Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Average Error: 6.3 → 2.3

Time: 25.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r36138162 = 2.0;
        double r36138163 = x;
        double r36138164 = y;
        double r36138165 = r36138163 * r36138164;
        double r36138166 = z;
        double r36138167 = t;
        double r36138168 = r36138166 * r36138167;
        double r36138169 = r36138165 + r36138168;
        double r36138170 = a;
        double r36138171 = b;
        double r36138172 = c;
        double r36138173 = r36138171 * r36138172;
        double r36138174 = r36138170 + r36138173;
        double r36138175 = r36138174 * r36138172;
        double r36138176 = i;
        double r36138177 = r36138175 * r36138176;
        double r36138178 = r36138169 - r36138177;
        double r36138179 = r36138162 * r36138178;
        return r36138179;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r36138180 = 2.0;
        double r36138181 = y;
        double r36138182 = x;
        double r36138183 = r36138181 * r36138182;
        double r36138184 = z;
        double r36138185 = t;
        double r36138186 = r36138184 * r36138185;
        double r36138187 = r36138183 + r36138186;
        double r36138188 = a;
        double r36138189 = b;
        double r36138190 = c;
        double r36138191 = r36138189 * r36138190;
        double r36138192 = r36138188 + r36138191;
        double r36138193 = i;
        double r36138194 = r36138190 * r36138193;
        double r36138195 = r36138192 * r36138194;
        double r36138196 = cbrt(r36138195);
        double r36138197 = r36138196 * r36138196;
        double r36138198 = cbrt(r36138192);
        double r36138199 = r36138194 * r36138198;
        double r36138200 = cbrt(r36138199);
        double r36138201 = r36138198 * r36138198;
        double r36138202 = cbrt(r36138201);
        double r36138203 = r36138200 * r36138202;
        double r36138204 = r36138197 * r36138203;
        double r36138205 = r36138187 - r36138204;
        double r36138206 = r36138180 * r36138205;
        return r36138206;
}

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

Target

Original	6.3
Target	2.0
Herbie	2.3

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

Derivation

1. Initial program 6.3

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

3. Applied associate-*l* 2.0

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

5. Applied add-cube-cbrt 2.3

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

7. Applied add-cube-cbrt 2.3

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

8. Applied associate-*l* 2.3

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

10. Applied cbrt-prod 2.3

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

11. Final simplification 2.3

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

Reproduce

herbie shell --seed 2019192 
(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))))