Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, I

Percentage Accurate: 91.6% → 93.5%

Time: 9.7s

Alternatives: 9

Speedup: 0.8×

• 28.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 93.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* 0.5 (* y (/ x a)))
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 52.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 94.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 94.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 94.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]

   if -inf.0 < (*.f64 x y)

   1. Initial program 93.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. fma-neg 94.4%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      2. associate-*l* 94.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, -\color{blue}{z \cdot \left(9 \cdot t\right)}\right)}{a \cdot 2} \]

      3. *-commutative 94.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, -z \cdot \color{blue}{\left(t \cdot 9\right)}\right)}{a \cdot 2} \]

      4. distribute-rgt-neg-in 94.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-t \cdot 9\right)}\right)}{a \cdot 2} \]

      5. distribute-rgt-neg-in 94.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      6. metadata-eval 94.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* 0.5 (* y (/ x a)))
   (* (+ (* x y) (* t (* z -9.0))) (/ 0.5 a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = ((x * y) + (t * (z * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = ((x * y) + (t * (z * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = ((x * y) + (t * (z * -9.0))) * (0.5 / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(Float64(Float64(x * y) + Float64(t * Float64(z * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (y * (x / a));
	else
		tmp = ((x * y) + (t * (z * -9.0))) * (0.5 / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 52.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 94.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 94.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 94.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]

   if -inf.0 < (*.f64 x y)

   1. Initial program 93.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
   2. Step-by-step derivation

      1. cancel-sign-sub-inv 93.9%

         \[\leadsto \frac{\color{blue}{x \cdot y + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      2. distribute-rgt-neg-in 93.9%

         \[\leadsto \frac{x \cdot y + \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t}{a \cdot 2} \]

      3. metadata-eval 93.9%

         \[\leadsto \frac{x \cdot y + \left(z \cdot \color{blue}{-9}\right) \cdot t}{a \cdot 2} \]

      4. associate-*r* 94.4%

         \[\leadsto \frac{x \cdot y + \color{blue}{z \cdot \left(-9 \cdot t\right)}}{a \cdot 2} \]

      5. *-commutative 94.4%

         \[\leadsto \frac{x \cdot y + z \cdot \color{blue}{\left(t \cdot -9\right)}}{a \cdot 2} \]

      6. fma-udef 94.8%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}{a \cdot 2} \]

      7. div-inv 94.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{1}{a \cdot 2}} \]

      8. *-commutative 94.7%

         \[\leadsto \mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right) \cdot \frac{1}{a \cdot 2} \]

      9. associate-*r* 94.3%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot -9\right) \cdot t}\right) \cdot \frac{1}{a \cdot 2} \]

      10. metadata-eval 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, \left(z \cdot \color{blue}{\left(-9\right)}\right) \cdot t\right) \cdot \frac{1}{a \cdot 2} \]

      11. distribute-rgt-neg-in 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-z \cdot 9\right)} \cdot t\right) \cdot \frac{1}{a \cdot 2} \]

      12. *-commutative 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{t \cdot \left(-z \cdot 9\right)}\right) \cdot \frac{1}{a \cdot 2} \]

      13. distribute-rgt-neg-in 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}\right) \cdot \frac{1}{a \cdot 2} \]

      14. metadata-eval 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, t \cdot \left(z \cdot \color{blue}{-9}\right)\right) \cdot \frac{1}{a \cdot 2} \]

      15. *-commutative 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} \]

      16. associate-/r* 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} \]

      17. metadata-eval 94.3%

          \[\leadsto \mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{\color{blue}{0.5}}{a} \]

   3. Applied egg-rr 94.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
   4. Step-by-step derivation

      1. fma-udef 93.9%

         \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot -9\right)\right)} \cdot \frac{0.5}{a} \]

   5. Applied egg-rr 93.9%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot -9\right)\right)} \cdot \frac{0.5}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + t \cdot \left(z \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 3: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* 0.5 (* y (/ x a)))
   (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (y * (x / a));
	else
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 52.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 94.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 94.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 94.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]

   if -inf.0 < (*.f64 x y)

   1. Initial program 93.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in z around 0 94.4%

      \[\leadsto \frac{x \cdot y - \color{blue}{9 \cdot \left(t \cdot z\right)}}{a \cdot 2} \]
   3. Step-by-step derivation

