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

Percentage Accurate: 97.7% → 99.0%

Time: 12.8s

Alternatives: 16

Speedup: 0.5×

• 33.0% 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: 97.7% 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: 99.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. associate--l+ 96.5%

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

   3. fma-def 98.0%

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

   4. associate-*l/ 98.0%

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

   5. fma-neg 98.8%

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

   6. sub-neg 98.8%

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

   7. distribute-neg-in 98.8%

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

   8. remove-double-neg 98.8%

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

   9. associate-/l* 98.7%

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

   10. distribute-frac-neg 98.7%

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

   11. associate-/r/ 98.8%

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

   12. fma-def 98.8%

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

   13. neg-mul-1 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{-1 \cdot a}}{4}, b, c\right)\right)\right) \]

   14. *-commutative 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\frac{\color{blue}{a \cdot -1}}{4}, b, c\right)\right)\right) \]

   15. associate-/l* 98.8%

       \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(\frac{z}{16}, t, \mathsf{fma}\left(\color{blue}{\frac{a}{\frac{4}{-1}}}, b, c\right)\right)\right) \]

   16. metadata-eval 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. fma-def 97.2%

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

   3. *-commutative 97.2%

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

   4. associate-/l* 97.2%

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

   5. associate-/l* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 3: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (+ c (* (* a b) -0.25)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = c + ((a * b) * -0.25);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = c + ((a * b) * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = c + ((a * b) * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(c + Float64(Float64(a * b) * -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = c + ((a * b) * -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4)) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) 16)) (/.f64 (*.f64 a b) 4))

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf 46.1%

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

      1. *-commutative 46.1%

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

   4. Simplified 46.1%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 4: 43.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq -5.6 \cdot 10^{-239}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-306}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq 1.45 \cdot 10^{-86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+18}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 1.15 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) -0.25)))
   (if (<= (* a b) -4.4e+125)
     t_1
     (if (<= (* a b) -5.6e-239)
       c
       (if (<= (* a b) 7.2e-306)
         (* (* z t) 0.0625)
         (if (<= (* a b) 1.45e-86)
           (* x y)
           (if (<= (* a b) 5e+18)
             c
             (if (<= (* a b) 1.15e+85) (* x y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -4.4e+125) {
		tmp = t_1;
	} else if ((a * b) <= -5.6e-239) {
		tmp = c;
	} else if ((a * b) <= 7.2e-306) {
		tmp = (z * t) * 0.0625;
	} else if ((a * b) <= 1.45e-86) {
		tmp = x * y;
	} else if ((a * b) <= 5e+18) {
		tmp = c;
	} else if ((a * b) <= 1.15e+85) {
		tmp = x * y;
	} 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 = (a * b) * (-0.25d0)
    if ((a * b) <= (-4.4d+125)) then
        tmp = t_1
    else if ((a * b) <= (-5.6d-239)) then
        tmp = c
    else if ((a * b) <= 7.2d-306) then
        tmp = (z * t) * 0.0625d0
    else if ((a * b) <= 1.45d-86) then
        tmp = x * y
    else if ((a * b) <= 5d+18) then
        tmp = c
    else if ((a * b) <= 1.15d+85) then
        tmp = x * y
    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 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -4.4e+125) {
		tmp = t_1;
	} else if ((a * b) <= -5.6e-239) {
		tmp = c;
	} else if ((a * b) <= 7.2e-306) {
		tmp = (z * t) * 0.0625;
	} else if ((a * b) <= 1.45e-86) {
		tmp = x * y;
	} else if ((a * b) <= 5e+18) {
		tmp = c;
	} else if ((a * b) <= 1.15e+85) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -4.4e+125:
		tmp = t_1
	elif (a * b) <= -5.6e-239:
		tmp = c
	elif (a * b) <= 7.2e-306:
		tmp = (z * t) * 0.0625
	elif (a * b) <= 1.45e-86:
		tmp = x * y
	elif (a * b) <= 5e+18:
		tmp = c
	elif (a * b) <= 1.15e+85:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -4.4e+125)
		tmp = t_1;
	elseif (Float64(a * b) <= -5.6e-239)
		tmp = c;
	elseif (Float64(a * b) <= 7.2e-306)
		tmp = Float64(Float64(z * t) * 0.0625);
	elseif (Float64(a * b) <= 1.45e-86)
		tmp = Float64(x * y);
	elseif (Float64(a * b) <= 5e+18)
		tmp = c;
	elseif (Float64(a * b) <= 1.15e+85)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -4.4e+125)
		tmp = t_1;
	elseif ((a * b) <= -5.6e-239)
		tmp = c;
	elseif ((a * b) <= 7.2e-306)
		tmp = (z * t) * 0.0625;
	elseif ((a * b) <= 1.45e-86)
		tmp = x * y;
	elseif ((a * b) <= 5e+18)
		tmp = c;
	elseif ((a * b) <= 1.15e+85)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -4.4e+125], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], -5.6e-239], c, If[LessEqual[N[(a * b), $MachinePrecision], 7.2e-306], N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.45e-86], N[(x * y), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+18], c, If[LessEqual[N[(a * b), $MachinePrecision], 1.15e+85], N[(x * y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -4.39999999999999982e125 or 1.1499999999999999e85 < (*.f64 a b)

