Quadratic roots, wide range

Percentage Accurate: 18.3% → 97.6%

Time: 18.8s

Alternatives: 8

Speedup: 29.0×

Specification

\[\left(\left(4.930380657631324 \cdot 10^{-32} < a \land a < 2.028240960365167 \cdot 10^{+31}\right) \land \left(4.930380657631324 \cdot 10^{-32} < b \land b < 2.028240960365167 \cdot 10^{+31}\right)\right) \land \left(4.930380657631324 \cdot 10^{-32} < c \land c < 2.028240960365167 \cdot 10^{+31}\right)\]

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - ((4.0d0 * a) * c)))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 18.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - ((4.0d0 * a) * c)))) / (2.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(4.0 * a) * c)))) / Float64(2.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((4.0 * a) * c)))) / (2.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(4.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(2 \cdot \frac{\left({c}^{4} \cdot {a}^{3}\right) \cdot -2.5}{{b}^{6}} - a \cdot {\left(\frac{-c}{b}\right)}^{2}\right) - c\right)}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/
  (fma
   -2.0
   (* (pow a 2.0) (/ (pow c 3.0) (pow b 4.0)))
   (-
    (-
     (* 2.0 (/ (* (* (pow c 4.0) (pow a 3.0)) -2.5) (pow b 6.0)))
     (* a (pow (/ (- c) b) 2.0)))
    c))
  b))

C

double code(double a, double b, double c) {
	return fma(-2.0, (pow(a, 2.0) * (pow(c, 3.0) / pow(b, 4.0))), (((2.0 * (((pow(c, 4.0) * pow(a, 3.0)) * -2.5) / pow(b, 6.0))) - (a * pow((-c / b), 2.0))) - c)) / b;
}

Julia

function code(a, b, c)
	return Float64(fma(-2.0, Float64((a ^ 2.0) * Float64((c ^ 3.0) / (b ^ 4.0))), Float64(Float64(Float64(2.0 * Float64(Float64(Float64((c ^ 4.0) * (a ^ 3.0)) * -2.5) / (b ^ 6.0))) - Float64(a * (Float64(Float64(-c) / b) ^ 2.0))) - c)) / b)
end

Wolfram

code[a_, b_, c_] := N[(N[(-2.0 * N[(N[Power[a, 2.0], $MachinePrecision] * N[(N[Power[c, 3.0], $MachinePrecision] / N[Power[b, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(2.0 * N[(N[(N[(N[Power[c, 4.0], $MachinePrecision] * N[Power[a, 3.0], $MachinePrecision]), $MachinePrecision] * -2.5), $MachinePrecision] / N[Power[b, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[Power[N[((-c) / b), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)} - b}{a \cdot 2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. add-sqr-sqrt 16.0%

      \[\leadsto \frac{\color{blue}{\sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}} \cdot \sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}} - b}{a \cdot 2} \]

   2. pow2 16.0%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}\right)}^{2}} - b}{a \cdot 2} \]

   3. pow1/2 16.0%

      \[\leadsto \frac{{\left(\sqrt{\color{blue}{{\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{0.5}}}\right)}^{2} - b}{a \cdot 2} \]

   4. sqrt-pow1 16.0%

      \[\leadsto \frac{{\color{blue}{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} - b}{a \cdot 2} \]

   5. pow2 16.0%

      \[\leadsto \frac{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, \color{blue}{{b}^{2}}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2} - b}{a \cdot 2} \]

   6. metadata-eval 16.0%

      \[\leadsto \frac{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{\color{blue}{0.25}}\right)}^{2} - b}{a \cdot 2} \]

6. Applied egg-rr 16.0%

   \[\leadsto \frac{\color{blue}{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{0.25}\right)}^{2}} - b}{a \cdot 2} \]
7. Step-by-step derivation

   1. pow-pow 15.4%

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{\left(0.25 \cdot 2\right)}} - b}{a \cdot 2} \]

   2. metadata-eval 15.4%

      \[\leadsto \frac{{\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{\color{blue}{0.5}} - b}{a \cdot 2} \]

