Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(a - 0.5\right) \cdot b + \left(\left(\left(y + z\right) - \log t \cdot z\right) + x\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(a - 0.5\right) \cdot b + \left(\left(\left(y + z\right) - \log t \cdot z\right) + x\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r18352544 = x;
        double r18352545 = y;
        double r18352546 = r18352544 + r18352545;
        double r18352547 = z;
        double r18352548 = r18352546 + r18352547;
        double r18352549 = t;
        double r18352550 = log(r18352549);
        double r18352551 = r18352547 * r18352550;
        double r18352552 = r18352548 - r18352551;
        double r18352553 = a;
        double r18352554 = 0.5;
        double r18352555 = r18352553 - r18352554;
        double r18352556 = b;
        double r18352557 = r18352555 * r18352556;
        double r18352558 = r18352552 + r18352557;
        return r18352558;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r18352559 = a;
        double r18352560 = 0.5;
        double r18352561 = r18352559 - r18352560;
        double r18352562 = b;
        double r18352563 = r18352561 * r18352562;
        double r18352564 = y;
        double r18352565 = z;
        double r18352566 = r18352564 + r18352565;
        double r18352567 = t;
        double r18352568 = log(r18352567);
        double r18352569 = r18352568 * r18352565;
        double r18352570 = r18352566 - r18352569;
        double r18352571 = x;
        double r18352572 = r18352570 + r18352571;
        double r18352573 = r18352563 + r18352572;
        return r18352573;
}

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
Target0.4
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. Taylor expanded around inf 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(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)))