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

Percentage Accurate: 97.5% → 98.8%

Time: 8.2s

Alternatives: 12

Speedup: 1.0×

• 33.1% 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: 97.5% 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: 98.8% 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 98.0%

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

   1. associate-+l- 98.0%

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

   2. +-commutative 98.0%

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

   3. associate--l+ 98.0%

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

   4. associate-*l/ 98.0%

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

   5. *-commutative 98.0%

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

   6. fma-def 98.8%

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

   7. fma-neg 98.8%

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

   8. neg-sub0 98.8%

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

   9. associate-+l- 98.8%

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

   10. neg-sub0 98.8%

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

   11. +-commutative 98.8%

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

   12. unsub-neg 98.8%

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

   13. *-commutative 98.8%

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

   14. associate-*r/ 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 44.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ t_2 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -1.08 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -8.5 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -8.2 \cdot 10^{-292}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 2.25 \cdot 10^{-184}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 8.8 \cdot 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))) (t_2 (* (* b a) -0.25)))
   (if (<= (* b a) -1.08e+102)
     t_2
     (if (<= (* b a) -8.5e-195)
       t_1
       (if (<= (* b a) -8.2e-292)
         c
         (if (<= (* b a) 2.25e-184)
           (* x y)
           (if (<= (* b a) 8.8e+191) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -1.08e+102) {
		tmp = t_2;
	} else if ((b * a) <= -8.5e-195) {
		tmp = t_1;
	} else if ((b * a) <= -8.2e-292) {
		tmp = c;
	} else if ((b * a) <= 2.25e-184) {
		tmp = x * y;
	} else if ((b * a) <= 8.8e+191) {
		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 = t * (z * 0.0625d0)
    t_2 = (b * a) * (-0.25d0)
    if ((b * a) <= (-1.08d+102)) then
        tmp = t_2
    else if ((b * a) <= (-8.5d-195)) then
        tmp = t_1
    else if ((b * a) <= (-8.2d-292)) then
        tmp = c
    else if ((b * a) <= 2.25d-184) then
        tmp = x * y
    else if ((b * a) <= 8.8d+191) 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 = t * (z * 0.0625);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -1.08e+102) {
		tmp = t_2;
	} else if ((b * a) <= -8.5e-195) {
		tmp = t_1;
	} else if ((b * a) <= -8.2e-292) {
		tmp = c;
	} else if ((b * a) <= 2.25e-184) {
		tmp = x * y;
	} else if ((b * a) <= 8.8e+191) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	t_2 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -1.08e+102:
		tmp = t_2
	elif (b * a) <= -8.5e-195:
		tmp = t_1
	elif (b * a) <= -8.2e-292:
		tmp = c
	elif (b * a) <= 2.25e-184:
		tmp = x * y
	elif (b * a) <= 8.8e+191:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	t_2 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -1.08e+102)
		tmp = t_2;
	elseif (Float64(b * a) <= -8.5e-195)
		tmp = t_1;
	elseif (Float64(b * a) <= -8.2e-292)
		tmp = c;
	elseif (Float64(b * a) <= 2.25e-184)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 8.8e+191)
		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 = t * (z * 0.0625);
	t_2 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -1.08e+102)
		tmp = t_2;
	elseif ((b * a) <= -8.5e-195)
		tmp = t_1;
	elseif ((b * a) <= -8.2e-292)
		tmp = c;
	elseif ((b * a) <= 2.25e-184)
		tmp = x * y;
	elseif ((b * a) <= 8.8e+191)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1.08e+102], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -8.5e-195], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -8.2e-292], c, If[LessEqual[N[(b * a), $MachinePrecision], 2.25e-184], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 8.8e+191], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.08000000000000002e102 or 8.80000000000000001e191 < (*.f64 a b)

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 92.5%

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

   3. Taylor expanded in a around inf 79.0%

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

      1. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   if -1.08000000000000002e102 < (*.f64 a b) < -8.50000000000000023e-195 or 2.2500000000000001e-184 < (*.f64 a b) < 8.80000000000000001e191

