → 0.3
Time: 4.9s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\frac{y - z}{\left(t - z\right) + 1}}{\frac{1}{a}}
double f(double x, double y, double z, double t, double a) {
        double r610987 = x;
        double r610988 = y;
        double r610989 = z;
        double r610990 = r610988 - r610989;
        double r610991 = t;
        double r610992 = r610991 - r610989;
        double r610993 = 1.0;
        double r610994 = r610992 + r610993;
        double r610995 = a;
        double r610996 = r610994 / r610995;
        double r610997 = r610990 / r610996;
        double r610998 = r610987 - r610997;
        return r610998;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r610999 = x;
        double r611000 = y;
        double r611001 = z;
        double r611002 = r611000 - r611001;
        double r611003 = t;
        double r611004 = r611003 - r611001;
        double r611005 = 1.0;
        double r611006 = r611004 + r611005;
        double r611007 = r611002 / r611006;
        double r611008 = 1.0;
        double r611009 = a;
        double r611010 = r611008 / r611009;
        double r611011 = r611007 / r611010;
        double r611012 = r610999 - r611011;
        return r611012;
}

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
Target0.3
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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019353 +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))))