Average Error: 6.2 → 2.0
Time: 20.3s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt[3]{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{c \cdot i}\right)\right)\]
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 r3854 = 2.0;
        double r3855 = x;
        double r3856 = y;
        double r3857 = r3855 * r3856;
        double r3858 = z;
        double r3859 = t;
        double r3860 = r3858 * r3859;
        double r3861 = r3857 + r3860;
        double r3862 = a;
        double r3863 = b;
        double r3864 = c;
        double r3865 = r3863 * r3864;
        double r3866 = r3862 + r3865;
        double r3867 = r3866 * r3864;
        double r3868 = i;
        double r3869 = r3867 * r3868;
        double r3870 = r3861 - r3869;
        double r3871 = r3854 * r3870;
        return r3871;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3872 = 2.0;
        double r3873 = x;
        double r3874 = y;
        double r3875 = r3873 * r3874;
        double r3876 = z;
        double r3877 = t;
        double r3878 = r3876 * r3877;
        double r3879 = r3875 + r3878;
        double r3880 = a;
        double r3881 = b;
        double r3882 = c;
        double r3883 = r3881 * r3882;
        double r3884 = r3880 + r3883;
        double r3885 = i;
        double r3886 = r3882 * r3885;
        double r3887 = r3884 * r3886;
        double r3888 = cbrt(r3887);
        double r3889 = r3888 * r3888;
        double r3890 = cbrt(r3884);
        double r3891 = cbrt(r3886);
        double r3892 = r3890 * r3891;
        double r3893 = r3889 * r3892;
        double r3894 = r3879 - r3893;
        double r3895 = r3872 * r3894;
        return r3895;
}

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))))