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

Percentage Accurate: 97.4% → 98.7%

Time: 8.7s

Alternatives: 13

Speedup: 1.0×

• 33.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.4% 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: 98.7% 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 98.4%

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

   7. fma-neg 99.2%

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

   8. neg-sub0 99.2%

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

   9. associate-+l- 99.2%

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

   10. neg-sub0 99.2%

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

   11. +-commutative 99.2%

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

   12. unsub-neg 99.2%

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

   13. *-commutative 99.2%

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

   14. associate-*r/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(t \cdot z\right) - t_1\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot y - t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-109}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-140}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)) (t_2 (- (* 0.0625 (* t z)) t_1)))
   (if (<= x -4.6e+52)
     (- (* x y) t_1)
     (if (<= x -2.2e-109)
       (+ c (* t (* z 0.0625)))
       (if (<= x 1.02e-292)
         t_2
         (if (<= x 8e-140)
           (+ c (* (* b a) -0.25))
           (if (<= x 8e-72) t_2 (+ c (* x y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = (0.0625 * (t * z)) - t_1;
	double tmp;
	if (x <= -4.6e+52) {
		tmp = (x * y) - t_1;
	} else if (x <= -2.2e-109) {
		tmp = c + (t * (z * 0.0625));
	} else if (x <= 1.02e-292) {
		tmp = t_2;
	} else if (x <= 8e-140) {
		tmp = c + ((b * a) * -0.25);
	} else if (x <= 8e-72) {
		tmp = t_2;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = (0.0625d0 * (t * z)) - t_1
    if (x <= (-4.6d+52)) then
        tmp = (x * y) - t_1
    else if (x <= (-2.2d-109)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (x <= 1.02d-292) then
        tmp = t_2
    else if (x <= 8d-140) then
        tmp = c + ((b * a) * (-0.25d0))
    else if (x <= 8d-72) then
        tmp = t_2
    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 t_1 = (b * a) * 0.25;
	double t_2 = (0.0625 * (t * z)) - t_1;
	double tmp;
	if (x <= -4.6e+52) {
		tmp = (x * y) - t_1;
	} else if (x <= -2.2e-109) {
		tmp = c + (t * (z * 0.0625));
	} else if (x <= 1.02e-292) {
		tmp = t_2;
	} else if (x <= 8e-140) {
		tmp = c + ((b * a) * -0.25);
	} else if (x <= 8e-72) {
		tmp = t_2;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = (0.0625 * (t * z)) - t_1
	tmp = 0
	if x <= -4.6e+52:
		tmp = (x * y) - t_1
	elif x <= -2.2e-109:
		tmp = c + (t * (z * 0.0625))
	elif x <= 1.02e-292:
		tmp = t_2
	elif x <= 8e-140:
		tmp = c + ((b * a) * -0.25)
	elif x <= 8e-72:
		tmp = t_2
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(Float64(0.0625 * Float64(t * z)) - t_1)
	tmp = 0.0
	if (x <= -4.6e+52)
		tmp = Float64(Float64(x * y) - t_1);
	elseif (x <= -2.2e-109)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (x <= 1.02e-292)
		tmp = t_2;
	elseif (x <= 8e-140)
		tmp = Float64(c + Float64(Float64(b * a) * -0.25));
	elseif (x <= 8e-72)
		tmp = t_2;
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	t_2 = (0.0625 * (t * z)) - t_1;
	tmp = 0.0;
	if (x <= -4.6e+52)
		tmp = (x * y) - t_1;
	elseif (x <= -2.2e-109)
		tmp = c + (t * (z * 0.0625));
	elseif (x <= 1.02e-292)
		tmp = t_2;
	elseif (x <= 8e-140)
		tmp = c + ((b * a) * -0.25);
	elseif (x <= 8e-72)
		tmp = t_2;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[x, -4.6e+52], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[x, -2.2e-109], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e-292], t$95$2, If[LessEqual[x, 8e-140], N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-72], t$95$2, N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.6e52

