Average Error: 2.0 → 0.8
Time: 6.1s
Precision: 64
\[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\]
↓
\[x - \frac{\sqrt[3]{a} \cdot \sqrt[3]{a}}{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}} \cdot \frac{y - z}{\frac{\sqrt[3]{\left(t - z\right) + 1}}{\sqrt[3]{a}}}\]
x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}
↓
x - \frac{\sqrt[3]{a} \cdot \sqrt[3]{a}}{\sqrt[3]{\left(t - z\right) + 1} \cdot \sqrt[3]{\left(t - z\right) + 1}} \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 r617946 = x;
        double r617947 = y;
        double r617948 = z;
        double r617949 = r617947 - r617948;
        double r617950 = t;
        double r617951 = r617950 - r617948;
        double r617952 = 1.0;
        double r617953 = r617951 + r617952;
        double r617954 = a;
        double r617955 = r617953 / r617954;
        double r617956 = r617949 / r617955;
        double r617957 = r617946 - r617956;
        return r617957;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r617958 = x;
        double r617959 = a;
        double r617960 = cbrt(r617959);
        double r617961 = r617960 * r617960;
        double r617962 = t;
        double r617963 = z;
        double r617964 = r617962 - r617963;
        double r617965 = 1.0;
        double r617966 = r617964 + r617965;
        double r617967 = cbrt(r617966);
        double r617968 = r617967 * r617967;
        double r617969 = r617961 / r617968;
        double r617970 = y;
        double r617971 = r617970 - r617963;
        double r617972 = r617967 / r617960;
        double r617973 = r617971 / r617972;
        double r617974 = r617969 * r617973;
        double r617975 = r617958 - r617974;
        return r617975;
}

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. Simplified0.8

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

  9. Final simplification0.8

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

Reproduce

herbie shell --seed 2019354 
(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))))