Average Error: 0.1 → 0.1
Time: 15.7s
Precision: 64
\[\left(x \cdot \log y - z\right) - y\]
↓
\[\left(\mathsf{fma}\left(x, 2 \cdot \log \left(\sqrt[3]{y}\right), x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - z\right) - y\]
\left(x \cdot \log y - z\right) - y
↓
\left(\mathsf{fma}\left(x, 2 \cdot \log \left(\sqrt[3]{y}\right), x \cdot \log \left({y}^{\frac{1}{3}}\right)\right) - z\right) - y
double f(double x, double y, double z) {
        double r24159 = x;
        double r24160 = y;
        double r24161 = log(r24160);
        double r24162 = r24159 * r24161;
        double r24163 = z;
        double r24164 = r24162 - r24163;
        double r24165 = r24164 - r24160;
        return r24165;
}
↓
double f(double x, double y, double z) {
        double r24166 = x;
        double r24167 = 2.0;
        double r24168 = y;
        double r24169 = cbrt(r24168);
        double r24170 = log(r24169);
        double r24171 = r24167 * r24170;
        double r24172 = 0.3333333333333333;
        double r24173 = pow(r24168, r24172);
        double r24174 = log(r24173);
        double r24175 = r24166 * r24174;
        double r24176 = fma(r24166, r24171, r24175);
        double r24177 = z;
        double r24178 = r24176 - r24177;
        double r24179 = r24178 - r24168;
        return r24179;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied fma-def0.1

    \[\leadsto \left(\color{blue}{\mathsf{fma}\left(x, 2 \cdot \log \left(\sqrt[3]{y}\right), x \cdot \log \left(\sqrt[3]{y}\right)\right)} - z\right) - y\]
  9. Using strategy rm

  10. Applied pow1/30.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson:$clogProbability from math-functions-0.1.5.2"
  :precision binary64
  (- (- (* x (log y)) z) y))