Average Error: 0.1 → 0.1
Time: 22.3s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(y + x\right) + \left(\left(-z\right) \cdot \left(\log t - 1\right) + \left(a - 0.5\right) \cdot b\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(y + x\right) + \left(\left(-z\right) \cdot \left(\log t - 1\right) + \left(a - 0.5\right) \cdot b\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r226715 = x;
        double r226716 = y;
        double r226717 = r226715 + r226716;
        double r226718 = z;
        double r226719 = r226717 + r226718;
        double r226720 = t;
        double r226721 = log(r226720);
        double r226722 = r226718 * r226721;
        double r226723 = r226719 - r226722;
        double r226724 = a;
        double r226725 = 0.5;
        double r226726 = r226724 - r226725;
        double r226727 = b;
        double r226728 = r226726 * r226727;
        double r226729 = r226723 + r226728;
        return r226729;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r226730 = y;
        double r226731 = x;
        double r226732 = r226730 + r226731;
        double r226733 = z;
        double r226734 = -r226733;
        double r226735 = t;
        double r226736 = log(r226735);
        double r226737 = 1.0;
        double r226738 = r226736 - r226737;
        double r226739 = r226734 * r226738;
        double r226740 = a;
        double r226741 = 0.5;
        double r226742 = r226740 - r226741;
        double r226743 = b;
        double r226744 = r226742 * r226743;
        double r226745 = r226739 + r226744;
        double r226746 = r226732 + r226745;
        return r226746;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.3
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
  2. Using strategy rm

  3. Applied associate--l+0.1

    \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b\]

  4. Applied associate-+l+0.1

    \[\leadsto \color{blue}{\left(x + y\right) + \left(\left(z - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\right)}\]

  5. Simplified0.1

    \[\leadsto \left(x + y\right) + \color{blue}{\left(\left(z - z \cdot \log t\right) + b \cdot \left(a - 0.5\right)\right)}\]

  6. Taylor expanded around -inf 64.0

    \[\leadsto \left(x + y\right) + \left(\color{blue}{-1 \cdot \left(\left(\log -1 - \left(\log \left(\frac{-1}{t}\right) + 1\right)\right) \cdot z\right)} + b \cdot \left(a - 0.5\right)\right)\]

  7. Simplified0.1

    \[\leadsto \left(x + y\right) + \left(\color{blue}{z \cdot \left(-\left(\left(0 + \log t\right) - 1\right)\right)} + b \cdot \left(a - 0.5\right)\right)\]

  8. Final simplification0.1

    \[\leadsto \left(y + x\right) + \left(\left(-z\right) \cdot \left(\log t - 1\right) + \left(a - 0.5\right) \cdot b\right)\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))