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

Percentage Accurate: 91.2% → 93.9%

Time: 9.6s

Alternatives: 6

Speedup: 0.6×

• 28.5% 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: 91.2% 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: 93.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (- (* x y) (* (* z 9.0) t)) 1e+294)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (fma -4.5 (* z (/ t a)) (* 0.5 (* x (/ y a))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - ((z * 9.0) * t)) <= 1e+294) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = fma(-4.5, (z * (t / a)), (0.5 * (x * (y / a))));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) <= 1e+294)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(0.5 * Float64(x * Float64(y / a))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], 1e+294], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 1.00000000000000007e294

   1. Initial program 96.2%

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

      1. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   if 1.00000000000000007e294 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 73.5%

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

      1. associate-*l* 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in x around 0 71.2%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. fma-def 71.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 82.0%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{\frac{a}{z}}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-/r/ 82.0%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{a} \cdot z}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      4. associate-*r/ 93.0%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)}\right) \]

   7. Simplified 93.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+294}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+57}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+57)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) 5e+108) (/ (* t -4.5) (/ a z)) (* 0.5 (/ y (/ a x))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+57) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 5e+108) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) <= (-5d+57)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= 5d+108) then
        tmp = (t * (-4.5d0)) / (a / z)
    else
        tmp = 0.5d0 * (y / (a / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+57) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= 5e+108) {
		tmp = (t * -4.5) / (a / z);
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+57:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= 5e+108:
		tmp = (t * -4.5) / (a / z)
	else:
		tmp = 0.5 * (y / (a / x))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+57)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= 5e+108)
		tmp = Float64(Float64(t * -4.5) / Float64(a / z));
	else
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+57)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= 5e+108)
		tmp = (t * -4.5) / (a / z);
	else
		tmp = 0.5 * (y / (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+57], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+108], N[(N[(t * -4.5), $MachinePrecision] / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999972e57

   1. Initial program 91.1%

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

      1. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in x around inf 80.1%

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

      1. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

   if -4.99999999999999972e57 < (*.f64 x y) < 4.99999999999999991e108

   1. Initial program 94.8%

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

      1. associate-*l* 94.7%

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

   3. Simplified 94.7%

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

      1. add-sqr-sqrt 41.2%

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

      2. sqrt-unprod 50.4%

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

      3. swap-sqr 50.3%

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

      4. metadata-eval 50.3%

         \[\leadsto \frac{x \cdot y - z \cdot \sqrt{\color{blue}{81} \cdot \left(t \cdot t\right)}}{a \cdot 2} \]

      5. metadata-eval 50.3%

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

      6. swap-sqr 50.4%

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

      7. *-commutative 50.4%

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

      8. *-commutative 50.4%

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

      9. sqrt-unprod 18.6%

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

      10. add-sqr-sqrt 31.6%

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

      11. add-cube-cbrt 31.6%

          \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)} \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}\right) \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}}}{a \cdot 2} \]

      12. pow3 31.6%

          \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)}\right)}^{3}}}{a \cdot 2} \]

   6. Applied egg-rr 94.0%

      \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{9 \cdot \left(z \cdot t\right)}\right)}^{3}}}{a \cdot 2} \]

   7. Taylor expanded in x around 0 72.5%

      \[\leadsto \color{blue}{-4.5 \cdot \left({1}^{0.3333333333333333} \cdot \frac{t \cdot z}{a}\right)} \]
   8. Step-by-step derivation

      1. pow-base-1 72.5%

         \[\leadsto -4.5 \cdot \left(\color{blue}{1} \cdot \frac{t \cdot z}{a}\right) \]

      2. associate-*r/ 72.5%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{1 \cdot \left(t \cdot z\right)}{a}} \]

      3. *-commutative 72.5%

         \[\leadsto -4.5 \cdot \frac{1 \cdot \color{blue}{\left(z \cdot t\right)}}{a} \]

      4. *-lft-identity 72.5%

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

      5. associate-*l/ 68.7%

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

      6. *-commutative 68.7%

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

   9. Simplified 68.7%

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

       1. associate-*r* 68.7%

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

       2. clear-num 68.3%

          \[\leadsto \left(-4.5 \cdot t\right) \cdot \color{blue}{\frac{1}{\frac{a}{z}}} \]

       3. un-div-inv 68.4%

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

   11. Applied egg-rr 68.4%

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

   if 4.99999999999999991e108 < (*.f64 x y)

   1. Initial program 84.6%

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

      1. associate-*l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in x around inf 80.1%

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

      1. associate-*r/ 91.0%

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

   7. Simplified 91.0%

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

      1. associate-*r/ 80.1%

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

      2. *-commutative 80.1%

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

      3. associate-/l* 90.9%

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

   9. Applied egg-rr 90.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+57}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+108}:\\ \;\;\;\;\frac{t \cdot -4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 2 \cdot 10^{+225}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 2e+225)
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
   (* 0.5 (* x (/ y a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 2e+225) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) <= 2d+225) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 2e+225) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 2e+225:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 2e+225)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 2e+225)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 2e+225], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 1.99999999999999986e225

