Quadratic roots, wide range

Percentage Accurate: 18.1% → 98.4%

Time: 25.0s

Alternatives: 11

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: 18.1% 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: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {a}^{4} \cdot {c}^{4}\\ \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(t\_0 \cdot 20\right), {\left(a \cdot c\right)}^{5} \cdot 16\right)}{a \cdot {b}^{8}} + \frac{t\_0}{a} \cdot \frac{20}{{b}^{6}}\right) + {a}^{5} \cdot \frac{{c}^{6} \cdot 168}{{b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (* (pow a 4.0) (pow c 4.0))))
   (/
    (fma
     -2.0
     (* (pow a 2.0) (/ (pow c 3.0) (pow b 4.0)))
     (-
      (-
       (*
        -0.25
        (+
         (+
          (/
           (fma 2.0 (* (* a c) (* t_0 20.0)) (* (pow (* a c) 5.0) 16.0))
           (* a (pow b 8.0)))
          (* (/ t_0 a) (/ 20.0 (pow b 6.0))))
         (* (pow a 5.0) (/ (* (pow c 6.0) 168.0) (pow b 10.0)))))
       (* a (/ (pow c 2.0) (pow b 2.0))))
      c))
    b)))

C

double code(double a, double b, double c) {
	double t_0 = pow(a, 4.0) * pow(c, 4.0);
	return fma(-2.0, (pow(a, 2.0) * (pow(c, 3.0) / pow(b, 4.0))), (((-0.25 * (((fma(2.0, ((a * c) * (t_0 * 20.0)), (pow((a * c), 5.0) * 16.0)) / (a * pow(b, 8.0))) + ((t_0 / a) * (20.0 / pow(b, 6.0)))) + (pow(a, 5.0) * ((pow(c, 6.0) * 168.0) / pow(b, 10.0))))) - (a * (pow(c, 2.0) / pow(b, 2.0)))) - c)) / b;
}

Julia

function code(a, b, c)
	t_0 = Float64((a ^ 4.0) * (c ^ 4.0))
	return Float64(fma(-2.0, Float64((a ^ 2.0) * Float64((c ^ 3.0) / (b ^ 4.0))), Float64(Float64(Float64(-0.25 * Float64(Float64(Float64(fma(2.0, Float64(Float64(a * c) * Float64(t_0 * 20.0)), Float64((Float64(a * c) ^ 5.0) * 16.0)) / Float64(a * (b ^ 8.0))) + Float64(Float64(t_0 / a) * Float64(20.0 / (b ^ 6.0)))) + Float64((a ^ 5.0) * Float64(Float64((c ^ 6.0) * 168.0) / (b ^ 10.0))))) - Float64(a * Float64((c ^ 2.0) / (b ^ 2.0)))) - c)) / b)
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(N[Power[a, 4.0], $MachinePrecision] * N[Power[c, 4.0], $MachinePrecision]), $MachinePrecision]}, 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[(-0.25 * N[(N[(N[(N[(2.0 * N[(N[(a * c), $MachinePrecision] * N[(t$95$0 * 20.0), $MachinePrecision]), $MachinePrecision] + N[(N[Power[N[(a * c), $MachinePrecision], 5.0], $MachinePrecision] * 16.0), $MachinePrecision]), $MachinePrecision] / N[(a * N[Power[b, 8.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 / a), $MachinePrecision] * N[(20.0 / N[Power[b, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[a, 5.0], $MachinePrecision] * N[(N[(N[Power[c, 6.0], $MachinePrecision] * 168.0), $MachinePrecision] / N[Power[b, 10.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[Power[c, 2.0], $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Initial program 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in b around inf 98.0%

   \[\leadsto \color{blue}{\frac{-2 \cdot \frac{{a}^{2} \cdot {c}^{3}}{{b}^{4}} + \left(-1 \cdot c + \left(-1 \cdot \frac{a \cdot {c}^{2}}{{b}^{2}} + \left(-0.25 \cdot \frac{2 \cdot \left(a \cdot \left(c \cdot \left(2 \cdot \left(a \cdot \left(c \cdot \left(4 \cdot \left({a}^{4} \cdot {c}^{4}\right) + 16 \cdot \left({a}^{4} \cdot {c}^{4}\right)\right)\right)\right) + 16 \cdot \left({a}^{5} \cdot {c}^{5}\right)\right)\right)\right) + \left(2 \cdot \left({a}^{2} \cdot \left({c}^{2} \cdot \left(4 \cdot \left({a}^{4} \cdot {c}^{4}\right) + 16 \cdot \left({a}^{4} \cdot {c}^{4}\right)\right)\right)\right) + 16 \cdot \left({a}^{6} \cdot {c}^{6}\right)\right)}{a \cdot {b}^{10}} + \left(-0.25 \cdot \frac{2 \cdot \left(a \cdot \left(c \cdot \left(4 \cdot \left({a}^{4} \cdot {c}^{4}\right) + 16 \cdot \left({a}^{4} \cdot {c}^{4}\right)\right)\right)\right) + 16 \cdot \left({a}^{5} \cdot {c}^{5}\right)}{a \cdot {b}^{8}} + -0.25 \cdot \frac{4 \cdot \left({a}^{4} \cdot {c}^{4}\right) + 16 \cdot \left({a}^{4} \cdot {c}^{4}\right)}{a \cdot {b}^{6}}\right)\right)\right)\right)}{b}} \]

