Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, C

Percentage Accurate: 97.8% → 98.9%

Time: 8.8s

Alternatives: 15

Speedup: 1.0×

• 32.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Initial Program: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

Alternative 1: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - b \cdot \frac{a}{4}\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (fma t (/ z 16.0) (fma x y (- c (* b (/ a 4.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(t, (z / 16.0), fma(x, y, (c - (b * (a / 4.0)))));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(t, Float64(z / 16.0), fma(x, y, Float64(c - Float64(b * Float64(a / 4.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(t * N[(z / 16.0), $MachinePrecision] + N[(x * y + N[(c - N[(b * N[(a / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

   1. associate-+l- 98.4%

      \[\leadsto \color{blue}{\left(x \cdot y + \frac{z \cdot t}{16}\right) - \left(\frac{a \cdot b}{4} - c\right)} \]

   2. +-commutative 98.4%

      \[\leadsto \color{blue}{\left(\frac{z \cdot t}{16} + x \cdot y\right)} - \left(\frac{a \cdot b}{4} - c\right) \]

   3. associate--l+ 98.4%

      \[\leadsto \color{blue}{\frac{z \cdot t}{16} + \left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   4. associate-*l/ 98.4%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + \left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   5. *-commutative 98.4%

      \[\leadsto \color{blue}{t \cdot \frac{z}{16}} + \left(x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right) \]

   6. fma-def 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z}{16}, x \cdot y - \left(\frac{a \cdot b}{4} - c\right)\right)} \]

   7. fma-neg 99.2%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \color{blue}{\mathsf{fma}\left(x, y, -\left(\frac{a \cdot b}{4} - c\right)\right)}\right) \]

   8. neg-sub0 99.2%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{0 - \left(\frac{a \cdot b}{4} - c\right)}\right)\right) \]

   9. associate-+l- 99.2%

      \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{\left(0 - \frac{a \cdot b}{4}\right) + c}\right)\right) \]

   10. neg-sub0 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{\left(-\frac{a \cdot b}{4}\right)} + c\right)\right) \]

   11. +-commutative 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{c + \left(-\frac{a \cdot b}{4}\right)}\right)\right) \]

   12. unsub-neg 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, \color{blue}{c - \frac{a \cdot b}{4}}\right)\right) \]

   13. *-commutative 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - \frac{\color{blue}{b \cdot a}}{4}\right)\right) \]

   14. associate-*r/ 99.2%

       \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - \color{blue}{b \cdot \frac{a}{4}}\right)\right) \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - b \cdot \frac{a}{4}\right)\right)} \]

4. Final simplification 99.2%

   \[\leadsto \mathsf{fma}\left(t, \frac{z}{16}, \mathsf{fma}\left(x, y, c - b \cdot \frac{a}{4}\right)\right) \]

Alternative 2: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -4:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-85}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+116}:\\ \;\;\;\;c + t \cdot \frac{z}{16}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* b a) 0.25))))
   (if (<= (* b a) -2e+54)
     t_1
     (if (<= (* b a) -4.0)
       (+ c (* b (* a -0.25)))
       (if (<= (* b a) 5e-85)
         (+ (* 0.0625 (* t z)) (* x y))
         (if (<= (* b a) 2e+116) (+ c (* t (/ z 16.0))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -2e+54) {
		tmp = t_1;
	} else if ((b * a) <= -4.0) {
		tmp = c + (b * (a * -0.25));
	} else if ((b * a) <= 5e-85) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else if ((b * a) <= 2e+116) {
		tmp = c + (t * (z / 16.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((b * a) * 0.25d0)
    if ((b * a) <= (-2d+54)) then
        tmp = t_1
    else if ((b * a) <= (-4.0d0)) then
        tmp = c + (b * (a * (-0.25d0)))
    else if ((b * a) <= 5d-85) then
        tmp = (0.0625d0 * (t * z)) + (x * y)
    else if ((b * a) <= 2d+116) then
        tmp = c + (t * (z / 16.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -2e+54) {
		tmp = t_1;
	} else if ((b * a) <= -4.0) {
		tmp = c + (b * (a * -0.25));
	} else if ((b * a) <= 5e-85) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else if ((b * a) <= 2e+116) {
		tmp = c + (t * (z / 16.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) - ((b * a) * 0.25)
	tmp = 0
	if (b * a) <= -2e+54:
		tmp = t_1
	elif (b * a) <= -4.0:
		tmp = c + (b * (a * -0.25))
	elif (b * a) <= 5e-85:
		tmp = (0.0625 * (t * z)) + (x * y)
	elif (b * a) <= 2e+116:
		tmp = c + (t * (z / 16.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25))
	tmp = 0.0
	if (Float64(b * a) <= -2e+54)
		tmp = t_1;
	elseif (Float64(b * a) <= -4.0)
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	elseif (Float64(b * a) <= 5e-85)
		tmp = Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y));
	elseif (Float64(b * a) <= 2e+116)
		tmp = Float64(c + Float64(t * Float64(z / 16.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) - ((b * a) * 0.25);
	tmp = 0.0;
	if ((b * a) <= -2e+54)
		tmp = t_1;
	elseif ((b * a) <= -4.0)
		tmp = c + (b * (a * -0.25));
	elseif ((b * a) <= 5e-85)
		tmp = (0.0625 * (t * z)) + (x * y);
	elseif ((b * a) <= 2e+116)
		tmp = c + (t * (z / 16.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2e+54], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -4.0], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e-85], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+116], N[(c + N[(t * N[(z / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -2.0000000000000002e54 or 2.00000000000000003e116 < (*.f64 a b)

