Average Error: 1.8 → 0.2
Time: 4.9s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{y - z}{\left(t - z\right) + 1} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r773484 = x;
        double r773485 = y;
        double r773486 = z;
        double r773487 = r773485 - r773486;
        double r773488 = t;
        double r773489 = r773488 - r773486;
        double r773490 = 1.0;
        double r773491 = r773489 + r773490;
        double r773492 = a;
        double r773493 = r773491 / r773492;
        double r773494 = r773487 / r773493;
        double r773495 = r773484 - r773494;
        return r773495;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r773496 = x;
        double r773497 = y;
        double r773498 = z;
        double r773499 = r773497 - r773498;
        double r773500 = t;
        double r773501 = r773500 - r773498;
        double r773502 = 1.0;
        double r773503 = r773501 + r773502;
        double r773504 = r773499 / r773503;
        double r773505 = a;
        double r773506 = r773504 * r773505;
        double r773507 = r773496 - r773506;
        return r773507;
}

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. Using strategy rm

  3. Applied associate-/r/0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019362 +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))))