Average Error: 6.2 → 2.0
Time: 7.5s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{c \cdot i}\right)\right)\]
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(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{c \cdot i}\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r777779 = 2.0;
        double r777780 = x;
        double r777781 = y;
        double r777782 = r777780 * r777781;
        double r777783 = z;
        double r777784 = t;
        double r777785 = r777783 * r777784;
        double r777786 = r777782 + r777785;
        double r777787 = a;
        double r777788 = b;
        double r777789 = c;
        double r777790 = r777788 * r777789;
        double r777791 = r777787 + r777790;
        double r777792 = r777791 * r777789;
        double r777793 = i;
        double r777794 = r777792 * r777793;
        double r777795 = r777786 - r777794;
        double r777796 = r777779 * r777795;
        return r777796;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r777797 = 2.0;
        double r777798 = x;
        double r777799 = y;
        double r777800 = r777798 * r777799;
        double r777801 = z;
        double r777802 = t;
        double r777803 = r777801 * r777802;
        double r777804 = r777800 + r777803;
        double r777805 = a;
        double r777806 = b;
        double r777807 = c;
        double r777808 = r777806 * r777807;
        double r777809 = r777805 + r777808;
        double r777810 = i;
        double r777811 = r777807 * r777810;
        double r777812 = r777809 * r777811;
        double r777813 = cbrt(r777812);
        double r777814 = r777813 * r777813;
        double r777815 = cbrt(r777809);
        double r777816 = cbrt(r777811);
        double r777817 = r777815 * r777816;
        double r777818 = r777814 * r777817;
        double r777819 = r777804 - r777818;
        double r777820 = r777797 * r777819;
        return r777820;
}

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

Original6.2
Target1.7
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 6.2

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

  3. Applied associate-*l*1.7

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

  5. Applied add-cube-cbrt2.1

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

  7. Applied cbrt-prod2.0

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

  8. Final simplification2.0

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{c \cdot i}\right)\right)\]

Reproduce

herbie shell --seed 2020025 
(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))))