   1. Initial program 97.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 90.1%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 86.6%

      \[\leadsto \color{blue}{y \cdot x - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2.0000000000000002e54 < (*.f64 a b) < -4

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 83.9%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 83.9%

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

      2. *-commutative 83.9%

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

      3. associate-*r* 83.9%

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

   4. Simplified 83.9%

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

   if -4 < (*.f64 a b) < 5.0000000000000002e-85

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 94.5%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   3. Taylor expanded in c around 0 76.9%

      \[\leadsto \color{blue}{y \cdot x + 0.0625 \cdot \left(t \cdot z\right)} \]

   if 5.0000000000000002e-85 < (*.f64 a b) < 2.00000000000000003e116

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 76.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. associate-*r* 76.1%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. metadata-eval 76.1%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 76.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 76.0%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 76.0%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 76.0%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 76.1%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   4. Simplified 76.1%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -4:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-85}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+116}:\\ \;\;\;\;c + t \cdot \frac{z}{16}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 3: 89.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+151}:\\ \;\;\;\;\left(c + t_1\right) - t_2\\ \mathbf{elif}\;b \cdot a \leq -4 \lor \neg \left(b \cdot a \leq 5 \cdot 10^{+102}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;c + \left(t_1 + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))) (t_2 (* (* b a) 0.25)))
   (if (<= (* b a) -5e+151)
     (- (+ c t_1) t_2)
     (if (or (<= (* b a) -4.0) (not (<= (* b a) 5e+102)))
       (- (+ c (* x y)) t_2)
       (+ c (+ t_1 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = (b * a) * 0.25;
	double tmp;
	if ((b * a) <= -5e+151) {
		tmp = (c + t_1) - t_2;
	} else if (((b * a) <= -4.0) || !((b * a) <= 5e+102)) {
		tmp = (c + (x * y)) - t_2;
	} else {
		tmp = c + (t_1 + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.0625d0 * (t * z)
    t_2 = (b * a) * 0.25d0
    if ((b * a) <= (-5d+151)) then
        tmp = (c + t_1) - t_2
    else if (((b * a) <= (-4.0d0)) .or. (.not. ((b * a) <= 5d+102))) then
        tmp = (c + (x * y)) - t_2
    else
        tmp = c + (t_1 + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = (b * a) * 0.25;
	double tmp;
	if ((b * a) <= -5e+151) {
		tmp = (c + t_1) - t_2;
	} else if (((b * a) <= -4.0) || !((b * a) <= 5e+102)) {
		tmp = (c + (x * y)) - t_2;
	} else {
		tmp = c + (t_1 + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	t_2 = (b * a) * 0.25
	tmp = 0
	if (b * a) <= -5e+151:
		tmp = (c + t_1) - t_2
	elif ((b * a) <= -4.0) or not ((b * a) <= 5e+102):
		tmp = (c + (x * y)) - t_2
	else:
		tmp = c + (t_1 + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	t_2 = Float64(Float64(b * a) * 0.25)
	tmp = 0.0
	if (Float64(b * a) <= -5e+151)
		tmp = Float64(Float64(c + t_1) - t_2);
	elseif ((Float64(b * a) <= -4.0) || !(Float64(b * a) <= 5e+102))
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	else
		tmp = Float64(c + Float64(t_1 + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	t_2 = (b * a) * 0.25;
	tmp = 0.0;
	if ((b * a) <= -5e+151)
		tmp = (c + t_1) - t_2;
	elseif (((b * a) <= -4.0) || ~(((b * a) <= 5e+102)))
		tmp = (c + (x * y)) - t_2;
	else
		tmp = c + (t_1 + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+151], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Or[LessEqual[N[(b * a), $MachinePrecision], -4.0], N[Not[LessEqual[N[(b * a), $MachinePrecision], 5e+102]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(c + N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000002e151