      1. associate-*r* 94.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{\left(9 \cdot t\right) \cdot z}}{a \cdot 2} \]

      2. *-commutative 94.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

      3. *-commutative 94.4%

         \[\leadsto \frac{x \cdot y - z \cdot \color{blue}{\left(t \cdot 9\right)}}{a \cdot 2} \]

   4. Simplified 94.4%

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(t \cdot 9\right)}}{a \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 4: 67.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-14} \lor \neg \left(y \leq 2.9 \cdot 10^{+79}\right) \land \left(y \leq 4 \cdot 10^{+121} \lor \neg \left(y \leq 2.75 \cdot 10^{+149}\right)\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8e-14)
         (and (not (<= y 2.9e+79)) (or (<= y 4e+121) (not (<= y 2.75e+149)))))
   (* 0.5 (* y (/ x a)))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8e-14) || (!(y <= 2.9e+79) && ((y <= 4e+121) || !(y <= 2.75e+149)))) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-8d-14)) .or. (.not. (y <= 2.9d+79)) .and. (y <= 4d+121) .or. (.not. (y <= 2.75d+149))) then
        tmp = 0.5d0 * (y * (x / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8e-14) || (!(y <= 2.9e+79) && ((y <= 4e+121) || !(y <= 2.75e+149)))) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8e-14) or (not (y <= 2.9e+79) and ((y <= 4e+121) or not (y <= 2.75e+149))):
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8e-14) || (!(y <= 2.9e+79) && ((y <= 4e+121) || !(y <= 2.75e+149))))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8e-14) || (~((y <= 2.9e+79)) && ((y <= 4e+121) || ~((y <= 2.75e+149)))))
		tmp = 0.5 * (y * (x / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8e-14], And[N[Not[LessEqual[y, 2.9e+79]], $MachinePrecision], Or[LessEqual[y, 4e+121], N[Not[LessEqual[y, 2.75e+149]], $MachinePrecision]]]], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.99999999999999999e-14 or 2.89999999999999992e79 < y < 4.00000000000000015e121 or 2.74999999999999999e149 < y

   1. Initial program 89.4%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 71.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 77.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 75.8%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 75.8%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]

   if -7.99999999999999999e-14 < y < 2.89999999999999992e79 or 4.00000000000000015e121 < y < 2.74999999999999999e149

   1. Initial program 92.2%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around 0 72.1%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-14} \lor \neg \left(y \leq 2.9 \cdot 10^{+79}\right) \land \left(y \leq 4 \cdot 10^{+121} \lor \neg \left(y \leq 2.75 \cdot 10^{+149}\right)\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]

Alternative 5: 74.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+49)
   (* 0.5 (/ y (/ a x)))
   (if (<= (* x y) 1e+35) (* -4.5 (/ (* z t) a)) (* 0.5 (* y (/ x a))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= 1e+35) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d+49)) then
        tmp = 0.5d0 * (y / (a / x))
    else if ((x * y) <= 1d+35) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= 1e+35) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e+49:
		tmp = 0.5 * (y / (a / x))
	elif (x * y) <= 1e+35:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+49)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (Float64(x * y) <= 1e+35)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e+49)
		tmp = 0.5 * (y / (a / x));
	elseif ((x * y) <= 1e+35)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+49], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+35], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999946e48

   1. Initial program 80.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 69.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 80.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 79.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{a}\right)} \]

      2. clear-num 79.3%

         \[\leadsto 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right) \]

      3. un-div-inv 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Applied egg-rr 79.4%

      \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   if -9.99999999999999946e48 < (*.f64 x y) < 9.9999999999999997e34