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. fma-def 94.0%

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

      3. *-commutative 94.0%

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

      4. associate-/l* 94.0%

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

      5. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. fma-udef 91.9%

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

      2. div-inv 91.9%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 91.9%

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

      4. div-inv 91.9%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 91.9%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 91.9%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in a around inf 68.9%

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

      1. *-commutative 68.9%

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

   8. Simplified 68.9%

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

   if -4.39999999999999982e125 < (*.f64 a b) < -5.60000000000000025e-239 or 1.45e-86 < (*.f64 a b) < 5e18

   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 c around inf 40.6%

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

   if -5.60000000000000025e-239 < (*.f64 a b) < 7.19999999999999982e-306

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 99.8%

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

      5. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. fma-udef 99.8%

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

      2. div-inv 100.0%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 100.0%

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

      4. div-inv 100.0%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in t around inf 49.7%

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

   if 7.19999999999999982e-306 < (*.f64 a b) < 1.45e-86 or 5e18 < (*.f64 a b) < 1.1499999999999999e85

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. div-inv 100.0%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 100.0%

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

      4. div-inv 100.0%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in x around inf 52.3%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -4.4 \cdot 10^{+125}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -5.6 \cdot 10^{-239}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 7.2 \cdot 10^{-306}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;a \cdot b \leq 1.45 \cdot 10^{-86}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+18}:\\ \;\;\;\;c\\ \mathbf{elif}\;a \cdot b \leq 1.15 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 5: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_3 := \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \cdot b \leq 9.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 2.7 \cdot 10^{+206}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ c (* t (* z 0.0625))))
        (t_3 (* (* a b) -0.25)))
   (if (<= (* a b) -1.15e+151)
     t_3
     (if (<= (* a b) -8.2e-223)
       t_1
       (if (<= (* a b) 4.4e-307)
         t_2
         (if (<= (* a b) 9.2e+84) t_1 (if (<= (* a b) 2.7e+206) t_2 t_3)))))))