   1. Initial program 96.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 92.3%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -5.0000000000000002e151 < (*.f64 a b) < -4 or 5e102 < (*.f64 a b)

   1. Initial program 98.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 96.7%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -4 < (*.f64 a b) < 5e102

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 94.4%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+151}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -4 \lor \neg \left(b \cdot a \leq 5 \cdot 10^{+102}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \]

Alternative 4: 59.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+36}:\\ \;\;\;\;c + t \cdot \frac{z}{16}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+60} \lor \neg \left(y \leq 5.9 \cdot 10^{+125}\right) \land y \leq 7.8 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))) (t_2 (+ c (* x y))))
   (if (<= y -2.1e-29)
     t_2
     (if (<= y -2.1e-301)
       t_1
       (if (<= y 5.1e+36)
         (+ c (* t (/ z 16.0)))
         (if (or (<= y 2.9e+60) (and (not (<= y 5.9e+125)) (<= y 7.8e+180)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if (y <= -2.1e-29) {
		tmp = t_2;
	} else if (y <= -2.1e-301) {
		tmp = t_1;
	} else if (y <= 5.1e+36) {
		tmp = c + (t * (z / 16.0));
	} else if ((y <= 2.9e+60) || (!(y <= 5.9e+125) && (y <= 7.8e+180))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    t_2 = c + (x * y)
    if (y <= (-2.1d-29)) then
        tmp = t_2
    else if (y <= (-2.1d-301)) then
        tmp = t_1
    else if (y <= 5.1d+36) then
        tmp = c + (t * (z / 16.0d0))
    else if ((y <= 2.9d+60) .or. (.not. (y <= 5.9d+125)) .and. (y <= 7.8d+180)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if (y <= -2.1e-29) {
		tmp = t_2;
	} else if (y <= -2.1e-301) {
		tmp = t_1;
	} else if (y <= 5.1e+36) {
		tmp = c + (t * (z / 16.0));
	} else if ((y <= 2.9e+60) || (!(y <= 5.9e+125) && (y <= 7.8e+180))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if y <= -2.1e-29:
		tmp = t_2
	elif y <= -2.1e-301:
		tmp = t_1
	elif y <= 5.1e+36:
		tmp = c + (t * (z / 16.0))
	elif (y <= 2.9e+60) or (not (y <= 5.9e+125) and (y <= 7.8e+180)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (y <= -2.1e-29)
		tmp = t_2;
	elseif (y <= -2.1e-301)
		tmp = t_1;
	elseif (y <= 5.1e+36)
		tmp = Float64(c + Float64(t * Float64(z / 16.0)));
	elseif ((y <= 2.9e+60) || (!(y <= 5.9e+125) && (y <= 7.8e+180)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if (y <= -2.1e-29)
		tmp = t_2;
	elseif (y <= -2.1e-301)
		tmp = t_1;
	elseif (y <= 5.1e+36)
		tmp = c + (t * (z / 16.0));
	elseif ((y <= 2.9e+60) || (~((y <= 5.9e+125)) && (y <= 7.8e+180)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e-29], t$95$2, If[LessEqual[y, -2.1e-301], t$95$1, If[LessEqual[y, 5.1e+36], N[(c + N[(t * N[(z / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.9e+60], And[N[Not[LessEqual[y, 5.9e+125]], $MachinePrecision], LessEqual[y, 7.8e+180]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999989e-29 or 2.9e60 < y < 5.9000000000000001e125 or 7.8000000000000002e180 < y