   3. pow1/2 15.4%

      \[\leadsto \frac{\color{blue}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)}} - b}{a \cdot 2} \]

   4. flip-- 15.4%

      \[\leadsto \frac{\color{blue}{\frac{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} \cdot \sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} - b \cdot b}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}}{a \cdot 2} \]

   5. add-sqr-sqrt 15.8%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} - b \cdot b}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}{a \cdot 2} \]

   6. unpow2 15.8%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right) - \color{blue}{{b}^{2}}}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}{a \cdot 2} \]

8. Applied egg-rr 15.8%

   \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right) - {b}^{2}}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}}{a \cdot 2} \]

9. Taylor expanded in b around inf 97.0%

   \[\leadsto \color{blue}{\frac{-2 \cdot \frac{{a}^{2} \cdot {c}^{3}}{{b}^{4}} + \left(-1 \cdot c + \left(-1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}} + 2 \cdot \frac{-2 \cdot \left({a}^{3} \cdot {c}^{4}\right) + -0.5 \cdot \left({a}^{3} \cdot {c}^{4}\right)}{{b}^{6}}\right)\right)}{b}} \]

11. Simplified 97.0%

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(2 \cdot \frac{\left({c}^{4} \cdot {a}^{3}\right) \cdot -2.5}{{b}^{6}} - a \cdot {\left(\frac{c}{-b}\right)}^{2}\right) - c\right)}{b}} \]

12. Final simplification 97.0%

    \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(2 \cdot \frac{\left({c}^{4} \cdot {a}^{3}\right) \cdot -2.5}{{b}^{6}} - a \cdot {\left(\frac{-c}{b}\right)}^{2}\right) - c\right)}{b} \]
13. Add Preprocessing

Alternative 2: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, \left(a \cdot \left(\frac{{c}^{4}}{{b}^{7}} \cdot 20\right)\right) \cdot -0.25\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (-
  (*
   a
   (-
    (*
     a
     (fma
      -2.0
      (/ (pow c 3.0) (pow b 5.0))
      (* (* a (* (/ (pow c 4.0) (pow b 7.0)) 20.0)) -0.25)))
    (/ (pow c 2.0) (pow b 3.0))))
  (/ c b)))

C

double code(double a, double b, double c) {
	return (a * ((a * fma(-2.0, (pow(c, 3.0) / pow(b, 5.0)), ((a * ((pow(c, 4.0) / pow(b, 7.0)) * 20.0)) * -0.25))) - (pow(c, 2.0) / pow(b, 3.0)))) - (c / b);
}

Julia

function code(a, b, c)
	return Float64(Float64(a * Float64(Float64(a * fma(-2.0, Float64((c ^ 3.0) / (b ^ 5.0)), Float64(Float64(a * Float64(Float64((c ^ 4.0) / (b ^ 7.0)) * 20.0)) * -0.25))) - Float64((c ^ 2.0) / (b ^ 3.0)))) - Float64(c / b))
end

Wolfram

code[a_, b_, c_] := N[(N[(a * N[(N[(a * N[(-2.0 * N[(N[Power[c, 3.0], $MachinePrecision] / N[Power[b, 5.0], $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(N[Power[c, 4.0], $MachinePrecision] / N[Power[b, 7.0], $MachinePrecision]), $MachinePrecision] * 20.0), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Power[c, 2.0], $MachinePrecision] / N[Power[b, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}} \]
4. Add Preprocessing

5. Taylor expanded in a around 0 97.0%

   \[\leadsto \color{blue}{-1 \cdot \frac{c}{b} + a \cdot \left(-1 \cdot \frac{{c}^{2}}{{b}^{3}} + a \cdot \left(-2 \cdot \frac{{c}^{3}}{{b}^{5}} + -0.25 \cdot \frac{a \cdot \left(4 \cdot \frac{{c}^{4}}{{b}^{6}} + 16 \cdot \frac{{c}^{4}}{{b}^{6}}\right)}{b}\right)\right)} \]
6. Step-by-step derivation

