Average Error: 2.0 → 0.3
Time: 17.6s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x + \frac{z - y}{\left(t + 1\right) - z} \cdot a\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x + \frac{z - y}{\left(t + 1\right) - z} \cdot a
double f(double x, double y, double z, double t, double a) {
        double r462517 = x;
        double r462518 = y;
        double r462519 = z;
        double r462520 = r462518 - r462519;
        double r462521 = t;
        double r462522 = r462521 - r462519;
        double r462523 = 1.0;
        double r462524 = r462522 + r462523;
        double r462525 = a;
        double r462526 = r462524 / r462525;
        double r462527 = r462520 / r462526;
        double r462528 = r462517 - r462527;
        return r462528;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r462529 = x;
        double r462530 = z;
        double r462531 = y;
        double r462532 = r462530 - r462531;
        double r462533 = t;
        double r462534 = 1.0;
        double r462535 = r462533 + r462534;
        double r462536 = r462535 - r462530;
        double r462537 = r462532 / r462536;
        double r462538 = a;
        double r462539 = r462537 * r462538;
        double r462540 = r462529 + r462539;
        return r462540;
}

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. Simplified2.0

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

  4. Applied associate-/r/0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"

  :herbie-target
  (- x (* (/ (- y z) (+ (- t z) 1.0)) a))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))