   1. Initial program 97.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 66.7%

      \[\leadsto \color{blue}{y \cdot x} + c \]

   if -2.09999999999999989e-29 < y < -2.0999999999999999e-301 or 5.09999999999999973e36 < y < 2.9e60 or 5.9000000000000001e125 < y < 7.8000000000000002e180

   1. Initial program 98.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 67.4%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-*r* 67.4%

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

   4. Simplified 67.4%

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

   if -2.0999999999999999e-301 < y < 5.09999999999999973e36

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 66.7%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. associate-*r* 66.7%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. metadata-eval 66.7%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 66.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 66.6%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 66.6%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 66.6%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 66.7%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   4. Simplified 66.7%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-29}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-301}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+36}:\\ \;\;\;\;c + t \cdot \frac{z}{16}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+60} \lor \neg \left(y \leq 5.9 \cdot 10^{+125}\right) \land y \leq 7.8 \cdot 10^{+180}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 5: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+176} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1e+176) (not (<= (* b a) 2e+116)))
   (- (* x y) (* (* b a) 0.25))
   (+ c (+ (* 0.0625 (* t z)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1e+176) || !((b * a) <= 2e+116)) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-1d+176)) .or. (.not. ((b * a) <= 2d+116))) then
        tmp = (x * y) - ((b * a) * 0.25d0)
    else
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1e+176) || !((b * a) <= 2e+116)) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1e+176) or not ((b * a) <= 2e+116):
		tmp = (x * y) - ((b * a) * 0.25)
	else:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1e+176) || !(Float64(b * a) <= 2e+116))
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -1e+176) || ~(((b * a) <= 2e+116)))
		tmp = (x * y) - ((b * a) * 0.25);
	else
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1e+176], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+116]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1e176 or 2.00000000000000003e116 < (*.f64 a b)

   1. Initial program 96.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 93.6%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 92.8%

      \[\leadsto \color{blue}{y \cdot x - 0.25 \cdot \left(a \cdot b\right)} \]

   if -1e176 < (*.f64 a b) < 2.00000000000000003e116

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 90.6%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+176} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+116}\right):\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \]

Alternative 6: 89.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4 \lor \neg \left(b \cdot a \leq 5 \cdot 10^{+102}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -4.0) (not (<= (* b a) 5e+102)))
   (- (+ c (* x y)) (* (* b a) 0.25))
   (+ c (+ (* 0.0625 (* t z)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -4.0) || !((b * a) <= 5e+102)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-4.0d0)) .or. (.not. ((b * a) <= 5d+102))) then
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    else
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -4.0) || !((b * a) <= 5e+102)) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -4.0) or not ((b * a) <= 5e+102):
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	else:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -4.0) || !(Float64(b * a) <= 5e+102))
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -4.0) || ~(((b * a) <= 5e+102)))
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	else
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -4.0], N[Not[LessEqual[N[(b * a), $MachinePrecision], 5e+102]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -4 or 5e102 < (*.f64 a b)

   1. Initial program 97.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 90.4%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -4 < (*.f64 a b) < 5e102

   1. Initial program 99.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 94.4%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -4 \lor \neg \left(b \cdot a \leq 5 \cdot 10^{+102}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \]

Alternative 7: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+167}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+116}:\\ \;\;\;\;c + \left(t_2 + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)) (t_2 (* 0.0625 (* t z))))
   (if (<= (* b a) -2e+167)
     (- t_2 t_1)
     (if (<= (* b a) 2e+116) (+ c (+ t_2 (* x y))) (- (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -2e+167) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 2e+116) {
		tmp = c + (t_2 + (x * y));
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = 0.0625d0 * (t * z)
    if ((b * a) <= (-2d+167)) then
        tmp = t_2 - t_1
    else if ((b * a) <= 2d+116) then
        tmp = c + (t_2 + (x * y))
    else
        tmp = (x * y) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -2e+167) {
		tmp = t_2 - t_1;
	} else if ((b * a) <= 2e+116) {
		tmp = c + (t_2 + (x * y));
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = 0.0625 * (t * z)
	tmp = 0
	if (b * a) <= -2e+167:
		tmp = t_2 - t_1
	elif (b * a) <= 2e+116:
		tmp = c + (t_2 + (x * y))
	else:
		tmp = (x * y) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (Float64(b * a) <= -2e+167)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(b * a) <= 2e+116)
		tmp = Float64(c + Float64(t_2 + Float64(x * y)));
	else
		tmp = Float64(Float64(x * y) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	t_2 = 0.0625 * (t * z);
	tmp = 0.0;
	if ((b * a) <= -2e+167)
		tmp = t_2 - t_1;
	elseif ((b * a) <= 2e+116)
		tmp = c + (t_2 + (x * y));
	else
		tmp = (x * y) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2e+167], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+116], N[(c + N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e167