   1. +-commutative 97.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \frac{{c}^{2}}{{b}^{3}} + a \cdot \left(-2 \cdot \frac{{c}^{3}}{{b}^{5}} + -0.25 \cdot \frac{a \cdot \left(4 \cdot \frac{{c}^{4}}{{b}^{6}} + 16 \cdot \frac{{c}^{4}}{{b}^{6}}\right)}{b}\right)\right) + -1 \cdot \frac{c}{b}} \]

   2. mul-1-neg 97.0%

      \[\leadsto a \cdot \left(-1 \cdot \frac{{c}^{2}}{{b}^{3}} + a \cdot \left(-2 \cdot \frac{{c}^{3}}{{b}^{5}} + -0.25 \cdot \frac{a \cdot \left(4 \cdot \frac{{c}^{4}}{{b}^{6}} + 16 \cdot \frac{{c}^{4}}{{b}^{6}}\right)}{b}\right)\right) + \color{blue}{\left(-\frac{c}{b}\right)} \]

   3. unsub-neg 97.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \frac{{c}^{2}}{{b}^{3}} + a \cdot \left(-2 \cdot \frac{{c}^{3}}{{b}^{5}} + -0.25 \cdot \frac{a \cdot \left(4 \cdot \frac{{c}^{4}}{{b}^{6}} + 16 \cdot \frac{{c}^{4}}{{b}^{6}}\right)}{b}\right)\right) - \frac{c}{b}} \]

7. Simplified 97.0%

   \[\leadsto \color{blue}{a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, \left(a \cdot \left(\frac{\frac{{c}^{4}}{{b}^{6}}}{b} \cdot 20\right)\right) \cdot -0.25\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b}} \]

8. Taylor expanded in c around 0 97.0%

   \[\leadsto a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, \left(a \cdot \left(\color{blue}{\frac{{c}^{4}}{{b}^{7}}} \cdot 20\right)\right) \cdot -0.25\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \]

9. Final simplification 97.0%

   \[\leadsto a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, \left(a \cdot \left(\frac{{c}^{4}}{{b}^{7}} \cdot 20\right)\right) \cdot -0.25\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \]
10. Add Preprocessing

Alternative 3: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, 2 \cdot \left(c \cdot \left(-2.5 \cdot \frac{{a}^{3}}{{b}^{7}}\right)\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right) \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (*
  c
  (fma
   c
   (-
    (*
     c
     (fma
      -2.0
      (/ (pow a 2.0) (pow b 5.0))
      (* 2.0 (* c (* -2.5 (/ (pow a 3.0) (pow b 7.0)))))))
    (/ a (pow b 3.0)))
   (/ -1.0 b))))

C

double code(double a, double b, double c) {
	return c * fma(c, ((c * fma(-2.0, (pow(a, 2.0) / pow(b, 5.0)), (2.0 * (c * (-2.5 * (pow(a, 3.0) / pow(b, 7.0))))))) - (a / pow(b, 3.0))), (-1.0 / b));
}

Julia

function code(a, b, c)
	return Float64(c * fma(c, Float64(Float64(c * fma(-2.0, Float64((a ^ 2.0) / (b ^ 5.0)), Float64(2.0 * Float64(c * Float64(-2.5 * Float64((a ^ 3.0) / (b ^ 7.0))))))) - Float64(a / (b ^ 3.0))), Float64(-1.0 / b)))
end

Wolfram

code[a_, b_, c_] := N[(c * N[(c * N[(N[(c * N[(-2.0 * N[(N[Power[a, 2.0], $MachinePrecision] / N[Power[b, 5.0], $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(c * N[(-2.5 * N[(N[Power[a, 3.0], $MachinePrecision] / N[Power[b, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[Power[b, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)} - b}{a \cdot 2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. add-sqr-sqrt 16.0%

      \[\leadsto \frac{\color{blue}{\sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}} \cdot \sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}} - b}{a \cdot 2} \]

   2. pow2 16.0%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}\right)}^{2}} - b}{a \cdot 2} \]

   3. pow1/2 16.0%

      \[\leadsto \frac{{\left(\sqrt{\color{blue}{{\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{0.5}}}\right)}^{2} - b}{a \cdot 2} \]

