Average Error: 2.2 → 0.3
Time: 10.2s
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 r708455 = x;
        double r708456 = y;
        double r708457 = z;
        double r708458 = r708456 - r708457;
        double r708459 = t;
        double r708460 = r708459 - r708457;
        double r708461 = 1.0;
        double r708462 = r708460 + r708461;
        double r708463 = a;
        double r708464 = r708462 / r708463;
        double r708465 = r708458 / r708464;
        double r708466 = r708455 - r708465;
        return r708466;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r708467 = x;
        double r708468 = y;
        double r708469 = z;
        double r708470 = r708468 - r708469;
        double r708471 = t;
        double r708472 = r708471 - r708469;
        double r708473 = 1.0;
        double r708474 = r708472 + r708473;
        double r708475 = r708470 / r708474;
        double r708476 = a;
        double r708477 = r708475 * r708476;
        double r708478 = r708467 - r708477;
        return r708478;
}

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

Derivation

  1. Initial program 2.2

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

  3. Applied *-un-lft-identity2.2

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

  4. Applied *-un-lft-identity2.2

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

  5. Applied times-frac2.2

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

  6. Applied *-un-lft-identity2.2

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

  7. Applied times-frac2.2

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

  8. Simplified2.2

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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))))