   1. Initial program 92.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 9.9999999999999997e34 < (*.f64 x y)

   1. Initial program 94.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 85.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 84.1%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 88.5%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 88.5%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;\frac{z}{a} \cdot \frac{t}{-0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+49)
   (* 0.5 (/ y (/ a x)))
   (if (<= (* x y) 1e+35)
     (* (/ z a) (/ t -0.2222222222222222))
     (* 0.5 (* y (/ x a))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= 1e+35) {
		tmp = (z / a) * (t / -0.2222222222222222);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d+49)) then
        tmp = 0.5d0 * (y / (a / x))
    else if ((x * y) <= 1d+35) then
        tmp = (z / a) * (t / (-0.2222222222222222d0))
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= 1e+35) {
		tmp = (z / a) * (t / -0.2222222222222222);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e+49:
		tmp = 0.5 * (y / (a / x))
	elif (x * y) <= 1e+35:
		tmp = (z / a) * (t / -0.2222222222222222)
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+49)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (Float64(x * y) <= 1e+35)
		tmp = Float64(Float64(z / a) * Float64(t / -0.2222222222222222));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e+49)
		tmp = 0.5 * (y / (a / x));
	elseif ((x * y) <= 1e+35)
		tmp = (z / a) * (t / -0.2222222222222222);
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+49], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+35], N[(N[(z / a), $MachinePrecision] * N[(t / -0.2222222222222222), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999946e48

   1. Initial program 80.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 69.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 80.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 79.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{a}\right)} \]

      2. clear-num 79.3%

         \[\leadsto 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right) \]

      3. un-div-inv 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Applied egg-rr 79.4%

      \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   if -9.99999999999999946e48 < (*.f64 x y) < 9.9999999999999997e34

   1. Initial program 92.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 79.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

   4. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 78.8%

         \[\leadsto \color{blue}{\frac{-4.5}{\frac{a}{t \cdot z}}} \]

      2. associate-/r* 76.8%

         \[\leadsto \frac{-4.5}{\color{blue}{\frac{\frac{a}{t}}{z}}} \]

      3. associate-/l* 76.5%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot z}{\frac{a}{t}}} \]

      4. associate-*r/ 77.1%

         \[\leadsto \color{blue}{-4.5 \cdot \frac{z}{\frac{a}{t}}} \]

      5. *-commutative 77.1%

         \[\leadsto \color{blue}{\frac{z}{\frac{a}{t}} \cdot -4.5} \]

      6. associate-/r/ 79.0%

         \[\leadsto \color{blue}{\left(\frac{z}{a} \cdot t\right)} \cdot -4.5 \]

      7. associate-*l/ 79.0%

         \[\leadsto \color{blue}{\frac{z \cdot t}{a}} \cdot -4.5 \]

      8. *-commutative 79.0%

         \[\leadsto \frac{\color{blue}{t \cdot z}}{a} \cdot -4.5 \]

      9. metadata-eval 79.0%

         \[\leadsto \frac{t \cdot z}{a} \cdot \color{blue}{\frac{-9}{2}} \]

      10. times-frac 79.1%

          \[\leadsto \color{blue}{\frac{\left(t \cdot z\right) \cdot -9}{a \cdot 2}} \]

      11. *-commutative 79.1%

          \[\leadsto \frac{\color{blue}{\left(z \cdot t\right)} \cdot -9}{a \cdot 2} \]

      12. associate-*r* 79.1%

          \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]

      13. times-frac 79.1%

          \[\leadsto \color{blue}{\frac{z}{a} \cdot \frac{t \cdot -9}{2}} \]

      14. associate-/l* 79.1%

          \[\leadsto \frac{z}{a} \cdot \color{blue}{\frac{t}{\frac{2}{-9}}} \]

      15. metadata-eval 79.1%

          \[\leadsto \frac{z}{a} \cdot \frac{t}{\color{blue}{-0.2222222222222222}} \]

   6. Applied egg-rr 79.1%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot \frac{t}{-0.2222222222222222}} \]

   if 9.9999999999999997e34 < (*.f64 x y)

   1. Initial program 94.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 85.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 84.1%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 88.5%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 88.5%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;\frac{z}{a} \cdot \frac{t}{-0.2222222222222222}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 7: 73.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;t \cdot \frac{z \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+49)
   (* 0.5 (/ y (/ a x)))
   (if (<= (* x y) 1e+35) (* t (/ (* z -4.5) a)) (* 0.5 (* y (/ x a))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= 1e+35) {
		tmp = t * ((z * -4.5) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d+49)) then
        tmp = 0.5d0 * (y / (a / x))
    else if ((x * y) <= 1d+35) then
        tmp = t * ((z * (-4.5d0)) / a)
    else
        tmp = 0.5d0 * (y * (x / a))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+49) {
		tmp = 0.5 * (y / (a / x));
	} else if ((x * y) <= 1e+35) {
		tmp = t * ((z * -4.5) / a);
	} else {
		tmp = 0.5 * (y * (x / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e+49:
		tmp = 0.5 * (y / (a / x))
	elif (x * y) <= 1e+35:
		tmp = t * ((z * -4.5) / a)
	else:
		tmp = 0.5 * (y * (x / a))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+49)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (Float64(x * y) <= 1e+35)
		tmp = Float64(t * Float64(Float64(z * -4.5) / a));
	else
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e+49)
		tmp = 0.5 * (y / (a / x));
	elseif ((x * y) <= 1e+35)
		tmp = t * ((z * -4.5) / a);
	else
		tmp = 0.5 * (y * (x / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+49], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+35], N[(t * N[(N[(z * -4.5), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999946e48