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 = c + (t * (z * 0.0625));
	double t_3 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.15e+151) {
		tmp = t_3;
	} else if ((a * b) <= -8.2e-223) {
		tmp = t_1;
	} else if ((a * b) <= 4.4e-307) {
		tmp = t_2;
	} else if ((a * b) <= 9.2e+84) {
		tmp = t_1;
	} else if ((a * b) <= 2.7e+206) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (t * (z * 0.0625d0))
    t_3 = (a * b) * (-0.25d0)
    if ((a * b) <= (-1.15d+151)) then
        tmp = t_3
    else if ((a * b) <= (-8.2d-223)) then
        tmp = t_1
    else if ((a * b) <= 4.4d-307) then
        tmp = t_2
    else if ((a * b) <= 9.2d+84) then
        tmp = t_1
    else if ((a * b) <= 2.7d+206) then
        tmp = t_2
    else
        tmp = t_3
    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 = c + (t * (z * 0.0625));
	double t_3 = (a * b) * -0.25;
	double tmp;
	if ((a * b) <= -1.15e+151) {
		tmp = t_3;
	} else if ((a * b) <= -8.2e-223) {
		tmp = t_1;
	} else if ((a * b) <= 4.4e-307) {
		tmp = t_2;
	} else if ((a * b) <= 9.2e+84) {
		tmp = t_1;
	} else if ((a * b) <= 2.7e+206) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (t * (z * 0.0625))
	t_3 = (a * b) * -0.25
	tmp = 0
	if (a * b) <= -1.15e+151:
		tmp = t_3
	elif (a * b) <= -8.2e-223:
		tmp = t_1
	elif (a * b) <= 4.4e-307:
		tmp = t_2
	elif (a * b) <= 9.2e+84:
		tmp = t_1
	elif (a * b) <= 2.7e+206:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_3 = Float64(Float64(a * b) * -0.25)
	tmp = 0.0
	if (Float64(a * b) <= -1.15e+151)
		tmp = t_3;
	elseif (Float64(a * b) <= -8.2e-223)
		tmp = t_1;
	elseif (Float64(a * b) <= 4.4e-307)
		tmp = t_2;
	elseif (Float64(a * b) <= 9.2e+84)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.7e+206)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (t * (z * 0.0625));
	t_3 = (a * b) * -0.25;
	tmp = 0.0;
	if ((a * b) <= -1.15e+151)
		tmp = t_3;
	elseif ((a * b) <= -8.2e-223)
		tmp = t_1;
	elseif ((a * b) <= 4.4e-307)
		tmp = t_2;
	elseif ((a * b) <= 9.2e+84)
		tmp = t_1;
	elseif ((a * b) <= 2.7e+206)
		tmp = t_2;
	else
		tmp = t_3;
	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[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.15e+151], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -8.2e-223], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 4.4e-307], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], 9.2e+84], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.7e+206], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.15e151 or 2.70000000000000003e206 < (*.f64 a b)

   1. Initial program 89.5%

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

      1. associate-+l- 89.5%

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

      2. fma-def 92.1%

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

      3. *-commutative 92.1%

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

      4. associate-/l* 92.1%

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

      5. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

      1. fma-udef 89.3%

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

      2. div-inv 89.3%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 89.3%

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

      4. div-inv 89.3%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 89.3%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 89.3%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in a around inf 80.2%

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

      1. *-commutative 80.2%

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

   8. Simplified 80.2%

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

   if -1.15e151 < (*.f64 a b) < -8.2000000000000003e-223 or 4.4e-307 < (*.f64 a b) < 9.1999999999999996e84

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf 71.2%

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

   if -8.2000000000000003e-223 < (*.f64 a b) < 4.4e-307 or 9.1999999999999996e84 < (*.f64 a b) < 2.70000000000000003e206

   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 66.6%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   4. Simplified 66.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1.15 \cdot 10^{+151}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq -8.2 \cdot 10^{-223}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 4.4 \cdot 10^{-307}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 9.2 \cdot 10^{+84}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2.7 \cdot 10^{+206}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 6: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;x \cdot y \leq -1.92 \cdot 10^{+170}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.3 \cdot 10^{-279}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* (* a b) -0.25))))
   (if (<= (* x y) -1.92e+170)
     (+ c (* x y))
     (if (<= (* x y) -4e-105)
       t_1
       (if (<= (* x y) 2.3e-279)
         (+ c (* t (* z 0.0625)))
         (if (<= (* x y) 3.8e+133) t_1 (+ (* x y) (* (* z t) 0.0625))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) * -0.25);
	double tmp;
	if ((x * y) <= -1.92e+170) {
		tmp = c + (x * y);
	} else if ((x * y) <= -4e-105) {
		tmp = t_1;
	} else if ((x * y) <= 2.3e-279) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 3.8e+133) {
		tmp = t_1;
	} else {
		tmp = (x * y) + ((z * t) * 0.0625);
	}
	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 + ((a * b) * (-0.25d0))
    if ((x * y) <= (-1.92d+170)) then
        tmp = c + (x * y)
    else if ((x * y) <= (-4d-105)) then
        tmp = t_1
    else if ((x * y) <= 2.3d-279) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((x * y) <= 3.8d+133) then
        tmp = t_1
    else
        tmp = (x * y) + ((z * t) * 0.0625d0)
    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 + ((a * b) * -0.25);
	double tmp;
	if ((x * y) <= -1.92e+170) {
		tmp = c + (x * y);
	} else if ((x * y) <= -4e-105) {
		tmp = t_1;
	} else if ((x * y) <= 2.3e-279) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 3.8e+133) {
		tmp = t_1;
	} else {
		tmp = (x * y) + ((z * t) * 0.0625);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((a * b) * -0.25)
	tmp = 0
	if (x * y) <= -1.92e+170:
		tmp = c + (x * y)
	elif (x * y) <= -4e-105:
		tmp = t_1
	elif (x * y) <= 2.3e-279:
		tmp = c + (t * (z * 0.0625))
	elif (x * y) <= 3.8e+133:
		tmp = t_1
	else:
		tmp = (x * y) + ((z * t) * 0.0625)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(a * b) * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -1.92e+170)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(x * y) <= -4e-105)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.3e-279)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(x * y) <= 3.8e+133)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((a * b) * -0.25);
	tmp = 0.0;
	if ((x * y) <= -1.92e+170)
		tmp = c + (x * y);
	elseif ((x * y) <= -4e-105)
		tmp = t_1;
	elseif ((x * y) <= 2.3e-279)
		tmp = c + (t * (z * 0.0625));
	elseif ((x * y) <= 3.8e+133)
		tmp = t_1;
	else
		tmp = (x * y) + ((z * t) * 0.0625);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.92e+170], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-105], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.3e-279], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+133], t$95$1, N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9199999999999999e170