   1. Initial program 95.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around 0 91.5%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 90.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   if -2.0000000000000001e167 < (*.f64 a b) < 2.00000000000000003e116

   1. Initial program 99.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 91.0%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   if 2.00000000000000003e116 < (*.f64 a b)

   1. Initial program 96.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in c around 0 100.0%

      \[\leadsto \color{blue}{y \cdot x - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+167}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+116}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 8: 36.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-139}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+36}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+57} \lor \neg \left(y \leq 3.9 \cdot 10^{+127}\right) \land y \leq 4.8 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))))
   (if (<= y -6.5e-139)
     (* x y)
     (if (<= y -5e-288)
       t_1
       (if (<= y 2.15e+36)
         (* 0.0625 (* t z))
         (if (or (<= y 1.5e+57) (and (not (<= y 3.9e+127)) (<= y 4.8e+181)))
           t_1
           (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if (y <= -6.5e-139) {
		tmp = x * y;
	} else if (y <= -5e-288) {
		tmp = t_1;
	} else if (y <= 2.15e+36) {
		tmp = 0.0625 * (t * z);
	} else if ((y <= 1.5e+57) || (!(y <= 3.9e+127) && (y <= 4.8e+181))) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (a * (-0.25d0))
    if (y <= (-6.5d-139)) then
        tmp = x * y
    else if (y <= (-5d-288)) then
        tmp = t_1
    else if (y <= 2.15d+36) then
        tmp = 0.0625d0 * (t * z)
    else if ((y <= 1.5d+57) .or. (.not. (y <= 3.9d+127)) .and. (y <= 4.8d+181)) then
        tmp = t_1
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b * (a * -0.25);
	double tmp;
	if (y <= -6.5e-139) {
		tmp = x * y;
	} else if (y <= -5e-288) {
		tmp = t_1;
	} else if (y <= 2.15e+36) {
		tmp = 0.0625 * (t * z);
	} else if ((y <= 1.5e+57) || (!(y <= 3.9e+127) && (y <= 4.8e+181))) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	tmp = 0
	if y <= -6.5e-139:
		tmp = x * y
	elif y <= -5e-288:
		tmp = t_1
	elif y <= 2.15e+36:
		tmp = 0.0625 * (t * z)
	elif (y <= 1.5e+57) or (not (y <= 3.9e+127) and (y <= 4.8e+181)):
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (y <= -6.5e-139)
		tmp = Float64(x * y);
	elseif (y <= -5e-288)
		tmp = t_1;
	elseif (y <= 2.15e+36)
		tmp = Float64(0.0625 * Float64(t * z));
	elseif ((y <= 1.5e+57) || (!(y <= 3.9e+127) && (y <= 4.8e+181)))
		tmp = t_1;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b * (a * -0.25);
	tmp = 0.0;
	if (y <= -6.5e-139)
		tmp = x * y;
	elseif (y <= -5e-288)
		tmp = t_1;
	elseif (y <= 2.15e+36)
		tmp = 0.0625 * (t * z);
	elseif ((y <= 1.5e+57) || (~((y <= 3.9e+127)) && (y <= 4.8e+181)))
		tmp = t_1;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e-139], N[(x * y), $MachinePrecision], If[LessEqual[y, -5e-288], t$95$1, If[LessEqual[y, 2.15e+36], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 1.5e+57], And[N[Not[LessEqual[y, 3.9e+127]], $MachinePrecision], LessEqual[y, 4.8e+181]]], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e-139 or 1.5e57 < y < 3.89999999999999981e127 or 4.80000000000000004e181 < y

   1. Initial program 97.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 81.4%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in y around inf 46.2%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -6.5e-139 < y < -5.00000000000000011e-288 or 2.15000000000000002e36 < y < 1.5e57 or 3.89999999999999981e127 < y < 4.80000000000000004e181

