Average Error: 6.1 → 1.8
Time: 21.8s
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 r817678 = 2.0;
        double r817679 = x;
        double r817680 = y;
        double r817681 = r817679 * r817680;
        double r817682 = z;
        double r817683 = t;
        double r817684 = r817682 * r817683;
        double r817685 = r817681 + r817684;
        double r817686 = a;
        double r817687 = b;
        double r817688 = c;
        double r817689 = r817687 * r817688;
        double r817690 = r817686 + r817689;
        double r817691 = r817690 * r817688;
        double r817692 = i;
        double r817693 = r817691 * r817692;
        double r817694 = r817685 - r817693;
        double r817695 = r817678 * r817694;
        return r817695;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r817696 = 2.0;
        double r817697 = x;
        double r817698 = y;
        double r817699 = r817697 * r817698;
        double r817700 = z;
        double r817701 = t;
        double r817702 = r817700 * r817701;
        double r817703 = r817699 + r817702;
        double r817704 = a;
        double r817705 = b;
        double r817706 = c;
        double r817707 = r817705 * r817706;
        double r817708 = r817704 + r817707;
        double r817709 = i;
        double r817710 = r817709 * r817706;
        double r817711 = r817708 * r817710;
        double r817712 = r817703 - r817711;
        double r817713 = r817696 * r817712;
        return r817713;
}

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

Original6.1
Target1.8
Herbie1.8
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.1

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

  3. Applied associate-*l*1.8

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

  4. Simplified1.8

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

  5. Final simplification1.8

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

Reproduce

herbie shell --seed 2020045 
(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))))