Average Error: 6.1 → 1.9
Time: 22.4s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(z \cdot t - \left(i \cdot c\right) \cdot \left(b \cdot c + a\right)\right) + x \cdot y\right)\]
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(z \cdot t - \left(i \cdot c\right) \cdot \left(b \cdot c + a\right)\right) + x \cdot y\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r560766 = 2.0;
        double r560767 = x;
        double r560768 = y;
        double r560769 = r560767 * r560768;
        double r560770 = z;
        double r560771 = t;
        double r560772 = r560770 * r560771;
        double r560773 = r560769 + r560772;
        double r560774 = a;
        double r560775 = b;
        double r560776 = c;
        double r560777 = r560775 * r560776;
        double r560778 = r560774 + r560777;
        double r560779 = r560778 * r560776;
        double r560780 = i;
        double r560781 = r560779 * r560780;
        double r560782 = r560773 - r560781;
        double r560783 = r560766 * r560782;
        return r560783;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r560784 = 2.0;
        double r560785 = z;
        double r560786 = t;
        double r560787 = r560785 * r560786;
        double r560788 = i;
        double r560789 = c;
        double r560790 = r560788 * r560789;
        double r560791 = b;
        double r560792 = r560791 * r560789;
        double r560793 = a;
        double r560794 = r560792 + r560793;
        double r560795 = r560790 * r560794;
        double r560796 = r560787 - r560795;
        double r560797 = x;
        double r560798 = y;
        double r560799 = r560797 * r560798;
        double r560800 = r560796 + r560799;
        double r560801 = r560784 * r560800;
        return r560801;
}

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
Target1.9
Herbie1.9
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

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. Simplified6.1

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

  4. Applied associate--l+6.1

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

  5. Simplified1.9

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

  6. Final simplification1.9

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

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

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