   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 x around 0 72.7%

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

   3. Taylor expanded in t around inf 44.2%

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

      1. associate-*r* 44.2%

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

      2. *-commutative 44.2%

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

      3. associate-*l* 44.2%

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

   5. Simplified 44.2%

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

   if -8.50000000000000023e-195 < (*.f64 a b) < -8.20000000000000087e-292

   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 c around inf 61.1%

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

   if -8.20000000000000087e-292 < (*.f64 a b) < 2.2500000000000001e-184

   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 0 83.9%

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

   3. Taylor expanded in y around inf 57.2%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.08 \cdot 10^{+102}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -8.5 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq -8.2 \cdot 10^{-292}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 2.25 \cdot 10^{-184}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 8.8 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 3: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;b \cdot a \leq -2.8 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -2.5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 6 \cdot 10^{-184}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* 0.0625 (* t z)))) (t_2 (- (* x y) (* (* b a) 0.25))))
   (if (<= (* b a) -2.8e+98)
     t_2
     (if (<= (* b a) -2.5e-56)
       t_1
       (if (<= (* b a) 6e-184)
         (+ c (* x y))
         (if (<= (* b a) 1.8e+31) 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 + (0.0625 * (t * z));
	double t_2 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -2.8e+98) {
		tmp = t_2;
	} else if ((b * a) <= -2.5e-56) {
		tmp = t_1;
	} else if ((b * a) <= 6e-184) {
		tmp = c + (x * y);
	} else if ((b * a) <= 1.8e+31) {
		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 + (0.0625d0 * (t * z))
    t_2 = (x * y) - ((b * a) * 0.25d0)
    if ((b * a) <= (-2.8d+98)) then
        tmp = t_2
    else if ((b * a) <= (-2.5d-56)) then
        tmp = t_1
    else if ((b * a) <= 6d-184) then
        tmp = c + (x * y)
    else if ((b * a) <= 1.8d+31) 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 + (0.0625 * (t * z));
	double t_2 = (x * y) - ((b * a) * 0.25);
	double tmp;
	if ((b * a) <= -2.8e+98) {
		tmp = t_2;
	} else if ((b * a) <= -2.5e-56) {
		tmp = t_1;
	} else if ((b * a) <= 6e-184) {
		tmp = c + (x * y);
	} else if ((b * a) <= 1.8e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (0.0625 * (t * z))
	t_2 = (x * y) - ((b * a) * 0.25)
	tmp = 0
	if (b * a) <= -2.8e+98:
		tmp = t_2
	elif (b * a) <= -2.5e-56:
		tmp = t_1
	elif (b * a) <= 6e-184:
		tmp = c + (x * y)
	elif (b * a) <= 1.8e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(0.0625 * Float64(t * z)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25))
	tmp = 0.0
	if (Float64(b * a) <= -2.8e+98)
		tmp = t_2;
	elseif (Float64(b * a) <= -2.5e-56)
		tmp = t_1;
	elseif (Float64(b * a) <= 6e-184)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(b * a) <= 1.8e+31)
		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 + (0.0625 * (t * z));
	t_2 = (x * y) - ((b * a) * 0.25);
	tmp = 0.0;
	if ((b * a) <= -2.8e+98)
		tmp = t_2;
	elseif ((b * a) <= -2.5e-56)
		tmp = t_1;
	elseif ((b * a) <= 6e-184)
		tmp = c + (x * y);
	elseif ((b * a) <= 1.8e+31)
		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[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2.8e+98], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -2.5e-56], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 6e-184], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1.8e+31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.8000000000000001e98 or 1.79999999999999998e31 < (*.f64 a b)

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 87.1%

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

   3. Taylor expanded in c around 0 82.3%

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

   if -2.8000000000000001e98 < (*.f64 a b) < -2.49999999999999999e-56 or 5.99999999999999982e-184 < (*.f64 a b) < 1.79999999999999998e31

