Average Error: 6.5 → 2.1
Time: 27.3s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(i \cdot c\right)\right)\right)\]
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]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(i \cdot c\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r864901 = 2.0;
        double r864902 = x;
        double r864903 = y;
        double r864904 = r864902 * r864903;
        double r864905 = z;
        double r864906 = t;
        double r864907 = r864905 * r864906;
        double r864908 = r864904 + r864907;
        double r864909 = a;
        double r864910 = b;
        double r864911 = c;
        double r864912 = r864910 * r864911;
        double r864913 = r864909 + r864912;
        double r864914 = r864913 * r864911;
        double r864915 = i;
        double r864916 = r864914 * r864915;
        double r864917 = r864908 - r864916;
        double r864918 = r864901 * r864917;
        return r864918;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r864919 = 2.0;
        double r864920 = x;
        double r864921 = y;
        double r864922 = r864920 * r864921;
        double r864923 = z;
        double r864924 = t;
        double r864925 = r864923 * r864924;
        double r864926 = r864922 + r864925;
        double r864927 = a;
        double r864928 = b;
        double r864929 = c;
        double r864930 = r864928 * r864929;
        double r864931 = r864927 + r864930;
        double r864932 = cbrt(r864931);
        double r864933 = r864932 * r864932;
        double r864934 = i;
        double r864935 = r864934 * r864929;
        double r864936 = r864932 * r864935;
        double r864937 = r864933 * r864936;
        double r864938 = r864926 - r864937;
        double r864939 = r864919 * r864938;
        return r864939;
}

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

Original6.5
Target1.8
Herbie2.1
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.5

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

  6. Applied add-cube-cbrt2.1

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

  7. Applied associate-*l*2.1

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

  8. Final simplification2.1

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

Reproduce

herbie shell --seed 2020046 
(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))))