   4. sqrt-pow1 16.0%

      \[\leadsto \frac{{\color{blue}{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} - b}{a \cdot 2} \]

   5. pow2 16.0%

      \[\leadsto \frac{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, \color{blue}{{b}^{2}}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2} - b}{a \cdot 2} \]

   6. metadata-eval 16.0%

      \[\leadsto \frac{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{\color{blue}{0.25}}\right)}^{2} - b}{a \cdot 2} \]

6. Applied egg-rr 16.0%

   \[\leadsto \frac{\color{blue}{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{0.25}\right)}^{2}} - b}{a \cdot 2} \]
7. Step-by-step derivation

   1. pow-pow 15.4%

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{\left(0.25 \cdot 2\right)}} - b}{a \cdot 2} \]

   2. metadata-eval 15.4%

      \[\leadsto \frac{{\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{\color{blue}{0.5}} - b}{a \cdot 2} \]

   3. pow1/2 15.4%

      \[\leadsto \frac{\color{blue}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)}} - b}{a \cdot 2} \]

   4. flip-- 15.4%

      \[\leadsto \frac{\color{blue}{\frac{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} \cdot \sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} - b \cdot b}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}}{a \cdot 2} \]

   5. add-sqr-sqrt 15.8%

      \[\leadsto \frac{\frac{\color{blue}{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} - b \cdot b}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}{a \cdot 2} \]

   6. unpow2 15.8%

      \[\leadsto \frac{\frac{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right) - \color{blue}{{b}^{2}}}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}{a \cdot 2} \]

8. Applied egg-rr 15.8%

   \[\leadsto \frac{\color{blue}{\frac{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right) - {b}^{2}}{\sqrt{\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)} + b}}}{a \cdot 2} \]

9. Taylor expanded in c around 0 96.6%

   \[\leadsto \color{blue}{c \cdot \left(c \cdot \left(-1 \cdot \frac{a}{{b}^{3}} + c \cdot \left(-2 \cdot \frac{{a}^{2}}{{b}^{5}} + 2 \cdot \left(c \cdot \left(-2 \cdot \frac{{a}^{3}}{{b}^{7}} + -0.5 \cdot \frac{{a}^{3}}{{b}^{7}}\right)\right)\right)\right) - \frac{1}{b}\right)} \]
10. Step-by-step derivation

    1. fma-neg 96.6%

       \[\leadsto c \cdot \color{blue}{\mathsf{fma}\left(c, -1 \cdot \frac{a}{{b}^{3}} + c \cdot \left(-2 \cdot \frac{{a}^{2}}{{b}^{5}} + 2 \cdot \left(c \cdot \left(-2 \cdot \frac{{a}^{3}}{{b}^{7}} + -0.5 \cdot \frac{{a}^{3}}{{b}^{7}}\right)\right)\right), -\frac{1}{b}\right)} \]

11. Simplified 96.6%

    \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, 2 \cdot \left(c \cdot \left(\frac{{a}^{3}}{{b}^{7}} \cdot -2.5\right)\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right)} \]

12. Final simplification 96.6%

    \[\leadsto c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, 2 \cdot \left(c \cdot \left(-2.5 \cdot \frac{{a}^{3}}{{b}^{7}}\right)\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right) \]
13. Add Preprocessing

Alternative 4: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \frac{\left(\frac{-2 \cdot \left({a}^{2} \cdot {c}^{3}\right)}{{b}^{4}} - c\right) - a \cdot {\left(\frac{-c}{b}\right)}^{2}}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/
  (-
   (- (/ (* -2.0 (* (pow a 2.0) (pow c 3.0))) (pow b 4.0)) c)
   (* a (pow (/ (- c) b) 2.0)))
  b))

C

double code(double a, double b, double c) {
	return ((((-2.0 * (pow(a, 2.0) * pow(c, 3.0))) / pow(b, 4.0)) - c) - (a * pow((-c / b), 2.0))) / b;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((((-2.0d0) * ((a ** 2.0d0) * (c ** 3.0d0))) / (b ** 4.0d0)) - c) - (a * ((-c / b) ** 2.0d0))) / b
end function