   1. Initial program 92.5%

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

   2. Taylor expanded in x around inf 80.4%

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

   if -1.9199999999999999e170 < (*.f64 x y) < -3.99999999999999986e-105 or 2.29999999999999995e-279 < (*.f64 x y) < 3.8000000000000002e133

   1. Initial program 98.2%

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

   2. Taylor expanded in a around inf 70.3%

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

      1. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   if -3.99999999999999986e-105 < (*.f64 x y) < 2.29999999999999995e-279

   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 inf 66.6%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   4. Simplified 66.6%

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

   if 3.8000000000000002e133 < (*.f64 x y)

   1. Initial program 94.7%

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

   2. Taylor expanded in a around 0 82.3%

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

   3. Taylor expanded in c around 0 77.1%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) + x \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.92 \cdot 10^{+170}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-105}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;x \cdot y \leq 2.3 \cdot 10^{-279}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+133}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + \left(z \cdot t\right) \cdot 0.0625\\ \end{array} \]

Alternative 7: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \left(a \cdot b\right) \cdot -0.25\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.16 \cdot 10^{+169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-281}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* (* a b) -0.25))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -1.16e+169)
     t_2
     (if (<= (* x y) -2.3e-107)
       t_1
       (if (<= (* x y) 3.2e-281)
         (+ c (* t (* z 0.0625)))
         (if (<= (* x y) 5.5e+135) 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 + ((a * b) * -0.25);
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.16e+169) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-107) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-281) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 5.5e+135) {
		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 + ((a * b) * (-0.25d0))
    t_2 = c + (x * y)
    if ((x * y) <= (-1.16d+169)) then
        tmp = t_2
    else if ((x * y) <= (-2.3d-107)) then
        tmp = t_1
    else if ((x * y) <= 3.2d-281) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((x * y) <= 5.5d+135) 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 + ((a * b) * -0.25);
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.16e+169) {
		tmp = t_2;
	} else if ((x * y) <= -2.3e-107) {
		tmp = t_1;
	} else if ((x * y) <= 3.2e-281) {
		tmp = c + (t * (z * 0.0625));
	} else if ((x * y) <= 5.5e+135) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((a * b) * -0.25)
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.16e+169:
		tmp = t_2
	elif (x * y) <= -2.3e-107:
		tmp = t_1
	elif (x * y) <= 3.2e-281:
		tmp = c + (t * (z * 0.0625))
	elif (x * y) <= 5.5e+135:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(a * b) * -0.25))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.16e+169)
		tmp = t_2;
	elseif (Float64(x * y) <= -2.3e-107)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.2e-281)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(x * y) <= 5.5e+135)
		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 + ((a * b) * -0.25);
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.16e+169)
		tmp = t_2;
	elseif ((x * y) <= -2.3e-107)
		tmp = t_1;
	elseif ((x * y) <= 3.2e-281)
		tmp = c + (t * (z * 0.0625));
	elseif ((x * y) <= 5.5e+135)
		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[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.16e+169], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -2.3e-107], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.2e-281], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.5e+135], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.16e169 or 5.4999999999999999e135 < (*.f64 x y)

