3.9.2 imaginary part (p56)

Average Error: 0 → 0

Time: 30.0s

Precision: 64

Math

\[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

↓

\[\Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]

C

double f() {
        double r1393180 = 1.0;
        double r1393181 = -r1393180;
        double r1393182 = 2.0;
        double r1393183 = r1393181 / r1393182;
        double r1393184 = 3.0;
        double r1393185 = sqrt(r1393184);
        double r1393186 = r1393185 / r1393182;
        double r1393187 = /* ERROR: no complex support in C */;
        double r1393188 = r1393187 * r1393187;
        double r1393189 = r1393188 * r1393187;
        double r1393190 = r1393189 * r1393187;
        double r1393191 = -r1393182;
        double r1393192 = 0.0;
        double r1393193 = /* ERROR: no complex support in C */;
        double r1393194 = r1393193 * r1393187;
        double r1393195 = r1393194 * r1393187;
        double r1393196 = r1393195 * r1393187;
        double r1393197 = r1393190 + r1393196;
        double r1393198 = 5.0;
        double r1393199 = /* ERROR: no complex support in C */;
        double r1393200 = r1393199 * r1393187;
        double r1393201 = r1393200 * r1393187;
        double r1393202 = r1393197 + r1393201;
        double r1393203 = 4.0;
        double r1393204 = /* ERROR: no complex support in C */;
        double r1393205 = r1393204 * r1393187;
        double r1393206 = r1393202 + r1393205;
        double r1393207 = 7.0;
        double r1393208 = /* ERROR: no complex support in C */;
        double r1393209 = r1393206 + r1393208;
        double r1393210 = /* ERROR: no complex support in C */;
        return r1393210;
}

↓

double f() {
        double r1393211 = 5.0;
        double r1393212 = 3.0;
        double r1393213 = sqrt(r1393212);
        double r1393214 = 2.0;
        double r1393215 = r1393213 / r1393214;
        double r1393216 = 4.0;
        double r1393217 = r1393215 * r1393216;
        double r1393218 = /* ERROR: no complex support in C */;
        double r1393219 = 0.25;
        double r1393220 = r1393215 * r1393215;
        double r1393221 = r1393219 - r1393220;
        double r1393222 = -r1393213;
        double r1393223 = r1393222 / r1393214;
        double r1393224 = /* ERROR: no complex support in C */;
        double r1393225 = 6.0;
        double r1393226 = -2.0;
        double r1393227 = r1393226 * r1393213;
        double r1393228 = r1393227 / r1393214;
        double r1393229 = /* ERROR: no complex support in C */;
        double r1393230 = r1393229 + r1393224;
        double r1393231 = r1393224 * r1393230;
        double r1393232 = r1393218 + r1393231;
        double r1393233 = /* ERROR: no complex support in C */;
        return r1393233;
}

Derivation

1. Initial program 0

   \[\Im(\left(\left(\left(\left(\left(\left(\left(\left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) + \left(\left(\left(\left(\left(-2\right) + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(\left(5 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(\left(4 + 0 i\right) \cdot \left(\frac{-1}{2} + \frac{\sqrt{3}}{2} i\right)\right)\right) + \left(7 + 0 i\right)\right))\]

2. Simplified 0

   \[\leadsto \color{blue}{\Im(\left(\left(5 + 4 \cdot \frac{\sqrt{3}}{2} i\right) + \left(\left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right) \cdot \left(\left(6 + \frac{\sqrt{3} \cdot -2}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{\sqrt{3}}{2} \cdot -1 i\right)\right)\right)\right))}\]

3. Final simplification 0

   \[\leadsto \Im(\left(\left(5 + \frac{\sqrt{3}}{2} \cdot 4 i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right) \cdot \left(\left(6 + \frac{-2 \cdot \sqrt{3}}{2} i\right) + \left(\left(\frac{1}{4} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}\right) + \frac{-\sqrt{3}}{2} i\right)\right)\right))\]

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore ()
  :name "3.9.2 imaginary part (p56)"
  (im (+.c (+.c (+.c (+.c (*.c (*.c (*.c (complex (/ (- 1) 2) (/ (sqrt 3) 2)) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (*.c (*.c (*.c (complex (- 2) 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (*.c (complex 5 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2))) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (*.c (complex 4 0) (complex (/ (- 1) 2) (/ (sqrt 3) 2)))) (complex 7 0))))