Java

public static double code(double a, double b, double c) {
	return ((((-2.0 * (Math.pow(a, 2.0) * Math.pow(c, 3.0))) / Math.pow(b, 4.0)) - c) - (a * Math.pow((-c / b), 2.0))) / b;
}

Python

def code(a, b, c):
	return ((((-2.0 * (math.pow(a, 2.0) * math.pow(c, 3.0))) / math.pow(b, 4.0)) - c) - (a * math.pow((-c / b), 2.0))) / b

Julia

function code(a, b, c)
	return Float64(Float64(Float64(Float64(Float64(-2.0 * Float64((a ^ 2.0) * (c ^ 3.0))) / (b ^ 4.0)) - c) - Float64(a * (Float64(Float64(-c) / b) ^ 2.0))) / b)
end

MATLAB

function tmp = code(a, b, c)
	tmp = ((((-2.0 * ((a ^ 2.0) * (c ^ 3.0))) / (b ^ 4.0)) - c) - (a * ((-c / b) ^ 2.0))) / b;
end

Wolfram

code[a_, b_, c_] := N[(N[(N[(N[(N[(-2.0 * N[(N[Power[a, 2.0], $MachinePrecision] * N[Power[c, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[b, 4.0], $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision] - N[(a * N[Power[N[((-c) / b), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)} - b}{a \cdot 2}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. add-sqr-sqrt 16.0%

      \[\leadsto \frac{\color{blue}{\sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}} \cdot \sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}} - b}{a \cdot 2} \]

   2. pow2 16.0%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt{\sqrt{\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)}}\right)}^{2}} - b}{a \cdot 2} \]

   3. pow1/2 16.0%

      \[\leadsto \frac{{\left(\sqrt{\color{blue}{{\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{0.5}}}\right)}^{2} - b}{a \cdot 2} \]

   4. sqrt-pow1 16.0%

      \[\leadsto \frac{{\color{blue}{\left({\left(\mathsf{fma}\left(a, c \cdot -4, b \cdot b\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} - b}{a \cdot 2} \]

   5. pow2 16.0%

      \[\leadsto \frac{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, \color{blue}{{b}^{2}}\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2} - b}{a \cdot 2} \]

   6. metadata-eval 16.0%

      \[\leadsto \frac{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{\color{blue}{0.25}}\right)}^{2} - b}{a \cdot 2} \]

6. Applied egg-rr 16.0%

   \[\leadsto \frac{\color{blue}{{\left({\left(\mathsf{fma}\left(a, c \cdot -4, {b}^{2}\right)\right)}^{0.25}\right)}^{2}} - b}{a \cdot 2} \]
7. Step-by-step derivation

   1. fma-undefine 16.0%

      \[\leadsto \frac{{\left({\color{blue}{\left(a \cdot \left(c \cdot -4\right) + {b}^{2}\right)}}^{0.25}\right)}^{2} - b}{a \cdot 2} \]

8. Applied egg-rr 16.0%

   \[\leadsto \frac{{\left({\color{blue}{\left(a \cdot \left(c \cdot -4\right) + {b}^{2}\right)}}^{0.25}\right)}^{2} - b}{a \cdot 2} \]

9. Taylor expanded in b around inf 96.3%

   \[\leadsto \color{blue}{\frac{-2 \cdot \frac{{a}^{2} \cdot {c}^{3}}{{b}^{4}} + \left(-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}\right)}{b}} \]
10. Step-by-step derivation

11. Simplified 96.3%

    \[\leadsto \color{blue}{\frac{\left(\frac{-2 \cdot \left({c}^{3} \cdot {a}^{2}\right)}{{b}^{4}} - c\right) - a \cdot {\left(\frac{c}{-b}\right)}^{2}}{b}} \]

12. Final simplification 96.3%

    \[\leadsto \frac{\left(\frac{-2 \cdot \left({a}^{2} \cdot {c}^{3}\right)}{{b}^{4}} - c\right) - a \cdot {\left(\frac{-c}{b}\right)}^{2}}{b} \]
13. Add Preprocessing