   1. Initial program 93.6%

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

   2. Taylor expanded in x around inf 76.1%

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

   if -1.16e169 < (*.f64 x y) < -2.30000000000000003e-107 or 3.2000000000000001e-281 < (*.f64 x y) < 5.4999999999999999e135

   1. Initial program 98.2%

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

   2. Taylor expanded in a around inf 70.3%

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

      1. *-commutative 70.3%

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

   4. Simplified 70.3%

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

   if -2.30000000000000003e-107 < (*.f64 x y) < 3.2000000000000001e-281

   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 inf 66.6%

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

      1. associate-*r* 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r* 66.6%

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

   4. Simplified 66.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.16 \cdot 10^{+169}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.3 \cdot 10^{-107}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;x \cdot y \leq 3.2 \cdot 10^{-281}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+135}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 8: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -1.18 \cdot 10^{+97} \lor \neg \left(x \cdot y \leq 1.75 \cdot 10^{+155}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= (* x y) -1.18e+97) (not (<= (* x y) 1.75e+155)))
     (- (+ c (* x y)) t_1)
     (- (+ c (* (* z t) 0.0625)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -1.18e+97) || !((x * y) <= 1.75e+155)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - 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 = (a * b) * 0.25d0
    if (((x * y) <= (-1.18d+97)) .or. (.not. ((x * y) <= 1.75d+155))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + ((z * t) * 0.0625d0)) - 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 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -1.18e+97) || !((x * y) <= 1.75e+155)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if ((x * y) <= -1.18e+97) or not ((x * y) <= 1.75e+155):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + ((z * t) * 0.0625)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if ((Float64(x * y) <= -1.18e+97) || !(Float64(x * y) <= 1.75e+155))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(Float64(z * t) * 0.0625)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if (((x * y) <= -1.18e+97) || ~(((x * y) <= 1.75e+155)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -1.18e+97], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.75e+155]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.18000000000000006e97 or 1.74999999999999992e155 < (*.f64 x y)

   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 88.7%

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

   if -1.18000000000000006e97 < (*.f64 x y) < 1.74999999999999992e155

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 94.0%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.18 \cdot 10^{+97} \lor \neg \left(x \cdot y \leq 1.75 \cdot 10^{+155}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 42.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.52 \cdot 10^{-49}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 9.6 \cdot 10^{-107}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+163}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -7.8e+85)
   (* x y)
   (if (<= (* x y) -1.52e-49)
     c
     (if (<= (* x y) 9.6e-107)
       (* (* z t) 0.0625)
       (if (<= (* x y) 2.5e+163) c (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -7.8e+85) {
		tmp = x * y;
	} else if ((x * y) <= -1.52e-49) {
		tmp = c;
	} else if ((x * y) <= 9.6e-107) {
		tmp = (z * t) * 0.0625;
	} else if ((x * y) <= 2.5e+163) {
		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 ((x * y) <= (-7.8d+85)) then
        tmp = x * y
    else if ((x * y) <= (-1.52d-49)) then
        tmp = c
    else if ((x * y) <= 9.6d-107) then
        tmp = (z * t) * 0.0625d0
    else if ((x * y) <= 2.5d+163) 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 ((x * y) <= -7.8e+85) {
		tmp = x * y;
	} else if ((x * y) <= -1.52e-49) {
		tmp = c;
	} else if ((x * y) <= 9.6e-107) {
		tmp = (z * t) * 0.0625;
	} else if ((x * y) <= 2.5e+163) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -7.8e+85:
		tmp = x * y
	elif (x * y) <= -1.52e-49:
		tmp = c
	elif (x * y) <= 9.6e-107:
		tmp = (z * t) * 0.0625
	elif (x * y) <= 2.5e+163:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -7.8e+85)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.52e-49)
		tmp = c;
	elseif (Float64(x * y) <= 9.6e-107)
		tmp = Float64(Float64(z * t) * 0.0625);
	elseif (Float64(x * y) <= 2.5e+163)
		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 ((x * y) <= -7.8e+85)
		tmp = x * y;
	elseif ((x * y) <= -1.52e-49)
		tmp = c;
	elseif ((x * y) <= 9.6e-107)
		tmp = (z * t) * 0.0625;
	elseif ((x * y) <= 2.5e+163)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -7.8e+85], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.52e-49], c, If[LessEqual[N[(x * y), $MachinePrecision], 9.6e-107], N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.5e+163], c, N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -7.80000000000000067e85 or 2.5e163 < (*.f64 x y)