   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 72.6%

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

   if -2.49999999999999999e-56 < (*.f64 a b) < 5.99999999999999982e-184

   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 x around inf 79.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2.8 \cdot 10^{+98}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -2.5 \cdot 10^{-56}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 6 \cdot 10^{-184}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 1.8 \cdot 10^{+31}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 4: 61.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -8.5 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 3.1 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5.5 \cdot 10^{-87}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2.3 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* (* b a) -0.25)))
   (if (<= (* b a) -8.5e+143)
     t_2
     (if (<= (* b a) 3.1e-177)
       t_1
       (if (<= (* b a) 5.5e-87)
         (* t (* z 0.0625))
         (if (<= (* b a) 2.3e+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 + (x * y);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -8.5e+143) {
		tmp = t_2;
	} else if ((b * a) <= 3.1e-177) {
		tmp = t_1;
	} else if ((b * a) <= 5.5e-87) {
		tmp = t * (z * 0.0625);
	} else if ((b * a) <= 2.3e+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 + (x * y)
    t_2 = (b * a) * (-0.25d0)
    if ((b * a) <= (-8.5d+143)) then
        tmp = t_2
    else if ((b * a) <= 3.1d-177) then
        tmp = t_1
    else if ((b * a) <= 5.5d-87) then
        tmp = t * (z * 0.0625d0)
    else if ((b * a) <= 2.3d+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 + (x * y);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -8.5e+143) {
		tmp = t_2;
	} else if ((b * a) <= 3.1e-177) {
		tmp = t_1;
	} else if ((b * a) <= 5.5e-87) {
		tmp = t * (z * 0.0625);
	} else if ((b * a) <= 2.3e+180) {
		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 (b * a) <= -8.5e+143:
		tmp = t_2
	elif (b * a) <= 3.1e-177:
		tmp = t_1
	elif (b * a) <= 5.5e-87:
		tmp = t * (z * 0.0625)
	elif (b * a) <= 2.3e+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(x * y))
	t_2 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -8.5e+143)
		tmp = t_2;
	elseif (Float64(b * a) <= 3.1e-177)
		tmp = t_1;
	elseif (Float64(b * a) <= 5.5e-87)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (Float64(b * a) <= 2.3e+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 + (x * y);
	t_2 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -8.5e+143)
		tmp = t_2;
	elseif ((b * a) <= 3.1e-177)
		tmp = t_1;
	elseif ((b * a) <= 5.5e-87)
		tmp = t * (z * 0.0625);
	elseif ((b * a) <= 2.3e+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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -8.5e+143], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 3.1e-177], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5.5e-87], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2.3e+180], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -8.4999999999999998e143 or 2.2999999999999999e180 < (*.f64 a b)

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 89.7%

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

   3. Taylor expanded in a around inf 79.7%

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

      1. *-commutative 79.7%

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

   5. Simplified 79.7%

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

   if -8.4999999999999998e143 < (*.f64 a b) < 3.10000000000000018e-177 or 5.5000000000000004e-87 < (*.f64 a b) < 2.2999999999999999e180

   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 x around inf 65.9%

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

   if 3.10000000000000018e-177 < (*.f64 a b) < 5.5000000000000004e-87

   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 x around 0 100.0%

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

   3. Taylor expanded in t around inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. *-commutative 83.4%

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

      3. associate-*l* 83.4%

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

   5. Simplified 83.4%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -8.5 \cdot 10^{+143}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 3.1 \cdot 10^{-177}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 5.5 \cdot 10^{-87}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2.3 \cdot 10^{+180}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 5: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -7.8 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 1.2 \cdot 10^{-183}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 9 \cdot 10^{+194}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -7.8e+152)
     t_1
     (if (<= (* b a) 1.2e-183)
       (+ c (* x y))
       (if (<= (* b a) 9e+194) (+ c (* 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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -7.8e+152) {
		tmp = t_1;
	} else if ((b * a) <= 1.2e-183) {
		tmp = c + (x * y);
	} else if ((b * a) <= 9e+194) {
		tmp = c + (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 = (b * a) * (-0.25d0)
    if ((b * a) <= (-7.8d+152)) then
        tmp = t_1
    else if ((b * a) <= 1.2d-183) then
        tmp = c + (x * y)
    else if ((b * a) <= 9d+194) then
        tmp = c + (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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -7.8e+152) {
		tmp = t_1;
	} else if ((b * a) <= 1.2e-183) {
		tmp = c + (x * y);
	} else if ((b * a) <= 9e+194) {
		tmp = c + (0.0625 * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -7.8e+152:
		tmp = t_1
	elif (b * a) <= 1.2e-183:
		tmp = c + (x * y)
	elif (b * a) <= 9e+194:
		tmp = c + (0.0625 * (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -7.8e+152)
		tmp = t_1;
	elseif (Float64(b * a) <= 1.2e-183)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(b * a) <= 9e+194)
		tmp = Float64(c + 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 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -7.8e+152)
		tmp = t_1;
	elseif ((b * a) <= 1.2e-183)
		tmp = c + (x * y);
	elseif ((b * a) <= 9e+194)
		tmp = c + (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[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -7.8e+152], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1.2e-183], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 9e+194], N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -7.80000000000000022e152 or 8.9999999999999997e194 < (*.f64 a b)