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 82.2%

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

   3. Taylor expanded in c around 0 70.7%

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

   if -4.6e52 < x < -2.1999999999999999e-109

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. associate-*r* 59.5%

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

      3. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   if -2.1999999999999999e-109 < x < 1.0200000000000001e-292 or 7.9999999999999999e-140 < x < 7.9999999999999997e-72

   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 89.4%

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

   3. Taylor expanded in c around 0 74.1%

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

   if 1.0200000000000001e-292 < x < 7.9999999999999999e-140

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 63.5%

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

      1. *-commutative 63.5%

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

   4. Simplified 63.5%

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

   if 7.9999999999999997e-72 < x

   1. Initial program 95.7%

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

   2. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{y \cdot x} + c \]
3. Recombined 5 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-109}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-292}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-140}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-72}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 3: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ t_3 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;x \leq -29500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-308}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (+ c (* x y)))
        (t_3 (* b (* a -0.25))))
   (if (<= x -29500000.0)
     t_2
     (if (<= x -4.6e-298)
       t_1
       (if (<= x 8e-308)
         t_3
         (if (<= x 6e-274)
           t_1
           (if (<= x 7e-256) t_3 (if (<= x 6.2e-72) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double t_3 = b * (a * -0.25);
	double tmp;
	if (x <= -29500000.0) {
		tmp = t_2;
	} else if (x <= -4.6e-298) {
		tmp = t_1;
	} else if (x <= 8e-308) {
		tmp = t_3;
	} else if (x <= 6e-274) {
		tmp = t_1;
	} else if (x <= 7e-256) {
		tmp = t_3;
	} else if (x <= 6.2e-72) {
		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) :: t_3
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = c + (x * y)
    t_3 = b * (a * (-0.25d0))
    if (x <= (-29500000.0d0)) then
        tmp = t_2
    else if (x <= (-4.6d-298)) then
        tmp = t_1
    else if (x <= 8d-308) then
        tmp = t_3
    else if (x <= 6d-274) then
        tmp = t_1
    else if (x <= 7d-256) then
        tmp = t_3
    else if (x <= 6.2d-72) 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 + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double t_3 = b * (a * -0.25);
	double tmp;
	if (x <= -29500000.0) {
		tmp = t_2;
	} else if (x <= -4.6e-298) {
		tmp = t_1;
	} else if (x <= 8e-308) {
		tmp = t_3;
	} else if (x <= 6e-274) {
		tmp = t_1;
	} else if (x <= 7e-256) {
		tmp = t_3;
	} else if (x <= 6.2e-72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (x * y)
	t_3 = b * (a * -0.25)
	tmp = 0
	if x <= -29500000.0:
		tmp = t_2
	elif x <= -4.6e-298:
		tmp = t_1
	elif x <= 8e-308:
		tmp = t_3
	elif x <= 6e-274:
		tmp = t_1
	elif x <= 7e-256:
		tmp = t_3
	elif x <= 6.2e-72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(x * y))
	t_3 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (x <= -29500000.0)
		tmp = t_2;
	elseif (x <= -4.6e-298)
		tmp = t_1;
	elseif (x <= 8e-308)
		tmp = t_3;
	elseif (x <= 6e-274)
		tmp = t_1;
	elseif (x <= 7e-256)
		tmp = t_3;
	elseif (x <= 6.2e-72)
		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 + (t * (z * 0.0625));
	t_2 = c + (x * y);
	t_3 = b * (a * -0.25);
	tmp = 0.0;
	if (x <= -29500000.0)
		tmp = t_2;
	elseif (x <= -4.6e-298)
		tmp = t_1;
	elseif (x <= 8e-308)
		tmp = t_3;
	elseif (x <= 6e-274)
		tmp = t_1;
	elseif (x <= 7e-256)
		tmp = t_3;
	elseif (x <= 6.2e-72)
		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[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -29500000.0], t$95$2, If[LessEqual[x, -4.6e-298], t$95$1, If[LessEqual[x, 8e-308], t$95$3, If[LessEqual[x, 6e-274], t$95$1, If[LessEqual[x, 7e-256], t$95$3, If[LessEqual[x, 6.2e-72], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.95e7 or 6.1999999999999996e-72 < x

