Average Error: 0.1 → 0.1
Time: 11.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y}\right) \cdot \left(3 \cdot x\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left(\sqrt[3]{y}\right) \cdot \left(3 \cdot x\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r118106 = x;
        double r118107 = y;
        double r118108 = log(r118107);
        double r118109 = r118106 * r118108;
        double r118110 = r118109 - r118107;
        double r118111 = z;
        double r118112 = r118110 - r118111;
        double r118113 = t;
        double r118114 = log(r118113);
        double r118115 = r118112 + r118114;
        return r118115;
}
↓
double f(double x, double y, double z, double t) {
        double r118116 = y;
        double r118117 = cbrt(r118116);
        double r118118 = log(r118117);
        double r118119 = 3.0;
        double r118120 = x;
        double r118121 = r118119 * r118120;
        double r118122 = r118118 * r118121;
        double r118123 = r118122 - r118116;
        double r118124 = z;
        double r118125 = r118123 - r118124;
        double r118126 = t;
        double r118127 = log(r118126);
        double r118128 = r118125 + r118127;
        return r118128;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

    \[\leadsto \left(\left(\left(\color{blue}{\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t\]

  7. Taylor expanded around 0 0.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))