   1. Initial program 98.3%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 83.9%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in a around inf 54.1%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 54.1%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 54.1%

         \[\leadsto \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      3. *-commutative 54.1%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} \]

   if -5.00000000000000011e-288 < y < 2.15000000000000002e36

   1. Initial program 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 68.5%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. associate-*r* 68.5%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. metadata-eval 68.5%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 68.4%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 68.4%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 68.4%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 68.4%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 68.5%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   4. Simplified 68.5%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   5. Taylor expanded in z around inf 47.0%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-139}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-288}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+36}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+57} \lor \neg \left(y \leq 3.9 \cdot 10^{+127}\right) \land y \leq 4.8 \cdot 10^{+181}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ c + \left(\left(\frac{t \cdot z}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ c (- (+ (/ (* t z) 16.0) (* x y)) (/ (* b a) 4.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = c + ((((t * z) / 16.0d0) + (x * y)) - ((b * a) / 4.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0));
}

Python

def code(x, y, z, t, a, b, c):
	return c + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(c + Float64(Float64(Float64(Float64(t * z) / 16.0) + Float64(x * y)) - Float64(Float64(b * a) / 4.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c + ((((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(c + N[(N[(N[(N[(t * z), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Final simplification 98.4%

   \[\leadsto c + \left(\left(\frac{t \cdot z}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\right) \]

Alternative 10: 52.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \leq -5.7 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-124}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* b (* a -0.25))))
   (if (<= a -5.7e+156)
     t_2
     (if (<= a 9.5e-239)
       t_1
       (if (<= a 8.5e-124) (* 0.0625 (* t z)) (if (<= a 1.05e+27) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (a <= -5.7e+156) {
		tmp = t_2;
	} else if (a <= 9.5e-239) {
		tmp = t_1;
	} else if (a <= 8.5e-124) {
		tmp = 0.0625 * (t * z);
	} else if (a <= 1.05e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = b * (a * (-0.25d0))
    if (a <= (-5.7d+156)) then
        tmp = t_2
    else if (a <= 9.5d-239) then
        tmp = t_1
    else if (a <= 8.5d-124) then
        tmp = 0.0625d0 * (t * z)
    else if (a <= 1.05d+27) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = b * (a * -0.25);
	double tmp;
	if (a <= -5.7e+156) {
		tmp = t_2;
	} else if (a <= 9.5e-239) {
		tmp = t_1;
	} else if (a <= 8.5e-124) {
		tmp = 0.0625 * (t * z);
	} else if (a <= 1.05e+27) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = b * (a * -0.25)
	tmp = 0
	if a <= -5.7e+156:
		tmp = t_2
	elif a <= 9.5e-239:
		tmp = t_1
	elif a <= 8.5e-124:
		tmp = 0.0625 * (t * z)
	elif a <= 1.05e+27:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (a <= -5.7e+156)
		tmp = t_2;
	elseif (a <= 9.5e-239)
		tmp = t_1;
	elseif (a <= 8.5e-124)
		tmp = Float64(0.0625 * Float64(t * z));
	elseif (a <= 1.05e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = b * (a * -0.25);
	tmp = 0.0;
	if (a <= -5.7e+156)
		tmp = t_2;
	elseif (a <= 9.5e-239)
		tmp = t_1;
	elseif (a <= 8.5e-124)
		tmp = 0.0625 * (t * z);
	elseif (a <= 1.05e+27)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.7e+156], t$95$2, If[LessEqual[a, 9.5e-239], t$95$1, If[LessEqual[a, 8.5e-124], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+27], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.69999999999999998e156 or 1.04999999999999997e27 < a

   1. Initial program 97.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 86.0%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in a around inf 67.4%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 67.4%

         \[\leadsto \color{blue}{\left(-0.25 \cdot a\right) \cdot b} \]

      2. *-commutative 67.4%

         \[\leadsto \color{blue}{\left(a \cdot -0.25\right)} \cdot b \]

      3. *-commutative 67.4%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} \]

   if -5.69999999999999998e156 < a < 9.4999999999999992e-239 or 8.5000000000000002e-124 < a < 1.04999999999999997e27