7. Simplified 98.0%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right), \mathsf{fma}\left(2, {a}^{2} \cdot \left({c}^{2} \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right)\right), \left(16 \cdot {a}^{6}\right) \cdot {c}^{6}\right)\right)}{a \cdot {b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b}} \]

8. Taylor expanded in a around 0 98.0%

   \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \color{blue}{\frac{{a}^{5} \cdot \left(2 \cdot \left(c \cdot \left(16 \cdot {c}^{5} + 40 \cdot {c}^{5}\right)\right) + \left(16 \cdot {c}^{6} + 40 \cdot {c}^{6}\right)\right)}{{b}^{10}}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]
9. Step-by-step derivation

   1. *-commutative 98.0%

      \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \frac{\color{blue}{\left(2 \cdot \left(c \cdot \left(16 \cdot {c}^{5} + 40 \cdot {c}^{5}\right)\right) + \left(16 \cdot {c}^{6} + 40 \cdot {c}^{6}\right)\right) \cdot {a}^{5}}}{{b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

   2. associate-/l* 98.0%

      \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \color{blue}{\left(2 \cdot \left(c \cdot \left(16 \cdot {c}^{5} + 40 \cdot {c}^{5}\right)\right) + \left(16 \cdot {c}^{6} + 40 \cdot {c}^{6}\right)\right) \cdot \frac{{a}^{5}}{{b}^{10}}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

10. Simplified 98.0%

    \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \color{blue}{\mathsf{fma}\left(2, {c}^{6} \cdot 56, {c}^{6} \cdot 56\right) \cdot \frac{{a}^{5}}{{b}^{10}}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

11. Taylor expanded in a around 0 98.0%

    \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \color{blue}{\frac{{a}^{5} \cdot \left(56 \cdot {c}^{6} + 112 \cdot {c}^{6}\right)}{{b}^{10}}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]
12. Step-by-step derivation

    1. associate-/l* 98.0%

       \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \color{blue}{{a}^{5} \cdot \frac{56 \cdot {c}^{6} + 112 \cdot {c}^{6}}{{b}^{10}}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

    2. distribute-rgt-out 98.0%

       \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + {a}^{5} \cdot \frac{\color{blue}{{c}^{6} \cdot \left(56 + 112\right)}}{{b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

    3. metadata-eval 98.0%

       \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + {a}^{5} \cdot \frac{{c}^{6} \cdot \color{blue}{168}}{{b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

13. Simplified 98.0%

    \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \left({a}^{5} \cdot {c}^{5}\right) \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + \color{blue}{{a}^{5} \cdot \frac{{c}^{6} \cdot 168}{{b}^{10}}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]
14. Step-by-step derivation

    1. pow-prod-down 98.0%

       \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \color{blue}{{\left(a \cdot c\right)}^{5}} \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + {a}^{5} \cdot \frac{{c}^{6} \cdot 168}{{b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

15. Applied egg-rr 98.0%

    \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), \color{blue}{{\left(a \cdot c\right)}^{5}} \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + {a}^{5} \cdot \frac{{c}^{6} \cdot 168}{{b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]

16. Final simplification 98.0%

    \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(-0.25 \cdot \left(\left(\frac{\mathsf{fma}\left(2, \left(a \cdot c\right) \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right), {\left(a \cdot c\right)}^{5} \cdot 16\right)}{a \cdot {b}^{8}} + \frac{{a}^{4} \cdot {c}^{4}}{a} \cdot \frac{20}{{b}^{6}}\right) + {a}^{5} \cdot \frac{{c}^{6} \cdot 168}{{b}^{10}}\right) - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]
17. Add Preprocessing

