Average Error: 2.0 → 0.3
Time: 9.7s
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 r554574 = x;
        double r554575 = y;
        double r554576 = z;
        double r554577 = r554575 - r554576;
        double r554578 = t;
        double r554579 = r554578 - r554576;
        double r554580 = 1.0;
        double r554581 = r554579 + r554580;
        double r554582 = a;
        double r554583 = r554581 / r554582;
        double r554584 = r554577 / r554583;
        double r554585 = r554574 - r554584;
        return r554585;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r554586 = x;
        double r554587 = y;
        double r554588 = z;
        double r554589 = r554587 - r554588;
        double r554590 = t;
        double r554591 = r554590 - r554588;
        double r554592 = 1.0;
        double r554593 = r554591 + r554592;
        double r554594 = r554589 / r554593;
        double r554595 = 1.0;
        double r554596 = a;
        double r554597 = r554595 / r554596;
        double r554598 = r554594 / r554597;
        double r554599 = r554586 - r554598;
        return r554599;
}

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

Original2.0
Target0.3
Herbie0.3
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

    \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
  2. Using strategy rm

  3. Applied div-inv2.0

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

  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 2020089 +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))))