   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 x around inf 61.4%

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

   if -2.95e7 < x < -4.6000000000000001e-298 or 8.00000000000000026e-308 < x < 5.99999999999999954e-274 or 7.00000000000000028e-256 < x < 6.1999999999999996e-72

   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 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-*r* 61.4%

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

      3. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   if -4.6000000000000001e-298 < x < 8.00000000000000026e-308 or 5.99999999999999954e-274 < x < 7.00000000000000028e-256

   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. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-lft-identity 99.8%

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

      11. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

      1. fma-udef 99.4%

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

      2. associate-/l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-/l* 99.4%

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

      5. div-inv 99.4%

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

      6. clear-num 99.6%

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

      7. div-inv 99.6%

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

      8. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*l* 63.8%

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

   8. Simplified 63.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29500000:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-298}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-308}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-274}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-256}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-72}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 4: 58.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \left(b \cdot a\right) \cdot -0.25\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -54000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-271}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* (* b a) -0.25))) (t_2 (+ c (* x y))))
   (if (<= x -2.2e+88)
     t_2
     (if (<= x -3.7e+53)
       t_1
       (if (<= x -54000000000.0)
         t_2
         (if (<= x -2.9e-271)
           (+ c (* t (* z 0.0625)))
           (if (<= x 8.5e-92) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((b * a) * -0.25);
	double t_2 = c + (x * y);
	double tmp;
	if (x <= -2.2e+88) {
		tmp = t_2;
	} else if (x <= -3.7e+53) {
		tmp = t_1;
	} else if (x <= -54000000000.0) {
		tmp = t_2;
	} else if (x <= -2.9e-271) {
		tmp = c + (t * (z * 0.0625));
	} else if (x <= 8.5e-92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + ((b * a) * (-0.25d0))
    t_2 = c + (x * y)
    if (x <= (-2.2d+88)) then
        tmp = t_2
    else if (x <= (-3.7d+53)) then
        tmp = t_1
    else if (x <= (-54000000000.0d0)) then
        tmp = t_2
    else if (x <= (-2.9d-271)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (x <= 8.5d-92) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((b * a) * -0.25);
	double t_2 = c + (x * y);
	double tmp;
	if (x <= -2.2e+88) {
		tmp = t_2;
	} else if (x <= -3.7e+53) {
		tmp = t_1;
	} else if (x <= -54000000000.0) {
		tmp = t_2;
	} else if (x <= -2.9e-271) {
		tmp = c + (t * (z * 0.0625));
	} else if (x <= 8.5e-92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((b * a) * -0.25)
	t_2 = c + (x * y)
	tmp = 0
	if x <= -2.2e+88:
		tmp = t_2
	elif x <= -3.7e+53:
		tmp = t_1
	elif x <= -54000000000.0:
		tmp = t_2
	elif x <= -2.9e-271:
		tmp = c + (t * (z * 0.0625))
	elif x <= 8.5e-92:
		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(b * a) * -0.25))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (x <= -2.2e+88)
		tmp = t_2;
	elseif (x <= -3.7e+53)
		tmp = t_1;
	elseif (x <= -54000000000.0)
		tmp = t_2;
	elseif (x <= -2.9e-271)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (x <= 8.5e-92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((b * a) * -0.25);
	t_2 = c + (x * y);
	tmp = 0.0;
	if (x <= -2.2e+88)
		tmp = t_2;
	elseif (x <= -3.7e+53)
		tmp = t_1;
	elseif (x <= -54000000000.0)
		tmp = t_2;
	elseif (x <= -2.9e-271)
		tmp = c + (t * (z * 0.0625));
	elseif (x <= 8.5e-92)
		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[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+88], t$95$2, If[LessEqual[x, -3.7e+53], t$95$1, If[LessEqual[x, -54000000000.0], t$95$2, If[LessEqual[x, -2.9e-271], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-92], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.20000000000000009e88 or -3.7e53 < x < -5.4e10 or 8.50000000000000067e-92 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around inf 60.7%