Alternative 5: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(-2 \cdot \left(a \cdot \frac{{c}^{3}}{{b}^{5}}\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (-
  (*
   a
   (- (* -2.0 (* a (/ (pow c 3.0) (pow b 5.0)))) (/ (pow c 2.0) (pow b 3.0))))
  (/ c b)))

C

double code(double a, double b, double c) {
	return (a * ((-2.0 * (a * (pow(c, 3.0) / pow(b, 5.0)))) - (pow(c, 2.0) / pow(b, 3.0)))) - (c / b);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (a * (((-2.0d0) * (a * ((c ** 3.0d0) / (b ** 5.0d0)))) - ((c ** 2.0d0) / (b ** 3.0d0)))) - (c / b)
end function

Java

public static double code(double a, double b, double c) {
	return (a * ((-2.0 * (a * (Math.pow(c, 3.0) / Math.pow(b, 5.0)))) - (Math.pow(c, 2.0) / Math.pow(b, 3.0)))) - (c / b);
}

Python

def code(a, b, c):
	return (a * ((-2.0 * (a * (math.pow(c, 3.0) / math.pow(b, 5.0)))) - (math.pow(c, 2.0) / math.pow(b, 3.0)))) - (c / b)

Julia

function code(a, b, c)
	return Float64(Float64(a * Float64(Float64(-2.0 * Float64(a * Float64((c ^ 3.0) / (b ^ 5.0)))) - Float64((c ^ 2.0) / (b ^ 3.0)))) - Float64(c / b))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (a * ((-2.0 * (a * ((c ^ 3.0) / (b ^ 5.0)))) - ((c ^ 2.0) / (b ^ 3.0)))) - (c / b);
end

Wolfram

code[a_, b_, c_] := N[(N[(a * N[(N[(-2.0 * N[(a * N[(N[Power[c, 3.0], $MachinePrecision] / N[Power[b, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Power[c, 2.0], $MachinePrecision] / N[Power[b, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}} \]
4. Add Preprocessing

5. Taylor expanded in a around 0 96.3%

   \[\leadsto \color{blue}{-1 \cdot \frac{c}{b} + a \cdot \left(-2 \cdot \frac{a \cdot {c}^{3}}{{b}^{5}} + -1 \cdot \frac{{c}^{2}}{{b}^{3}}\right)} \]
6. Step-by-step derivation

   1. +-commutative 96.3%

      \[\leadsto \color{blue}{a \cdot \left(-2 \cdot \frac{a \cdot {c}^{3}}{{b}^{5}} + -1 \cdot \frac{{c}^{2}}{{b}^{3}}\right) + -1 \cdot \frac{c}{b}} \]

   2. mul-1-neg 96.3%

      \[\leadsto a \cdot \left(-2 \cdot \frac{a \cdot {c}^{3}}{{b}^{5}} + -1 \cdot \frac{{c}^{2}}{{b}^{3}}\right) + \color{blue}{\left(-\frac{c}{b}\right)} \]

   3. unsub-neg 96.3%

      \[\leadsto \color{blue}{a \cdot \left(-2 \cdot \frac{a \cdot {c}^{3}}{{b}^{5}} + -1 \cdot \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b}} \]

   4. mul-1-neg 96.3%

      \[\leadsto a \cdot \left(-2 \cdot \frac{a \cdot {c}^{3}}{{b}^{5}} + \color{blue}{\left(-\frac{{c}^{2}}{{b}^{3}}\right)}\right) - \frac{c}{b} \]

   5. unsub-neg 96.3%

      \[\leadsto a \cdot \color{blue}{\left(-2 \cdot \frac{a \cdot {c}^{3}}{{b}^{5}} - \frac{{c}^{2}}{{b}^{3}}\right)} - \frac{c}{b} \]

   6. associate-/l* 96.3%

      \[\leadsto a \cdot \left(-2 \cdot \color{blue}{\left(a \cdot \frac{{c}^{3}}{{b}^{5}}\right)} - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \]

