Average Error: 0.1 → 0.1
Time: 19.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r94116 = x;
        double r94117 = y;
        double r94118 = log(r94117);
        double r94119 = r94116 * r94118;
        double r94120 = r94119 - r94117;
        double r94121 = z;
        double r94122 = r94120 - r94121;
        double r94123 = t;
        double r94124 = log(r94123);
        double r94125 = r94122 + r94124;
        return r94125;
}
↓
double f(double x, double y, double z, double t) {
        double r94126 = x;
        double r94127 = 2.0;
        double r94128 = y;
        double r94129 = cbrt(r94128);
        double r94130 = log(r94129);
        double r94131 = r94127 * r94130;
        double r94132 = r94126 * r94131;
        double r94133 = 0.3333333333333333;
        double r94134 = pow(r94128, r94133);
        double r94135 = log(r94134);
        double r94136 = r94126 * r94135;
        double r94137 = r94132 + r94136;
        double r94138 = r94137 - r94128;
        double r94139 = z;
        double r94140 = r94138 - r94139;
        double r94141 = t;
        double r94142 = log(r94141);
        double r94143 = r94140 + r94142;
        return r94143;
}

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

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

  8. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left({y}^{\frac{1}{3}}\right)}\right) - y\right) - z\right) + \log t\]

  9. Final simplification0.1

    \[\leadsto \left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - y\right) - z\right) + \log t\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(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)))