Alternative 2: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 20 \cdot \frac{{c}^{4}}{{b}^{6}}\\ a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, a \cdot \left(-0.25 \cdot \left(\frac{t\_0}{b} + a \cdot \frac{\mathsf{fma}\left(2, c \cdot \frac{t\_0}{{b}^{2}}, 16 \cdot \frac{{c}^{5}}{{b}^{8}}\right)}{b}\right)\right)\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (* 20.0 (/ (pow c 4.0) (pow b 6.0)))))
   (-
    (*
     a
     (-
      (*
       a
       (fma
        -2.0
        (/ (pow c 3.0) (pow b 5.0))
        (*
         a
         (*
          -0.25
          (+
           (/ t_0 b)
           (*
            a
            (/
             (fma
              2.0
              (* c (/ t_0 (pow b 2.0)))
              (* 16.0 (/ (pow c 5.0) (pow b 8.0))))
             b)))))))
      (/ (pow c 2.0) (pow b 3.0))))
    (/ c b))))

C

double code(double a, double b, double c) {
	double t_0 = 20.0 * (pow(c, 4.0) / pow(b, 6.0));
	return (a * ((a * fma(-2.0, (pow(c, 3.0) / pow(b, 5.0)), (a * (-0.25 * ((t_0 / b) + (a * (fma(2.0, (c * (t_0 / pow(b, 2.0))), (16.0 * (pow(c, 5.0) / pow(b, 8.0)))) / b))))))) - (pow(c, 2.0) / pow(b, 3.0)))) - (c / b);
}

Julia

function code(a, b, c)
	t_0 = Float64(20.0 * Float64((c ^ 4.0) / (b ^ 6.0)))
	return Float64(Float64(a * Float64(Float64(a * fma(-2.0, Float64((c ^ 3.0) / (b ^ 5.0)), Float64(a * Float64(-0.25 * Float64(Float64(t_0 / b) + Float64(a * Float64(fma(2.0, Float64(c * Float64(t_0 / (b ^ 2.0))), Float64(16.0 * Float64((c ^ 5.0) / (b ^ 8.0)))) / b))))))) - Float64((c ^ 2.0) / (b ^ 3.0)))) - Float64(c / b))
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(20.0 * N[(N[Power[c, 4.0], $MachinePrecision] / N[Power[b, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(a * N[(N[(a * N[(-2.0 * N[(N[Power[c, 3.0], $MachinePrecision] / N[Power[b, 5.0], $MachinePrecision]), $MachinePrecision] + N[(a * N[(-0.25 * N[(N[(t$95$0 / b), $MachinePrecision] + N[(a * N[(N[(2.0 * N[(c * N[(t$95$0 / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(16.0 * N[(N[Power[c, 5.0], $MachinePrecision] / N[Power[b, 8.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in a around 0 97.6%

   \[\leadsto \color{blue}{-1 \cdot \frac{c}{b} + a \cdot \left(-1 \cdot \frac{{c}^{2}}{{b}^{3}} + a \cdot \left(-2 \cdot \frac{{c}^{3}}{{b}^{5}} + a \cdot \left(-0.25 \cdot \frac{a \cdot \left(2 \cdot \frac{c \cdot \left(4 \cdot \frac{{c}^{4}}{{b}^{6}} + 16 \cdot \frac{{c}^{4}}{{b}^{6}}\right)}{{b}^{2}} + 16 \cdot \frac{{c}^{5}}{{b}^{8}}\right)}{b} + -0.25 \cdot \frac{4 \cdot \frac{{c}^{4}}{{b}^{6}} + 16 \cdot \frac{{c}^{4}}{{b}^{6}}}{b}\right)\right)\right)} \]

7. Simplified 97.6%

   \[\leadsto \color{blue}{a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, a \cdot \left(-0.25 \cdot \left(\frac{\frac{{c}^{4}}{{b}^{6}} \cdot 20}{b} + a \cdot \frac{\mathsf{fma}\left(2, c \cdot \frac{\frac{{c}^{4}}{{b}^{6}} \cdot 20}{{b}^{2}}, 16 \cdot \frac{{c}^{5}}{{b}^{8}}\right)}{b}\right)\right)\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b}} \]

8. Final simplification 97.6%

   \[\leadsto a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, a \cdot \left(-0.25 \cdot \left(\frac{20 \cdot \frac{{c}^{4}}{{b}^{6}}}{b} + a \cdot \frac{\mathsf{fma}\left(2, c \cdot \frac{20 \cdot \frac{{c}^{4}}{{b}^{6}}}{{b}^{2}}, 16 \cdot \frac{{c}^{5}}{{b}^{8}}\right)}{b}\right)\right)\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \]
9. Add Preprocessing