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 92.0%

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

   3. Taylor expanded in a around inf 81.8%

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

      1. *-commutative 81.8%

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

   5. Simplified 81.8%

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

   if -7.80000000000000022e152 < (*.f64 a b) < 1.19999999999999996e-183

   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 x around inf 69.9%

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

   if 1.19999999999999996e-183 < (*.f64 a b) < 8.9999999999999997e194

   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 66.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -7.8 \cdot 10^{+152}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 1.2 \cdot 10^{-183}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 9 \cdot 10^{+194}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 6: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -9.4 \cdot 10^{+147}:\\ \;\;\;\;c + t_1\\ \mathbf{elif}\;b \cdot a \leq 5.5 \cdot 10^{-179}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 6.3 \cdot 10^{+199}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -9.4e+147)
     (+ c t_1)
     (if (<= (* b a) 5.5e-179)
       (+ c (* x y))
       (if (<= (* b a) 6.3e+199) (+ c (* 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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -9.4e+147) {
		tmp = c + t_1;
	} else if ((b * a) <= 5.5e-179) {
		tmp = c + (x * y);
	} else if ((b * a) <= 6.3e+199) {
		tmp = c + (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 = (b * a) * (-0.25d0)
    if ((b * a) <= (-9.4d+147)) then
        tmp = c + t_1
    else if ((b * a) <= 5.5d-179) then
        tmp = c + (x * y)
    else if ((b * a) <= 6.3d+199) then
        tmp = c + (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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -9.4e+147) {
		tmp = c + t_1;
	} else if ((b * a) <= 5.5e-179) {
		tmp = c + (x * y);
	} else if ((b * a) <= 6.3e+199) {
		tmp = c + (0.0625 * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -9.4e+147:
		tmp = c + t_1
	elif (b * a) <= 5.5e-179:
		tmp = c + (x * y)
	elif (b * a) <= 6.3e+199:
		tmp = c + (0.0625 * (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -9.4e+147)
		tmp = Float64(c + t_1);
	elseif (Float64(b * a) <= 5.5e-179)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(b * a) <= 6.3e+199)
		tmp = Float64(c + 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 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -9.4e+147)
		tmp = c + t_1;
	elseif ((b * a) <= 5.5e-179)
		tmp = c + (x * y);
	elseif ((b * a) <= 6.3e+199)
		tmp = c + (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[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -9.4e+147], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5.5e-179], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 6.3e+199], N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -9.4000000000000006e147

   1. Initial program 92.7%

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

   2. Taylor expanded in a around inf 86.1%

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

      1. *-commutative 86.1%

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

   4. Simplified 86.1%

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

   if -9.4000000000000006e147 < (*.f64 a b) < 5.5000000000000003e-179

   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 x around inf 69.9%

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

   if 5.5000000000000003e-179 < (*.f64 a b) < 6.2999999999999999e199

   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 66.3%

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

   if 6.2999999999999999e199 < (*.f64 a b)

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 87.6%

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

   3. Taylor expanded in a around inf 81.2%

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

      1. *-commutative 81.2%

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

   5. Simplified 81.2%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -9.4 \cdot 10^{+147}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 5.5 \cdot 10^{-179}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 6.3 \cdot 10^{+199}:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 7: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.05 \cdot 10^{+104} \lor \neg \left(b \cdot a \leq 2.3 \cdot 10^{+198}\right):\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1.05e+104) (not (<= (* b a) 2.3e+198)))
   (- (* x y) (* (* b a) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* t z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1.05e+104) || !((b * a) <= 2.3e+198)) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	}
	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) <= (-1.05d+104)) .or. (.not. ((b * a) <= 2.3d+198))) then
        tmp = (x * y) - ((b * a) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (t * z)))
    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) <= -1.05e+104) || !((b * a) <= 2.3e+198)) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1.05e+104) or not ((b * a) <= 2.3e+198):
		tmp = (x * y) - ((b * a) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (t * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1.05e+104) || !(Float64(b * a) <= 2.3e+198))
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -1.05e+104) || ~(((b * a) <= 2.3e+198)))
		tmp = (x * y) - ((b * a) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1.05e+104], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2.3e+198]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.0499999999999999e104 or 2.3000000000000001e198 < (*.f64 a b)