7. Simplified 96.3%

   \[\leadsto \color{blue}{a \cdot \left(-2 \cdot \left(a \cdot \frac{{c}^{3}}{{b}^{5}}\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b}} \]

8. Final simplification 96.3%

   \[\leadsto a \cdot \left(-2 \cdot \left(a \cdot \frac{{c}^{3}}{{b}^{5}}\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \]
9. Add Preprocessing

Alternative 6: 96.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ c \cdot \left(c \cdot \left(-2 \cdot \frac{{a}^{2} \cdot c}{{b}^{5}} - \frac{a}{{b}^{3}}\right) + \frac{-1}{b}\right) \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (*
  c
  (+
   (* c (- (* -2.0 (/ (* (pow a 2.0) c) (pow b 5.0))) (/ a (pow b 3.0))))
   (/ -1.0 b))))

C

double code(double a, double b, double c) {
	return c * ((c * ((-2.0 * ((pow(a, 2.0) * c) / pow(b, 5.0))) - (a / pow(b, 3.0)))) + (-1.0 / b));
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c * ((c * (((-2.0d0) * (((a ** 2.0d0) * c) / (b ** 5.0d0))) - (a / (b ** 3.0d0)))) + ((-1.0d0) / b))
end function

Java

public static double code(double a, double b, double c) {
	return c * ((c * ((-2.0 * ((Math.pow(a, 2.0) * c) / Math.pow(b, 5.0))) - (a / Math.pow(b, 3.0)))) + (-1.0 / b));
}

Python

def code(a, b, c):
	return c * ((c * ((-2.0 * ((math.pow(a, 2.0) * c) / math.pow(b, 5.0))) - (a / math.pow(b, 3.0)))) + (-1.0 / b))

Julia

function code(a, b, c)
	return Float64(c * Float64(Float64(c * Float64(Float64(-2.0 * Float64(Float64((a ^ 2.0) * c) / (b ^ 5.0))) - Float64(a / (b ^ 3.0)))) + Float64(-1.0 / b)))
end

MATLAB

function tmp = code(a, b, c)
	tmp = c * ((c * ((-2.0 * (((a ^ 2.0) * c) / (b ^ 5.0))) - (a / (b ^ 3.0)))) + (-1.0 / b));
end

Wolfram

code[a_, b_, c_] := N[(c * N[(N[(c * N[(N[(-2.0 * N[(N[(N[Power[a, 2.0], $MachinePrecision] * c), $MachinePrecision] / N[Power[b, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[Power[b, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}} \]
4. Add Preprocessing

5. Taylor expanded in c around 0 95.9%

   \[\leadsto \color{blue}{c \cdot \left(c \cdot \left(-2 \cdot \frac{{a}^{2} \cdot c}{{b}^{5}} + -1 \cdot \frac{a}{{b}^{3}}\right) - \frac{1}{b}\right)} \]

6. Final simplification 95.9%

   \[\leadsto c \cdot \left(c \cdot \left(-2 \cdot \frac{{a}^{2} \cdot c}{{b}^{5}} - \frac{a}{{b}^{3}}\right) + \frac{-1}{b}\right) \]
7. Add Preprocessing

Alternative 7: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{a \cdot \left(-{\left(\frac{-c}{b}\right)}^{2}\right) - c}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (- (* a (- (pow (/ (- c) b) 2.0))) c) b))

C

double code(double a, double b, double c) {
	return ((a * -pow((-c / b), 2.0)) - c) / b;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = ((a * -((-c / b) ** 2.0d0)) - c) / b
end function

Java

public static double code(double a, double b, double c) {
	return ((a * -Math.pow((-c / b), 2.0)) - c) / b;
}

Python

def code(a, b, c):
	return ((a * -math.pow((-c / b), 2.0)) - c) / b

Julia

function code(a, b, c)
	return Float64(Float64(Float64(a * Float64(-(Float64(Float64(-c) / b) ^ 2.0))) - c) / b)
end