Alternative 3: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(\frac{-0.25 \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right)}{a \cdot {b}^{6}} - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/
  (fma
   -2.0
   (* (pow a 2.0) (/ (pow c 3.0) (pow b 4.0)))
   (-
    (-
     (/ (* -0.25 (* (* (pow a 4.0) (pow c 4.0)) 20.0)) (* a (pow b 6.0)))
     (* a (/ (pow c 2.0) (pow 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))), ((((-0.25 * ((pow(a, 4.0) * pow(c, 4.0)) * 20.0)) / (a * pow(b, 6.0))) - (a * (pow(c, 2.0) / pow(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(Float64(-0.25 * Float64(Float64((a ^ 4.0) * (c ^ 4.0)) * 20.0)) / Float64(a * (b ^ 6.0))) - Float64(a * Float64((c ^ 2.0) / (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[(N[(-0.25 * N[(N[(N[Power[a, 4.0], $MachinePrecision] * N[Power[c, 4.0], $MachinePrecision]), $MachinePrecision] * 20.0), $MachinePrecision]), $MachinePrecision] / N[(a * N[Power[b, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[Power[c, 2.0], $MachinePrecision] / N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - c), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in b around inf 97.0%

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

7. Simplified 97.0%

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

8. Final simplification 97.0%

   \[\leadsto \frac{\mathsf{fma}\left(-2, {a}^{2} \cdot \frac{{c}^{3}}{{b}^{4}}, \left(\frac{-0.25 \cdot \left(\left({a}^{4} \cdot {c}^{4}\right) \cdot 20\right)}{a \cdot {b}^{6}} - a \cdot \frac{{c}^{2}}{{b}^{2}}\right) - c\right)}{b} \]
9. Add Preprocessing

Alternative 4: 97.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(a \cdot \mathsf{fma}\left(-2, \frac{{c}^{3}}{{b}^{5}}, -0.25 \cdot \left(a \cdot \frac{20 \cdot \frac{{c}^{4}}{{b}^{6}}}{b}\right)\right) - \frac{{c}^{2}}{{b}^{3}}\right) - \frac{c}{b} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (-
  (*
   a
   (-
    (*
     a
     (fma
      -2.0
      (/ (pow c 3.0) (pow b 5.0))
      (* -0.25 (* a (/ (* 20.0 (/ (pow c 4.0) (pow b 6.0))) b)))))
    (/ (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)), (-0.25 * (a * ((20.0 * (pow(c, 4.0) / pow(b, 6.0))) / b))))) - (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(-0.25 * Float64(a * Float64(Float64(20.0 * Float64((c ^ 4.0) / (b ^ 6.0))) / b))))) - 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[(-0.25 * N[(a * N[(N[(20.0 * N[(N[Power[c, 4.0], $MachinePrecision] / N[Power[b, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $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 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

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

8. Final simplification 97.0%

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

Alternative 5: 97.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, -0.25 \cdot \left(c \cdot \frac{20 \cdot {a}^{3}}{{b}^{7}}\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right) \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (*
  c
  (fma
   c
   (-
    (*
     c
     (fma
      -2.0
      (/ (pow a 2.0) (pow b 5.0))
      (* -0.25 (* c (/ (* 20.0 (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)), (-0.25 * (c * ((20.0 * 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(-0.25 * Float64(c * Float64(Float64(20.0 * (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[(-0.25 * N[(c * N[(N[(20.0 * N[Power[a, 3.0], $MachinePrecision]), $MachinePrecision] / N[Power[b, 7.0], $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 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in c around 0 96.6%

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

   1. fma-neg 96.6%

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

7. Simplified 96.6%

   \[\leadsto \color{blue}{c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, -0.25 \cdot \left(c \cdot \left(\frac{\frac{{a}^{4}}{{b}^{6}}}{a} \cdot \frac{20}{b}\right)\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right)} \]

8. Taylor expanded in a around 0 96.6%

   \[\leadsto c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, -0.25 \cdot \left(c \cdot \color{blue}{\left(20 \cdot \frac{{a}^{3}}{{b}^{7}}\right)}\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right) \]
9. Step-by-step derivation

   1. associate-*r/ 96.6%

      \[\leadsto c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, -0.25 \cdot \left(c \cdot \color{blue}{\frac{20 \cdot {a}^{3}}{{b}^{7}}}\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right) \]

10. Simplified 96.6%

    \[\leadsto c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, -0.25 \cdot \left(c \cdot \color{blue}{\frac{20 \cdot {a}^{3}}{{b}^{7}}}\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right) \]