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

   if -2.20000000000000009e88 < x < -3.7e53 or -2.90000000000000014e-271 < x < 8.50000000000000067e-92

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 61.9%

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

      1. *-commutative 61.9%

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

   4. Simplified 61.9%

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

   if -5.4e10 < x < -2.90000000000000014e-271

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 62.9%

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

      3. *-commutative 62.9%

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

   4. Simplified 62.9%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+88}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;x \leq -54000000000:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-271}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-92}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 5: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+52} \lor \neg \left(x \leq 3.6 \cdot 10^{-72}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)))
   (if (or (<= x -4.6e+52) (not (<= x 3.6e-72)))
     (- (+ c (* x y)) t_1)
     (- (+ 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 ((x <= -4.6e+52) || !(x <= 3.6e-72)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (t * z))) - 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 ((x <= (-4.6d+52)) .or. (.not. (x <= 3.6d-72))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + (0.0625d0 * (t * z))) - 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 ((x <= -4.6e+52) || !(x <= 3.6e-72)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + (0.0625 * (t * z))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	tmp = 0
	if (x <= -4.6e+52) or not (x <= 3.6e-72):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + (0.0625 * (t * z))) - 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 ((x <= -4.6e+52) || !(x <= 3.6e-72))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(0.0625 * Float64(t * z))) - 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 ((x <= -4.6e+52) || ~((x <= 3.6e-72)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + (0.0625 * (t * z))) - 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[Or[LessEqual[x, -4.6e+52], N[Not[LessEqual[x, 3.6e-72]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.6e52 or 3.6e-72 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 79.1%

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

   if -4.6e52 < x < 3.6e-72

   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 91.4%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+52} \lor \neg \left(x \leq 3.6 \cdot 10^{-72}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 6: 97.4% 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 7: 77.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ \mathbf{if}\;z \leq -6 \cdot 10^{+197}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)))
   (if (<= z -6e+197)
     (+ c (* t (* z 0.0625)))
     (if (<= z 1.5e-8) (- (+ c (* x y)) t_1) (- (* 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 (z <= -6e+197) {
		tmp = c + (t * (z * 0.0625));
	} else if (z <= 1.5e-8) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (0.0625 * (t * z)) - 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 (z <= (-6d+197)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (z <= 1.5d-8) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (0.0625d0 * (t * z)) - 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 (z <= -6e+197) {
		tmp = c + (t * (z * 0.0625));
	} else if (z <= 1.5e-8) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (0.0625 * (t * z)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	tmp = 0
	if z <= -6e+197:
		tmp = c + (t * (z * 0.0625))
	elif z <= 1.5e-8:
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (0.0625 * (t * z)) - 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 (z <= -6e+197)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (z <= 1.5e-8)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(0.0625 * Float64(t * z)) - 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 (z <= -6e+197)
		tmp = c + (t * (z * 0.0625));
	elseif (z <= 1.5e-8)
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (0.0625 * (t * z)) - 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[z, -6e+197], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-8], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000004e197

   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 inf 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-*r* 76.5%