   1. Initial program 93.3%

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

      1. associate-+l- 93.3%

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

      2. fma-def 95.6%

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

      3. *-commutative 95.6%

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

      4. associate-/l* 95.6%

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

      5. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. fma-udef 93.3%

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

      2. div-inv 93.3%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 93.3%

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

      4. div-inv 93.3%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 93.3%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in x around inf 66.2%

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

   if -7.80000000000000067e85 < (*.f64 x y) < -1.52e-49 or 9.59999999999999977e-107 < (*.f64 x y) < 2.5e163

   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 c around inf 44.5%

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

   if -1.52e-49 < (*.f64 x y) < 9.59999999999999977e-107

   1. Initial program 97.1%

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

      1. associate-+l- 97.1%

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

      2. fma-def 97.1%

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

      3. *-commutative 97.1%

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

      4. associate-/l* 97.0%

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

      5. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

      1. fma-udef 96.9%

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

      2. div-inv 97.0%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 97.0%

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

      4. div-inv 97.0%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 97.0%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in t around inf 36.8%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -7.8 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.52 \cdot 10^{-49}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 9.6 \cdot 10^{-107}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625\\ \mathbf{elif}\;x \cdot y \leq 2.5 \cdot 10^{+163}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 10: 87.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9 \cdot 10^{+162} \lor \neg \left(a \cdot b \leq 3.9 \cdot 10^{+204}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -9e+162) (not (<= (* a b) 3.9e+204)))
   (- (* x y) (* (* a b) 0.25))
   (+ c (+ (* x y) (* (* z t) 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -9e+162) || !((a * b) <= 3.9e+204)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	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 (((a * b) <= (-9d+162)) .or. (.not. ((a * b) <= 3.9d+204))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + ((z * t) * 0.0625d0))
    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 (((a * b) <= -9e+162) || !((a * b) <= 3.9e+204)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -9e+162) or not ((a * b) <= 3.9e+204):
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + ((z * t) * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -9e+162) || !(Float64(a * b) <= 3.9e+204))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(Float64(z * t) * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -9e+162) || ~(((a * b) <= 3.9e+204)))
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + ((z * t) * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -9e+162], N[Not[LessEqual[N[(a * b), $MachinePrecision], 3.9e+204]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -8.99999999999999944e162 or 3.90000000000000017e204 < (*.f64 a b)

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0 89.0%

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

   3. Taylor expanded in c around 0 88.3%

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

   if -8.99999999999999944e162 < (*.f64 a b) < 3.90000000000000017e204

   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 91.1%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9 \cdot 10^{+162} \lor \neg \left(a \cdot b \leq 3.9 \cdot 10^{+204}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \end{array} \]

Alternative 11: 87.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;a \cdot b \leq -2.4 \cdot 10^{+127}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;a \cdot b \leq 1.86 \cdot 10^{+205}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* (* z t) 0.0625)))
   (if (<= (* a b) -2.4e+127)
     (- t_2 t_1)
     (if (<= (* a b) 1.86e+205) (+ c (+ (* x y) t_2)) (- (* x y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if ((a * b) <= -2.4e+127) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 1.86e+205) {
		tmp = c + ((x * y) + t_2);
	} 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 = (a * b) * 0.25d0
    t_2 = (z * t) * 0.0625d0
    if ((a * b) <= (-2.4d+127)) then
        tmp = t_2 - t_1
    else if ((a * b) <= 1.86d+205) then
        tmp = c + ((x * y) + t_2)
    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 = (a * b) * 0.25;
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if ((a * b) <= -2.4e+127) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 1.86e+205) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (x * y) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = (z * t) * 0.0625
	tmp = 0
	if (a * b) <= -2.4e+127:
		tmp = t_2 - t_1
	elif (a * b) <= 1.86e+205:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (x * y) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if (Float64(a * b) <= -2.4e+127)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(a * b) <= 1.86e+205)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	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 = (a * b) * 0.25;
	t_2 = (z * t) * 0.0625;
	tmp = 0.0;
	if ((a * b) <= -2.4e+127)
		tmp = t_2 - t_1;
	elseif ((a * b) <= 1.86e+205)
		tmp = c + ((x * y) + t_2);
	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[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2.4e+127], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.86e+205], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.4000000000000002e127

