Average Error: 6.6 → 2.0
Time: 18.3s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\]
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r446751 = 2.0;
        double r446752 = x;
        double r446753 = y;
        double r446754 = r446752 * r446753;
        double r446755 = z;
        double r446756 = t;
        double r446757 = r446755 * r446756;
        double r446758 = r446754 + r446757;
        double r446759 = a;
        double r446760 = b;
        double r446761 = c;
        double r446762 = r446760 * r446761;
        double r446763 = r446759 + r446762;
        double r446764 = r446763 * r446761;
        double r446765 = i;
        double r446766 = r446764 * r446765;
        double r446767 = r446758 - r446766;
        double r446768 = r446751 * r446767;
        return r446768;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r446769 = 2.0;
        double r446770 = x;
        double r446771 = y;
        double r446772 = r446770 * r446771;
        double r446773 = z;
        double r446774 = t;
        double r446775 = r446773 * r446774;
        double r446776 = r446772 + r446775;
        double r446777 = a;
        double r446778 = b;
        double r446779 = c;
        double r446780 = r446778 * r446779;
        double r446781 = r446777 + r446780;
        double r446782 = i;
        double r446783 = r446782 * r446779;
        double r446784 = r446781 * r446783;
        double r446785 = r446776 - r446784;
        double r446786 = r446769 * r446785;
        return r446786;
}

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

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.6
Target2.0
Herbie2.0
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.6

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

  3. Applied associate-*l*2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

  4. Simplified2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \color{blue}{\left(i \cdot c\right)}\right)\]

  5. Final simplification2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))