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

      3. *-commutative 76.5%

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

   4. Simplified 76.5%

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

   if -6.0000000000000004e197 < z < 1.49999999999999987e-8

   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 z around 0 81.6%

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

   if 1.49999999999999987e-8 < z

   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 79.9%

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

   3. Taylor expanded in c around 0 67.4%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+197}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-8}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 8: 51.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+156}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -4.2e-51)
     t_2
     (if (<= b 1.1e+126)
       t_1
       (if (<= b 8.5e+156)
         (* 0.0625 (* t z))
         (if (<= b 1.42e+197) 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 <= -4.2e-51) {
		tmp = t_2;
	} else if (b <= 1.1e+126) {
		tmp = t_1;
	} else if (b <= 8.5e+156) {
		tmp = 0.0625 * (t * z);
	} else if (b <= 1.42e+197) {
		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 <= (-4.2d-51)) then
        tmp = t_2
    else if (b <= 1.1d+126) then
        tmp = t_1
    else if (b <= 8.5d+156) then
        tmp = 0.0625d0 * (t * z)
    else if (b <= 1.42d+197) 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 <= -4.2e-51) {
		tmp = t_2;
	} else if (b <= 1.1e+126) {
		tmp = t_1;
	} else if (b <= 8.5e+156) {
		tmp = 0.0625 * (t * z);
	} else if (b <= 1.42e+197) {
		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 <= -4.2e-51:
		tmp = t_2
	elif b <= 1.1e+126:
		tmp = t_1
	elif b <= 8.5e+156:
		tmp = 0.0625 * (t * z)
	elif b <= 1.42e+197:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(b * Float64(a * -0.25))
	tmp = 0.0
	if (b <= -4.2e-51)
		tmp = t_2;
	elseif (b <= 1.1e+126)
		tmp = t_1;
	elseif (b <= 8.5e+156)
		tmp = Float64(0.0625 * Float64(t * z));
	elseif (b <= 1.42e+197)
		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 <= -4.2e-51)
		tmp = t_2;
	elseif (b <= 1.1e+126)
		tmp = t_1;
	elseif (b <= 8.5e+156)
		tmp = 0.0625 * (t * z);
	elseif (b <= 1.42e+197)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e-51], t$95$2, If[LessEqual[b, 1.1e+126], t$95$1, If[LessEqual[b, 8.5e+156], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.42e+197], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.20000000000000003e-51 or 1.42000000000000006e197 < b

   1. Initial program 96.8%

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

      1. associate-+l- 96.8%

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

      2. sub-neg 96.8%

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

      3. neg-mul-1 96.8%

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

      4. metadata-eval 96.8%

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

      5. metadata-eval 96.8%

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

      6. cancel-sign-sub-inv 96.8%

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

      7. fma-def 96.8%

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

      8. associate-/l* 96.8%

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

      9. metadata-eval 96.8%

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

      10. *-lft-identity 96.8%

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

      11. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

      1. fma-udef 96.7%

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

      2. associate-/l* 96.7%

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

      3. +-commutative 96.7%

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

      4. associate-/l* 96.7%

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

      5. div-inv 96.7%

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

      6. clear-num 96.7%

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

      7. div-inv 96.7%

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

      8. metadata-eval 96.7%

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

   5. Applied egg-rr 96.7%

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

   6. Taylor expanded in a around inf 45.8%

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

      1. *-commutative 45.8%

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

      2. *-commutative 45.8%

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

      3. associate-*l* 45.8%

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

   8. Simplified 45.8%

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

   if -4.20000000000000003e-51 < b < 1.09999999999999999e126 or 8.49999999999999948e156 < b < 1.42000000000000006e197

   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 x around inf 59.9%

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

   if 1.09999999999999999e126 < b < 8.49999999999999948e156

   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. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 100.0%

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

      9. metadata-eval 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

      1. fma-udef 100.0%

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

      2. associate-/l* 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. div-inv 100.0%

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

      6. clear-num 100.0%

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

      7. div-inv 100.0%

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

      8. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in z around inf 39.2%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+126}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+156}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \leq 1.42 \cdot 10^{+197}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 9: 60.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-273}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-92}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -4.6e+52)
   (- (* x y) (* (* b a) 0.25))
   (if (<= x -9e-273)
     (+ c (* t (* z 0.0625)))
     (if (<= x 8.5e-92) (+ c (* (* b a) -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 (x <= -4.6e+52) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if (x <= -9e-273) {
		tmp = c + (t * (z * 0.0625));
	} else if (x <= 8.5e-92) {
		tmp = c + ((b * a) * -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 (x <= (-4.6d+52)) then
        tmp = (x * y) - ((b * a) * 0.25d0)
    else if (x <= (-9d-273)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (x <= 8.5d-92) then
        tmp = c + ((b * a) * (-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 (x <= -4.6e+52) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if (x <= -9e-273) {
		tmp = c + (t * (z * 0.0625));
	} else if (x <= 8.5e-92) {
		tmp = c + ((b * a) * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -4.6e+52:
		tmp = (x * y) - ((b * a) * 0.25)
	elif x <= -9e-273:
		tmp = c + (t * (z * 0.0625))
	elif x <= 8.5e-92:
		tmp = c + ((b * a) * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -4.6e+52)
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	elseif (x <= -9e-273)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (x <= 8.5e-92)
		tmp = Float64(c + Float64(Float64(b * a) * -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 (x <= -4.6e+52)
		tmp = (x * y) - ((b * a) * 0.25);
	elseif (x <= -9e-273)
		tmp = c + (t * (z * 0.0625));
	elseif (x <= 8.5e-92)
		tmp = c + ((b * a) * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -4.6e+52], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9e-273], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-92], N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.6e52