   1. Initial program 94.4%

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

      1. associate-*l* 94.4%

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

   3. Simplified 94.4%

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

   if 1.99999999999999986e225 < (*.f64 x y)

   1. Initial program 76.0%

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

      1. associate-*l* 76.0%

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

   3. Simplified 76.0%

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

   5. Taylor expanded in x around inf 79.6%

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

      1. associate-*r/ 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 2 \cdot 10^{+225}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 1600:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.8e-182)
   (* -4.5 (/ (* z t) a))
   (if (<= t 1600.0) (* 0.5 (* x (/ y a))) (* -4.5 (/ t (/ a z))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e-182) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1600.0) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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 <= (-5.8d-182)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (t <= 1600.0d0) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.8e-182) {
		tmp = -4.5 * ((z * t) / a);
	} else if (t <= 1600.0) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.8e-182:
		tmp = -4.5 * ((z * t) / a)
	elif t <= 1600.0:
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.8e-182)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (t <= 1600.0)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.8e-182)
		tmp = -4.5 * ((z * t) / a);
	elseif (t <= 1600.0)
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.8e-182], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1600.0], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.79999999999999974e-182

   1. Initial program 92.9%

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

      1. associate-*l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around 0 61.7%

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

   if -5.79999999999999974e-182 < t < 1600

   1. Initial program 93.2%

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

      1. associate-*l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf 69.8%

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

      1. associate-*r/ 67.9%

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

   7. Simplified 67.9%

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

   if 1600 < t

   1. Initial program 90.1%

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

      1. associate-*l* 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around 0 69.1%

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

      1. associate-/l* 70.7%

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

   7. Simplified 70.7%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-182}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;t \leq 1600:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) * (t * (z / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-*l* 92.4%

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

3. Simplified 92.4%

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

   1. add-sqr-sqrt 40.7%

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

   2. sqrt-unprod 56.7%

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

   3. swap-sqr 56.6%

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

   4. metadata-eval 56.6%

      \[\leadsto \frac{x \cdot y - z \cdot \sqrt{\color{blue}{81} \cdot \left(t \cdot t\right)}}{a \cdot 2} \]

   5. metadata-eval 56.6%

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

   6. swap-sqr 56.7%

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

   7. *-commutative 56.7%

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

   8. *-commutative 56.7%

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

   9. sqrt-unprod 25.2%

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

   10. add-sqr-sqrt 45.5%

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

   11. add-cube-cbrt 45.5%

       \[\leadsto \frac{x \cdot y - \color{blue}{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)} \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}\right) \cdot \sqrt[3]{z \cdot \left(t \cdot -9\right)}}}{a \cdot 2} \]

   12. pow3 45.5%

       \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{z \cdot \left(t \cdot -9\right)}\right)}^{3}}}{a \cdot 2} \]

6. Applied egg-rr 91.9%

   \[\leadsto \frac{x \cdot y - \color{blue}{{\left(\sqrt[3]{9 \cdot \left(z \cdot t\right)}\right)}^{3}}}{a \cdot 2} \]

7. Taylor expanded in x around 0 54.2%

   \[\leadsto \color{blue}{-4.5 \cdot \left({1}^{0.3333333333333333} \cdot \frac{t \cdot z}{a}\right)} \]
8. Step-by-step derivation

   1. pow-base-1 54.2%

      \[\leadsto -4.5 \cdot \left(\color{blue}{1} \cdot \frac{t \cdot z}{a}\right) \]

   2. associate-*r/ 54.2%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{1 \cdot \left(t \cdot z\right)}{a}} \]

   3. *-commutative 54.2%

      \[\leadsto -4.5 \cdot \frac{1 \cdot \color{blue}{\left(z \cdot t\right)}}{a} \]

   4. *-lft-identity 54.2%

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

   5. associate-*l/ 52.4%

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

   6. *-commutative 52.4%

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

9. Simplified 52.4%

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

10. Final simplification 52.4%

    \[\leadsto -4.5 \cdot \left(t \cdot \frac{z}{a}\right) \]
11. Add Preprocessing

Alternative 6: 52.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a 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) * (t / (a / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-*l* 92.4%

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

3. Simplified 92.4%

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

5. Taylor expanded in x around 0 54.2%

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

   1. associate-/l* 52.2%

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

7. Simplified 52.2%

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

8. Final simplification 52.2%

   \[\leadsto -4.5 \cdot \frac{t}{\frac{a}{z}} \]
9. Add Preprocessing

Developer target: 93.7% accurate, 0.5× 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 2024024 
(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)))