Average Error: 9.6 → 0.4
Time: 1.0m
Precision: 64
\[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]
↓
\[\left(z \cdot \left(\left(\log 1 - 1 \cdot y\right) - \frac{\frac{1}{2}}{\frac{1}{y} \cdot \frac{1}{y}}\right) + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - t\]
\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t
↓
\left(z \cdot \left(\left(\log 1 - 1 \cdot y\right) - \frac{\frac{1}{2}}{\frac{1}{y} \cdot \frac{1}{y}}\right) + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) - t
double f(double x, double y, double z, double t) {
        double r20713101 = x;
        double r20713102 = y;
        double r20713103 = log(r20713102);
        double r20713104 = r20713101 * r20713103;
        double r20713105 = z;
        double r20713106 = 1.0;
        double r20713107 = r20713106 - r20713102;
        double r20713108 = log(r20713107);
        double r20713109 = r20713105 * r20713108;
        double r20713110 = r20713104 + r20713109;
        double r20713111 = t;
        double r20713112 = r20713110 - r20713111;
        return r20713112;
}
↓
double f(double x, double y, double z, double t) {
        double r20713113 = z;
        double r20713114 = 1.0;
        double r20713115 = log(r20713114);
        double r20713116 = y;
        double r20713117 = r20713114 * r20713116;
        double r20713118 = r20713115 - r20713117;
        double r20713119 = 0.5;
        double r20713120 = r20713114 / r20713116;
        double r20713121 = r20713120 * r20713120;
        double r20713122 = r20713119 / r20713121;
        double r20713123 = r20713118 - r20713122;
        double r20713124 = r20713113 * r20713123;
        double r20713125 = cbrt(r20713116);
        double r20713126 = log(r20713125);
        double r20713127 = r20713126 + r20713126;
        double r20713128 = x;
        double r20713129 = r20713127 * r20713128;
        double r20713130 = 0.3333333333333333;
        double r20713131 = pow(r20713116, r20713130);
        double r20713132 = log(r20713131);
        double r20713133 = r20713128 * r20713132;
        double r20713134 = r20713129 + r20713133;
        double r20713135 = r20713124 + r20713134;
        double r20713136 = t;
        double r20713137 = r20713135 - r20713136;
        return r20713137;
}

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

Target

Original9.6
Target0.3
Herbie0.4
\[\left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{0.3333333333333333148296162562473909929395}{1 \cdot \left(1 \cdot 1\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right)\]

Derivation

  1. Initial program 9.6

    \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t\]

  2. Taylor expanded around 0 0.4

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

  3. Simplified0.4

    \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\left(\log 1 - 1 \cdot y\right) - \frac{\frac{1}{2}}{\frac{1}{y} \cdot \frac{1}{y}}\right)}\right) - t\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.4

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

  6. Applied log-prod0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  10. Applied pow1/30.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"

  :herbie-target
  (- (* (- z) (+ (+ (* 0.5 (* y y)) y) (* (/ 0.3333333333333333 (* 1.0 (* 1.0 1.0))) (* y (* y y))))) (- t (* x (log y))))

  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))