Average Error: 2.0 → 0.8
Time: 7.8s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{1}{\frac{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \frac{y - z}{\frac{\sqrt[3]{\left(t - z\right) + 1}}{\sqrt[3]{a}}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{1}{\frac{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \frac{y - z}{\frac{\sqrt[3]{\left(t - z\right) + 1}}{\sqrt[3]{a}}}
double f(double x, double y, double z, double t, double a) {
        double r489335 = x;
        double r489336 = y;
        double r489337 = z;
        double r489338 = r489336 - r489337;
        double r489339 = t;
        double r489340 = r489339 - r489337;
        double r489341 = 1.0;
        double r489342 = r489340 + r489341;
        double r489343 = a;
        double r489344 = r489342 / r489343;
        double r489345 = r489338 / r489344;
        double r489346 = r489335 - r489345;
        return r489346;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r489347 = x;
        double r489348 = 1.0;
        double r489349 = t;
        double r489350 = z;
        double r489351 = r489349 - r489350;
        double r489352 = 1.0;
        double r489353 = r489351 + r489352;
        double r489354 = cbrt(r489353);
        double r489355 = r489354 * r489354;
        double r489356 = a;
        double r489357 = cbrt(r489356);
        double r489358 = r489357 * r489357;
        double r489359 = r489355 / r489358;
        double r489360 = r489348 / r489359;
        double r489361 = y;
        double r489362 = r489361 - r489350;
        double r489363 = r489354 / r489357;
        double r489364 = r489362 / r489363;
        double r489365 = r489360 * r489364;
        double r489366 = r489347 - r489365;
        return r489366;
}

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
Target0.2
Herbie0.8
\[x - \frac{y - z}{\left(t - z\right) + 1} \cdot a\]

Derivation

  1. Initial program 2.0

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

  3. Applied add-cube-cbrt2.5

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

  4. Applied add-cube-cbrt2.6

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

  5. Applied times-frac2.6

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

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

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

  7. Applied times-frac0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019354 +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))))