   1. Initial program 89.6%

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

   2. Taylor expanded in x around 0 87.8%

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

   3. Taylor expanded in c around 0 86.9%

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

   if -2.4000000000000002e127 < (*.f64 a b) < 1.8600000000000001e205

   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 91.9%

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

   if 1.8600000000000001e205 < (*.f64 a b)

   1. Initial program 90.0%

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

   2. Taylor expanded in z around 0 93.3%

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

   3. Taylor expanded in c around 0 93.3%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2.4 \cdot 10^{+127}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 1.86 \cdot 10^{+205}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 12: 88.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := \left(z \cdot t\right) \cdot 0.0625\\ \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+127}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{+135}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* (* z t) 0.0625)))
   (if (<= (* a b) -5.2e+127)
     (- t_2 t_1)
     (if (<= (* a b) 1.4e+135) (+ c (+ (* x y) t_2)) (- (+ c (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if ((a * b) <= -5.2e+127) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 1.4e+135) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (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 = (a * b) * 0.25d0
    t_2 = (z * t) * 0.0625d0
    if ((a * b) <= (-5.2d+127)) then
        tmp = t_2 - t_1
    else if ((a * b) <= 1.4d+135) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + (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 = (a * b) * 0.25;
	double t_2 = (z * t) * 0.0625;
	double tmp;
	if ((a * b) <= -5.2e+127) {
		tmp = t_2 - t_1;
	} else if ((a * b) <= 1.4e+135) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + (x * y)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = (z * t) * 0.0625
	tmp = 0
	if (a * b) <= -5.2e+127:
		tmp = t_2 - t_1
	elif (a * b) <= 1.4e+135:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + (x * y)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(Float64(z * t) * 0.0625)
	tmp = 0.0
	if (Float64(a * b) <= -5.2e+127)
		tmp = Float64(t_2 - t_1);
	elseif (Float64(a * b) <= 1.4e+135)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = (z * t) * 0.0625;
	tmp = 0.0;
	if ((a * b) <= -5.2e+127)
		tmp = t_2 - t_1;
	elseif ((a * b) <= 1.4e+135)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + (x * y)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5.2e+127], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.4e+135], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.2000000000000004e127

   1. Initial program 89.6%

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

   2. Taylor expanded in x around 0 87.8%

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

   3. Taylor expanded in c around 0 86.9%

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

   if -5.2000000000000004e127 < (*.f64 a b) < 1.40000000000000001e135

   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 94.1%

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

   if 1.40000000000000001e135 < (*.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 88.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5.2 \cdot 10^{+127}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 1.4 \cdot 10^{+135}:\\ \;\;\;\;c + \left(x \cdot y + \left(z \cdot t\right) \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 13: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.6 \cdot 10^{+96} \lor \neg \left(x \cdot y \leq 2.7 \cdot 10^{+163}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -3.6e+96) (not (<= (* x y) 2.7e+163)))
   (- (* x y) (* (* a b) 0.25))
   (+ c (* (* a b) -0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -3.6e+96) || !((x * y) <= 2.7e+163)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((a * b) * -0.25);
	}
	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 (((x * y) <= (-3.6d+96)) .or. (.not. ((x * y) <= 2.7d+163))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = c + ((a * b) * (-0.25d0))
    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 (((x * y) <= -3.6e+96) || !((x * y) <= 2.7e+163)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((a * b) * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -3.6e+96) or not ((x * y) <= 2.7e+163):
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = c + ((a * b) * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -3.6e+96) || !(Float64(x * y) <= 2.7e+163))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(a * b) * -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -3.6e+96) || ~(((x * y) <= 2.7e+163)))
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = c + ((a * b) * -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.6e+96], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.7e+163]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.60000000000000013e96 or 2.69999999999999999e163 < (*.f64 x y)