   1. Initial program 98.6%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 58.3%

      \[\leadsto \color{blue}{y \cdot x} + c \]

   if 9.4999999999999992e-239 < a < 8.5000000000000002e-124

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 62.2%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. associate-*r* 62.2%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. metadata-eval 62.2%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 61.9%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 62.0%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 62.0%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 62.0%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 62.2%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   4. Simplified 62.2%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   5. Taylor expanded in z around inf 47.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.7 \cdot 10^{+156}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-239}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-124}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 11: 56.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-239}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-180}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* b (* a -0.25)))))
   (if (<= a -2.2e+97)
     t_1
     (if (<= a 4.3e-239)
       (+ c (* x y))
       (if (<= a 3.15e-180) (* 0.0625 (* t z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if (a <= -2.2e+97) {
		tmp = t_1;
	} else if (a <= 4.3e-239) {
		tmp = c + (x * y);
	} else if (a <= 3.15e-180) {
		tmp = 0.0625 * (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (b * (a * (-0.25d0)))
    if (a <= (-2.2d+97)) then
        tmp = t_1
    else if (a <= 4.3d-239) then
        tmp = c + (x * y)
    else if (a <= 3.15d-180) then
        tmp = 0.0625d0 * (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (b * (a * -0.25));
	double tmp;
	if (a <= -2.2e+97) {
		tmp = t_1;
	} else if (a <= 4.3e-239) {
		tmp = c + (x * y);
	} else if (a <= 3.15e-180) {
		tmp = 0.0625 * (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (b * (a * -0.25))
	tmp = 0
	if a <= -2.2e+97:
		tmp = t_1
	elif a <= 4.3e-239:
		tmp = c + (x * y)
	elif a <= 3.15e-180:
		tmp = 0.0625 * (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (a <= -2.2e+97)
		tmp = t_1;
	elseif (a <= 4.3e-239)
		tmp = Float64(c + Float64(x * y));
	elseif (a <= 3.15e-180)
		tmp = Float64(0.0625 * Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (b * (a * -0.25));
	tmp = 0.0;
	if (a <= -2.2e+97)
		tmp = t_1;
	elseif (a <= 4.3e-239)
		tmp = c + (x * y);
	elseif (a <= 3.15e-180)
		tmp = 0.0625 * (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+97], t$95$1, If[LessEqual[a, 4.3e-239], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.15e-180], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.2000000000000001e97 or 3.1499999999999998e-180 < a

   1. Initial program 98.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 63.2%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 63.2%

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

      2. *-commutative 63.2%

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

      3. associate-*r* 63.2%

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

   4. Simplified 63.2%

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

   if -2.2000000000000001e97 < a < 4.3e-239

   1. Initial program 98.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in x around inf 62.1%

      \[\leadsto \color{blue}{y \cdot x} + c \]

   if 4.3e-239 < a < 3.1499999999999998e-180

   1. Initial program 99.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 63.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. associate-*r* 63.3%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. metadata-eval 63.3%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 63.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 63.2%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 63.2%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 63.2%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 63.3%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   4. Simplified 63.3%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   5. Taylor expanded in z around inf 50.3%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-239}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq 3.15 \cdot 10^{-180}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 12: 58.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-123} \lor \neg \left(b \leq 8.5 \cdot 10^{+76}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.3e-123) (not (<= b 8.5e+76)))
   (+ c (* b (* a -0.25)))
   (+ (* 0.0625 (* t z)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.3e-123) || !(b <= 8.5e+76)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = (0.0625 * (t * z)) + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.3d-123)) .or. (.not. (b <= 8.5d+76))) then
        tmp = c + (b * (a * (-0.25d0)))
    else
        tmp = (0.0625d0 * (t * z)) + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.3e-123) || !(b <= 8.5e+76)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = (0.0625 * (t * z)) + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.3e-123) or not (b <= 8.5e+76):
		tmp = c + (b * (a * -0.25))
	else:
		tmp = (0.0625 * (t * z)) + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.3e-123) || !(b <= 8.5e+76))
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	else
		tmp = Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.3e-123) || ~((b <= 8.5e+76)))
		tmp = c + (b * (a * -0.25));
	else
		tmp = (0.0625 * (t * z)) + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.3e-123], N[Not[LessEqual[b, 8.5e+76]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.29999999999999998e-123 or 8.49999999999999992e76 < b

   1. Initial program 97.9%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around inf 61.6%

      \[\leadsto \color{blue}{-0.25 \cdot \left(a \cdot b\right)} + c \]
   3. Step-by-step derivation