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 92.5%

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

   3. Taylor expanded in c around 0 90.3%

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

   if -1.0499999999999999e104 < (*.f64 a b) < 2.3000000000000001e198

   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 0 92.7%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1.05 \cdot 10^{+104} \lor \neg \left(b \cdot a \leq 2.3 \cdot 10^{+198}\right):\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \end{array} \]

Alternative 8: 87.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;b \cdot a \leq -2.3 \cdot 10^{+99}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{elif}\;b \cdot a \leq 6.8 \cdot 10^{+191}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)))
   (if (<= (* b a) -2.3e+99)
     (- (+ c (* x y)) t_1)
     (if (<= (* b a) 6.8e+191)
       (+ c (+ (* x y) (* 0.0625 (* t z))))
       (- (* 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 tmp;
	if ((b * a) <= -2.3e+99) {
		tmp = (c + (x * y)) - t_1;
	} else if ((b * a) <= 6.8e+191) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} 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) :: tmp
    t_1 = (b * a) * 0.25d0
    if ((b * a) <= (-2.3d+99)) then
        tmp = (c + (x * y)) - t_1
    else if ((b * a) <= 6.8d+191) then
        tmp = c + ((x * y) + (0.0625d0 * (t * z)))
    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 tmp;
	if ((b * a) <= -2.3e+99) {
		tmp = (c + (x * y)) - t_1;
	} else if ((b * a) <= 6.8e+191) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	tmp = 0
	if (b * a) <= -2.3e+99:
		tmp = (c + (x * y)) - t_1
	elif (b * a) <= 6.8e+191:
		tmp = c + ((x * y) + (0.0625 * (t * z)))
	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)
	tmp = 0.0
	if (Float64(b * a) <= -2.3e+99)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(b * a) <= 6.8e+191)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z))));
	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;
	tmp = 0.0;
	if ((b * a) <= -2.3e+99)
		tmp = (c + (x * y)) - t_1;
	elseif ((b * a) <= 6.8e+191)
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	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]}, If[LessEqual[N[(b * a), $MachinePrecision], -2.3e+99], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 6.8e+191], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.30000000000000019e99

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 95.8%

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

   if -2.30000000000000019e99 < (*.f64 a b) < 6.80000000000000018e191

   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 0 92.7%

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

   if 6.80000000000000018e191 < (*.f64 a b)

