Average Error: 2.0 → 0.5
Time: 6.0s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1}} \cdot a\right)\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1}} \cdot a\right)
double f(double x, double y, double z, double t, double a) {
        double r751381 = x;
        double r751382 = y;
        double r751383 = z;
        double r751384 = r751382 - r751383;
        double r751385 = t;
        double r751386 = r751385 - r751383;
        double r751387 = 1.0;
        double r751388 = r751386 + r751387;
        double r751389 = a;
        double r751390 = r751388 / r751389;
        double r751391 = r751384 / r751390;
        double r751392 = r751381 - r751391;
        return r751392;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r751393 = x;
        double r751394 = y;
        double r751395 = z;
        double r751396 = r751394 - r751395;
        double r751397 = cbrt(r751396);
        double r751398 = r751397 * r751397;
        double r751399 = t;
        double r751400 = r751399 - r751395;
        double r751401 = 1.0;
        double r751402 = r751400 + r751401;
        double r751403 = cbrt(r751402);
        double r751404 = r751403 * r751403;
        double r751405 = r751398 / r751404;
        double r751406 = r751397 / r751403;
        double r751407 = a;
        double r751408 = r751406 * r751407;
        double r751409 = r751405 * r751408;
        double r751410 = r751393 - r751409;
        return r751410;
}

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
Herbie0.5
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

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

  3. Applied associate-/r/0.3

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

  5. Applied add-cube-cbrt0.7

    \[\leadsto x - \frac{y - z}{\color{blue}{\left(\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}\right) \cdot \sqrt[3]{\left(t - z\right) + 1}}} \cdot a\]

  6. Applied add-cube-cbrt0.7

    \[\leadsto x - \frac{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}}{\left(\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}\right) \cdot \sqrt[3]{\left(t - z\right) + 1}} \cdot a\]

  7. Applied times-frac0.7

    \[\leadsto x - \color{blue}{\left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1}}\right)} \cdot a\]

  8. Applied associate-*l*0.5

    \[\leadsto x - \color{blue}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{\left(t - z\right) + 1}} \cdot a\right)}\]

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2020089 
(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))))