11. Final simplification 96.6%

    \[\leadsto c \cdot \mathsf{fma}\left(c, c \cdot \mathsf{fma}\left(-2, \frac{{a}^{2}}{{b}^{5}}, -0.25 \cdot \left(c \cdot \frac{20 \cdot {a}^{3}}{{b}^{7}}\right)\right) - \frac{a}{{b}^{3}}, \frac{-1}{b}\right) \]
12. Add Preprocessing

Alternative 6: 96.8% accurate, 0.3× speedup

Math

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

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(Float64(a * (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[(N[(a * N[Power[c, 3.0], $MachinePrecision]), $MachinePrecision] / N[Power[b, 5.0], $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 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in a around 0 96.0%

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

   1. +-commutative 96.0%

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

   2. mul-1-neg 96.0%

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

   3. unsub-neg 96.0%

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

   4. mul-1-neg 96.0%

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

   5. unsub-neg 96.0%

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

7. Simplified 96.0%

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

8. Final simplification 96.0%

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

Alternative 7: 96.5% accurate, 0.4× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c) {
	return c * ((((pow((a * c), 2.0) * (-2.0 / pow(b, 2.0))) - (a * c)) / 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 * ((((((a * c) ** 2.0d0) * ((-2.0d0) / (b ** 2.0d0))) - (a * c)) / (b ** 3.0d0)) + ((-1.0d0) / b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in c around 0 95.7%

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

6. Taylor expanded in b around inf 95.7%

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

   1. mul-1-neg 95.7%

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

   2. unsub-neg 95.7%

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

   3. *-commutative 95.7%

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

   4. unpow2 95.7%

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

   5. unpow2 95.7%

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

   6. swap-sqr 95.7%

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

   7. unpow2 95.7%

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

   8. associate-*l/ 95.7%

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

   9. associate-/l* 95.7%

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

8. Simplified 95.7%

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

9. Final simplification 95.7%

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

Alternative 8: 95.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double a, double b, double c) {
	return (-c - (a * (pow(c, 2.0) / pow(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 = (-c - (a * ((c ** 2.0d0) / (b ** 2.0d0)))) / b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in b around inf 94.4%

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

   1. mul-1-neg 94.4%

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

   2. unsub-neg 94.4%

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

   3. mul-1-neg 94.4%

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

   4. associate-/l* 94.4%

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

7. Simplified 94.4%

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

8. Final simplification 94.4%

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

Alternative 9: 95.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in a around 0 94.4%

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

   1. mul-1-neg 94.4%

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

   2. unsub-neg 94.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{c}{b} - \frac{a \cdot {c}^{2}}{{b}^{3}}} \]

   3. mul-1-neg 94.4%

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

   4. distribute-neg-frac2 94.4%

      \[\leadsto \color{blue}{\frac{c}{-b}} - \frac{a \cdot {c}^{2}}{{b}^{3}} \]

7. Simplified 94.4%

   \[\leadsto \color{blue}{\frac{c}{-b} - \frac{a \cdot {c}^{2}}{{b}^{3}}} \]

8. Taylor expanded in b around inf 94.4%

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

   1. distribute-lft-out 94.4%

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

   2. associate-*r/ 94.4%

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

   3. mul-1-neg 94.4%

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

   4. distribute-neg-frac2 94.4%

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

   5. +-commutative 94.4%

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

   6. associate-/l* 94.4%

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

   7. fma-define 94.4%

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

   8. unpow2 94.4%

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

   9. unpow2 94.4%

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

   10. times-frac 94.4%

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

   11. sqr-neg 94.4%

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

   12. distribute-frac-neg2 94.4%

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

   13. distribute-frac-neg2 94.4%

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

   14. unpow2 94.4%

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

10. Simplified 94.4%

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

11. Final simplification 94.4%

    \[\leadsto \frac{\mathsf{fma}\left(a, {\left(\frac{c}{-b}\right)}^{2}, c\right)}{-b} \]
12. Add Preprocessing

Alternative 10: 94.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * (((-1.0d0) / b) - ((a * c) / (b ** 3.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in c around 0 94.0%

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

   1. associate-*r/ 94.0%

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

   2. neg-mul-1 94.0%

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

   3. distribute-rgt-neg-in 94.0%

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

7. Simplified 94.0%

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

8. Final simplification 94.0%

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

Alternative 11: 90.2% 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(c / Float64(-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 19.8%

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

   1. *-commutative 19.8%

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

3. Simplified 19.8%

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

5. Taylor expanded in b around inf 89.2%

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

   1. associate-*r/ 89.2%

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

   2. mul-1-neg 89.2%

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

7. Simplified 89.2%

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

8. Final simplification 89.2%

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

Reproduce

herbie shell --seed 2024053 
(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)))