MATLAB

function tmp = code(a, b, c)
	tmp = ((a * -((-c / b) ^ 2.0)) - c) / b;
end

Wolfram

code[a_, b_, c_] := N[(N[(N[(a * (-N[Power[N[((-c) / b), $MachinePrecision], 2.0], $MachinePrecision])), $MachinePrecision] - c), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}} \]
4. Add Preprocessing

5. Taylor expanded in c around 0 94.6%

   \[\leadsto \color{blue}{c \cdot \left(-1 \cdot \frac{a \cdot c}{{b}^{3}} - \frac{1}{b}\right)} \]
6. Step-by-step derivation

   1. associate-*r/ 94.6%

      \[\leadsto c \cdot \left(\color{blue}{\frac{-1 \cdot \left(a \cdot c\right)}{{b}^{3}}} - \frac{1}{b}\right) \]

   2. neg-mul-1 94.6%

      \[\leadsto c \cdot \left(\frac{\color{blue}{-a \cdot c}}{{b}^{3}} - \frac{1}{b}\right) \]

   3. distribute-rgt-neg-in 94.6%

      \[\leadsto c \cdot \left(\frac{\color{blue}{a \cdot \left(-c\right)}}{{b}^{3}} - \frac{1}{b}\right) \]

7. Simplified 94.6%

   \[\leadsto \color{blue}{c \cdot \left(\frac{a \cdot \left(-c\right)}{{b}^{3}} - \frac{1}{b}\right)} \]

8. Taylor expanded in b around inf 94.6%

   \[\leadsto c \cdot \color{blue}{\frac{-1 \cdot \frac{a \cdot c}{{b}^{2}} - 1}{b}} \]

9. Taylor expanded in b around inf 95.0%

   \[\leadsto \color{blue}{\frac{-1 \cdot c + -1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}}}{b}} \]
10. Step-by-step derivation

11. Simplified 95.0%

    \[\leadsto \color{blue}{\frac{\left(-c\right) - a \cdot {\left(\frac{c}{-b}\right)}^{2}}{b}} \]

12. Final simplification 95.0%

    \[\leadsto \frac{a \cdot \left(-{\left(\frac{-c}{b}\right)}^{2}\right) - c}{b} \]
13. Add Preprocessing

Alternative 8: 90.0% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ \frac{-c}{b} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (/ (- c) b))

C

double code(double a, double b, double c) {
	return -c / b;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = -c / b
end function

Java

public static double code(double a, double b, double c) {
	return -c / b;
}

Python

def code(a, b, c):
	return -c / b

Julia

function code(a, b, c)
	return Float64(Float64(-c) / b)
end

MATLAB

function tmp = code(a, b, c)
	tmp = -c / b;
end

Wolfram

code[a_, b_, c_] := N[((-c) / b), $MachinePrecision]

Derivation

1. Initial program 15.4%

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a} \]
2. Step-by-step derivation

   1. *-commutative 15.4%

      \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{\color{blue}{a \cdot 2}} \]

3. Simplified 15.4%

   \[\leadsto \color{blue}{\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a \cdot 2}} \]
4. Add Preprocessing

5. Taylor expanded in b around inf 91.5%

   \[\leadsto \color{blue}{-1 \cdot \frac{c}{b}} \]
6. Step-by-step derivation

   1. associate-*r/ 91.5%

      \[\leadsto \color{blue}{\frac{-1 \cdot c}{b}} \]

   2. mul-1-neg 91.5%

      \[\leadsto \frac{\color{blue}{-c}}{b} \]

7. Simplified 91.5%

   \[\leadsto \color{blue}{\frac{-c}{b}} \]

8. Final simplification 91.5%

   \[\leadsto \frac{-c}{b} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024068 
(FPCore (a b c)
  :name "Quadratic roots, wide range"
  :precision binary64
  :pre (and (and (and (< 4.930380657631324e-32 a) (< a 2.028240960365167e+31)) (and (< 4.930380657631324e-32 b) (< b 2.028240960365167e+31))) (and (< 4.930380657631324e-32 c) (< c 2.028240960365167e+31)))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))