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 87.6%

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

   3. Taylor expanded in c around 0 87.6%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2.3 \cdot 10^{+99}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 6.8 \cdot 10^{+191}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{-83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-268}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+105}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* z 0.0625))))
   (if (<= y -3.15e-83)
     (* x y)
     (if (<= y -9.5e-285)
       t_1
       (if (<= y 1.35e-268)
         c
         (if (<= y 2.5e+70)
           t_1
           (if (<= y 6.5e+105) c (if (<= y 4.8e+131) t_1 (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (z * 0.0625);
	double tmp;
	if (y <= -3.15e-83) {
		tmp = x * y;
	} else if (y <= -9.5e-285) {
		tmp = t_1;
	} else if (y <= 1.35e-268) {
		tmp = c;
	} else if (y <= 2.5e+70) {
		tmp = t_1;
	} else if (y <= 6.5e+105) {
		tmp = c;
	} else if (y <= 4.8e+131) {
		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 = t * (z * 0.0625d0)
    if (y <= (-3.15d-83)) then
        tmp = x * y
    else if (y <= (-9.5d-285)) then
        tmp = t_1
    else if (y <= 1.35d-268) then
        tmp = c
    else if (y <= 2.5d+70) then
        tmp = t_1
    else if (y <= 6.5d+105) then
        tmp = c
    else if (y <= 4.8d+131) 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 = t * (z * 0.0625);
	double tmp;
	if (y <= -3.15e-83) {
		tmp = x * y;
	} else if (y <= -9.5e-285) {
		tmp = t_1;
	} else if (y <= 1.35e-268) {
		tmp = c;
	} else if (y <= 2.5e+70) {
		tmp = t_1;
	} else if (y <= 6.5e+105) {
		tmp = c;
	} else if (y <= 4.8e+131) {
		tmp = t_1;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = t * (z * 0.0625)
	tmp = 0
	if y <= -3.15e-83:
		tmp = x * y
	elif y <= -9.5e-285:
		tmp = t_1
	elif y <= 1.35e-268:
		tmp = c
	elif y <= 2.5e+70:
		tmp = t_1
	elif y <= 6.5e+105:
		tmp = c
	elif y <= 4.8e+131:
		tmp = t_1
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (y <= -3.15e-83)
		tmp = Float64(x * y);
	elseif (y <= -9.5e-285)
		tmp = t_1;
	elseif (y <= 1.35e-268)
		tmp = c;
	elseif (y <= 2.5e+70)
		tmp = t_1;
	elseif (y <= 6.5e+105)
		tmp = c;
	elseif (y <= 4.8e+131)
		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 = t * (z * 0.0625);
	tmp = 0.0;
	if (y <= -3.15e-83)
		tmp = x * y;
	elseif (y <= -9.5e-285)
		tmp = t_1;
	elseif (y <= 1.35e-268)
		tmp = c;
	elseif (y <= 2.5e+70)
		tmp = t_1;
	elseif (y <= 6.5e+105)
		tmp = c;
	elseif (y <= 4.8e+131)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e-83], N[(x * y), $MachinePrecision], If[LessEqual[y, -9.5e-285], t$95$1, If[LessEqual[y, 1.35e-268], c, If[LessEqual[y, 2.5e+70], t$95$1, If[LessEqual[y, 6.5e+105], c, If[LessEqual[y, 4.8e+131], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.14999999999999983e-83 or 4.7999999999999999e131 < y

   1. Initial program 97.5%

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

   2. Taylor expanded in z around 0 75.4%

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

   3. Taylor expanded in y around inf 49.0%

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

   if -3.14999999999999983e-83 < y < -9.4999999999999997e-285 or 1.35e-268 < y < 2.5000000000000001e70 or 6.50000000000000049e105 < y < 4.7999999999999999e131

   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 x around 0 86.7%

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

   3. Taylor expanded in t around inf 30.6%

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

      1. associate-*r* 30.6%

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

      2. *-commutative 30.6%

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

      3. associate-*l* 30.6%

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

   5. Simplified 30.6%

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

   if -9.4999999999999997e-285 < y < 1.35e-268 or 2.5000000000000001e70 < y < 6.50000000000000049e105

   1. Initial program 94.4%

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

   2. Taylor expanded in c around inf 48.8%

      \[\leadsto \color{blue}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-83}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-285}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-268}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+105}:\\ \;\;\;\;c\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+131}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 10: 97.5% 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 98.0%

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

2. Final simplification 98.0%

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

Alternative 11: 34.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-158}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+114}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.8e-158) (* x y) (if (<= y 6.8e+114) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.8e-158) {
		tmp = x * y;
	} else if (y <= 6.8e+114) {
		tmp = c;
	} 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 <= (-1.8d-158)) then
        tmp = x * y
    else if (y <= 6.8d+114) then
        tmp = c
    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 <= -1.8e-158) {
		tmp = x * y;
	} else if (y <= 6.8e+114) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.8e-158:
		tmp = x * y
	elif y <= 6.8e+114:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.8e-158)
		tmp = Float64(x * y);
	elseif (y <= 6.8e+114)
		tmp = c;
	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 <= -1.8e-158)
		tmp = x * y;
	elseif (y <= 6.8e+114)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -1.8e-158], N[(x * y), $MachinePrecision], If[LessEqual[y, 6.8e+114], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999995e-158 or 6.8000000000000001e114 < y

   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 74.0%

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

   3. Taylor expanded in y around inf 42.6%

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

   if -1.79999999999999995e-158 < y < 6.8000000000000001e114

   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 c around inf 28.5%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-158}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+114}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12: 22.0% 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 98.0%

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

2. Taylor expanded in c around inf 18.9%

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

3. Final simplification 18.9%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023185 
(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))