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

      3. associate-*r* 61.6%

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

   4. Simplified 61.6%

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

   if -1.29999999999999998e-123 < b < 8.49999999999999992e76

   1. Initial program 99.1%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0 85.4%

      \[\leadsto \color{blue}{\left(y \cdot x + 0.0625 \cdot \left(t \cdot z\right)\right)} + c \]

   3. Taylor expanded in c around 0 65.4%

      \[\leadsto \color{blue}{y \cdot x + 0.0625 \cdot \left(t \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-123} \lor \neg \left(b \leq 8.5 \cdot 10^{+76}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \end{array} \]

Alternative 13: 37.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+52}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -2.7e-167) (* x y) (if (<= y 2.4e+52) (* 0.0625 (* t z)) (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -2.7e-167) {
		tmp = x * y;
	} else if (y <= 2.4e+52) {
		tmp = 0.0625 * (t * z);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-2.7d-167)) then
        tmp = x * y
    else if (y <= 2.4d+52) then
        tmp = 0.0625d0 * (t * z)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -2.7e-167) {
		tmp = x * y;
	} else if (y <= 2.4e+52) {
		tmp = 0.0625 * (t * z);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -2.7e-167:
		tmp = x * y
	elif y <= 2.4e+52:
		tmp = 0.0625 * (t * z)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -2.7e-167)
		tmp = Float64(x * y);
	elseif (y <= 2.4e+52)
		tmp = Float64(0.0625 * Float64(t * z));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -2.7e-167)
		tmp = x * y;
	elseif (y <= 2.4e+52)
		tmp = 0.0625 * (t * z);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -2.7e-167], N[(x * y), $MachinePrecision], If[LessEqual[y, 2.4e+52], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7000000000000001e-167 or 2.4e52 < y

   1. Initial program 98.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 82.8%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in y around inf 45.0%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -2.7000000000000001e-167 < y < 2.4e52

   1. Initial program 99.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} + c \]
   3. Step-by-step derivation

      1. associate-*r* 60.6%

         \[\leadsto \color{blue}{\left(0.0625 \cdot t\right) \cdot z} + c \]

      2. metadata-eval 60.6%

         \[\leadsto \left(\color{blue}{\frac{1}{16}} \cdot t\right) \cdot z + c \]

      3. associate-/r/ 60.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{16}{t}}} \cdot z + c \]

      4. associate-*l/ 60.5%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\frac{16}{t}}} + c \]

      5. *-commutative 60.5%

         \[\leadsto \frac{\color{blue}{z \cdot 1}}{\frac{16}{t}} + c \]

      6. *-rgt-identity 60.5%

         \[\leadsto \frac{\color{blue}{z}}{\frac{16}{t}} + c \]

      7. associate-/r/ 60.6%

         \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   4. Simplified 60.6%

      \[\leadsto \color{blue}{\frac{z}{16} \cdot t} + c \]

   5. Taylor expanded in z around inf 39.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-167}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+52}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 14: 37.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.75 \cdot 10^{+177}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -3.75e+177) c (if (<= c 1.7e+128) (* x y) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -3.75e+177) {
		tmp = c;
	} else if (c <= 1.7e+128) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-3.75d+177)) then
        tmp = c
    else if (c <= 1.7d+128) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -3.75e+177) {
		tmp = c;
	} else if (c <= 1.7e+128) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -3.75e+177:
		tmp = c
	elif c <= 1.7e+128:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -3.75e+177)
		tmp = c;
	elseif (c <= 1.7e+128)
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -3.75e+177)
		tmp = c;
	elseif (c <= 1.7e+128)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -3.75e+177], c, If[LessEqual[c, 1.7e+128], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -3.7500000000000002e177 or 1.6999999999999999e128 < c

   1. Initial program 98.5%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in c around inf 59.2%

      \[\leadsto \color{blue}{c} \]

   if -3.7500000000000002e177 < c < 1.6999999999999999e128

   1. Initial program 98.4%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in z around 0 70.9%

      \[\leadsto \color{blue}{\left(c + y \cdot x\right) - 0.25 \cdot \left(a \cdot b\right)} \]

   3. Taylor expanded in y around inf 34.9%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.75 \cdot 10^{+177}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{+128}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 15: 22.8% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Python

def code(x, y, z, t, a, b, c):
	return c

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 98.4%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Taylor expanded in c around inf 20.8%

   \[\leadsto \color{blue}{c} \]

3. Final simplification 20.8%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))