   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 88.6%

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

   3. Taylor expanded in c around 0 82.8%

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

   if -3.60000000000000013e96 < (*.f64 x y) < 2.69999999999999999e163

   1. Initial program 98.2%

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

   2. Taylor expanded in a around inf 66.0%

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

      1. *-commutative 66.0%

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

   4. Simplified 66.0%

      \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot -0.25} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.6 \cdot 10^{+96} \lor \neg \left(x \cdot y \leq 2.7 \cdot 10^{+163}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 14: 63.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+150} \lor \neg \left(a \cdot b \leq 10^{+181}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -9.5e+150) (not (<= (* a b) 1e+181)))
   (* (* a b) -0.25)
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -9.5e+150) || !((a * b) <= 1e+181)) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = c + (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 (((a * b) <= (-9.5d+150)) .or. (.not. ((a * b) <= 1d+181))) then
        tmp = (a * b) * (-0.25d0)
    else
        tmp = c + (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 (((a * b) <= -9.5e+150) || !((a * b) <= 1e+181)) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -9.5e+150) or not ((a * b) <= 1e+181):
		tmp = (a * b) * -0.25
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -9.5e+150) || !(Float64(a * b) <= 1e+181))
		tmp = Float64(Float64(a * b) * -0.25);
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -9.5e+150) || ~(((a * b) <= 1e+181)))
		tmp = (a * b) * -0.25;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -9.5e+150], N[Not[LessEqual[N[(a * b), $MachinePrecision], 1e+181]], $MachinePrecision]], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.5000000000000001e150 or 9.9999999999999992e180 < (*.f64 a b)

   1. Initial program 89.7%

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

      1. associate-+l- 89.7%

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

      2. fma-def 92.3%

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

      3. *-commutative 92.3%

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

      4. associate-/l* 92.3%

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

      5. associate-/l* 92.1%

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

   3. Simplified 92.1%

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

      1. fma-udef 89.6%

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

      2. div-inv 89.6%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 89.6%

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

      4. div-inv 89.6%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 89.6%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 89.6%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in a around inf 79.4%

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

      1. *-commutative 79.4%

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

   8. Simplified 79.4%

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

   if -9.5000000000000001e150 < (*.f64 a b) < 9.9999999999999992e180

   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 x around inf 64.4%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -9.5 \cdot 10^{+150} \lor \neg \left(a \cdot b \leq 10^{+181}\right):\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 15: 41.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{+163}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -2e+75) (* x y) (if (<= (* x y) 2.7e+163) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -2e+75) {
		tmp = x * y;
	} else if ((x * y) <= 2.7e+163) {
		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 ((x * y) <= (-2d+75)) then
        tmp = x * y
    else if ((x * y) <= 2.7d+163) 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 ((x * y) <= -2e+75) {
		tmp = x * y;
	} else if ((x * y) <= 2.7e+163) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -2e+75:
		tmp = x * y
	elif (x * y) <= 2.7e+163:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -2e+75)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= 2.7e+163)
		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 ((x * y) <= -2e+75)
		tmp = x * y;
	elseif ((x * y) <= 2.7e+163)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+75], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.7e+163], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999985e75 or 2.69999999999999999e163 < (*.f64 x y)

   1. Initial program 93.3%

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

      1. associate-+l- 93.3%

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

      2. fma-def 95.6%

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

      3. *-commutative 95.6%

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

      4. associate-/l* 95.6%

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

      5. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. fma-udef 93.3%

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

      2. div-inv 93.3%

         \[\leadsto \left(x \cdot y + \color{blue}{t \cdot \frac{1}{\frac{16}{z}}}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      3. clear-num 93.3%

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

      4. div-inv 93.3%

         \[\leadsto \left(x \cdot y + t \cdot \color{blue}{\left(z \cdot \frac{1}{16}\right)}\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

      5. metadata-eval 93.3%

         \[\leadsto \left(x \cdot y + t \cdot \left(z \cdot \color{blue}{0.0625}\right)\right) - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   5. Applied egg-rr 93.3%

      \[\leadsto \color{blue}{\left(x \cdot y + t \cdot \left(z \cdot 0.0625\right)\right)} - \left(\frac{a}{\frac{4}{b}} - c\right) \]

   6. Taylor expanded in x around inf 66.2%

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

   if -1.99999999999999985e75 < (*.f64 x y) < 2.69999999999999999e163

   1. Initial program 98.2%

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

   2. Taylor expanded in c around inf 31.7%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2.7 \cdot 10^{+163}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 16: 21.9% 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 96.5%

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

2. Taylor expanded in c around inf 23.1%

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

3. Final simplification 23.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023275 
(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))