   1. Initial program 80.6%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 69.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 80.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 79.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]
   5. Step-by-step derivation

      1. *-commutative 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{a}\right)} \]

      2. clear-num 79.3%

         \[\leadsto 0.5 \cdot \left(y \cdot \color{blue}{\frac{1}{\frac{a}{x}}}\right) \]

      3. un-div-inv 79.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   6. Applied egg-rr 79.4%

      \[\leadsto 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} \]

   if -9.99999999999999946e48 < (*.f64 x y) < 9.9999999999999997e34

   1. Initial program 92.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 79.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

   4. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]
   5. Step-by-step derivation

      1. associate-/l* 78.8%

         \[\leadsto \color{blue}{\frac{-4.5}{\frac{a}{t \cdot z}}} \]

      2. associate-/r* 76.8%

         \[\leadsto \frac{-4.5}{\color{blue}{\frac{\frac{a}{t}}{z}}} \]

      3. associate-/l* 76.5%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot z}{\frac{a}{t}}} \]

      4. associate-/r/ 78.5%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot z}{a} \cdot t} \]

      5. *-commutative 78.5%

         \[\leadsto \frac{\color{blue}{z \cdot -4.5}}{a} \cdot t \]

   6. Applied egg-rr 78.5%

      \[\leadsto \color{blue}{\frac{z \cdot -4.5}{a} \cdot t} \]

   if 9.9999999999999997e34 < (*.f64 x y)

   1. Initial program 94.3%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around inf 85.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 84.1%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

      2. associate-/r/ 88.5%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)} \]

   4. Simplified 88.5%

      \[\leadsto \color{blue}{0.5 \cdot \left(\frac{x}{a} \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+49}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+35}:\\ \;\;\;\;t \cdot \frac{z \cdot -4.5}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 8: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 4.6 \cdot 10^{-94}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 4.6e-94) (* -4.5 (/ (* z t) a)) (* -4.5 (/ z (/ a t)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.6e-94) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 4.6d-94) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (-4.5d0) * (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.6e-94) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (z / (a / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 4.6e-94:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = -4.5 * (z / (a / t))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 4.6e-94)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 4.6e-94)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = -4.5 * (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 4.6e-94], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.5999999999999999e-94

   1. Initial program 93.7%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around 0 50.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]

   if 4.5999999999999999e-94 < t

   1. Initial program 85.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Taylor expanded in x around 0 58.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   3. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto -4.5 \cdot \frac{\color{blue}{z \cdot t}}{a} \]

      2. associate-/l* 63.9%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{z}{\frac{a}{t}}} \]

   4. Simplified 63.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{z}{\frac{a}{t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.6 \cdot 10^{-94}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 9: 51.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ -4.5 \cdot \frac{z}{\frac{a}{t}} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (/ z (/ a t))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z / (a / t));
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (-4.5d0) * (z / (a / t))
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z / (a / t));
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	return -4.5 * (z / (a / t))

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(z / Float64(a / t)))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (z / (a / t));
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

2. Taylor expanded in x around 0 53.0%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Step-by-step derivation

   1. *-commutative 53.0%

      \[\leadsto -4.5 \cdot \frac{\color{blue}{z \cdot t}}{a} \]

   2. associate-/l* 53.0%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{z}{\frac{a}{t}}} \]

4. Simplified 53.0%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{z}{\frac{a}{t}}} \]

5. Final simplification 53.0%

   \[\leadsto -4.5 \cdot \frac{z}{\frac{a}{t}} \]

Developer target: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))