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0 82.2%

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

   3. Taylor expanded in c around 0 70.7%

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

   if -4.6e52 < x < -8.99999999999999921e-273

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 59.9%

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

      1. *-commutative 59.9%

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

      2. associate-*r* 59.9%

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

      3. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   if -8.99999999999999921e-273 < x < 8.50000000000000067e-92

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 62.5%

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

      1. *-commutative 62.5%

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

   4. Simplified 62.5%

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

   if 8.50000000000000067e-92 < x

   1. Initial program 95.9%

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

   2. Taylor expanded in x around inf 57.8%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-273}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-92}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 10: 37.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -64000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-282}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+98}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+156}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -64000.0)
   (* x y)
   (if (<= y 2.9e-282)
     (* b (* a -0.25))
     (if (<= y 2.1e+98) (* 0.0625 (* t z)) (if (<= y 1.1e+156) c (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -64000.0) {
		tmp = x * y;
	} else if (y <= 2.9e-282) {
		tmp = b * (a * -0.25);
	} else if (y <= 2.1e+98) {
		tmp = 0.0625 * (t * z);
	} else if (y <= 1.1e+156) {
		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 <= (-64000.0d0)) then
        tmp = x * y
    else if (y <= 2.9d-282) then
        tmp = b * (a * (-0.25d0))
    else if (y <= 2.1d+98) then
        tmp = 0.0625d0 * (t * z)
    else if (y <= 1.1d+156) 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 <= -64000.0) {
		tmp = x * y;
	} else if (y <= 2.9e-282) {
		tmp = b * (a * -0.25);
	} else if (y <= 2.1e+98) {
		tmp = 0.0625 * (t * z);
	} else if (y <= 1.1e+156) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -64000.0:
		tmp = x * y
	elif y <= 2.9e-282:
		tmp = b * (a * -0.25)
	elif y <= 2.1e+98:
		tmp = 0.0625 * (t * z)
	elif y <= 1.1e+156:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -64000.0)
		tmp = Float64(x * y);
	elseif (y <= 2.9e-282)
		tmp = Float64(b * Float64(a * -0.25));
	elseif (y <= 2.1e+98)
		tmp = Float64(0.0625 * Float64(t * z));
	elseif (y <= 1.1e+156)
		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 <= -64000.0)
		tmp = x * y;
	elseif (y <= 2.9e-282)
		tmp = b * (a * -0.25);
	elseif (y <= 2.1e+98)
		tmp = 0.0625 * (t * z);
	elseif (y <= 1.1e+156)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -64000.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 2.9e-282], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+98], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+156], c, N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -64000 or 1.10000000000000002e156 < y

   1. Initial program 94.8%

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

      1. associate-+l- 94.8%

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

      2. sub-neg 94.8%

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

      3. neg-mul-1 94.8%

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

      4. metadata-eval 94.8%

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

      5. metadata-eval 94.8%

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

      6. cancel-sign-sub-inv 94.8%

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

      7. fma-def 94.8%

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

      8. associate-/l* 94.8%

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

      9. metadata-eval 94.8%

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

      10. *-lft-identity 94.8%

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

      11. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

      1. fma-udef 94.7%

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

      2. associate-/l* 94.7%

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

      3. +-commutative 94.7%

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

      4. associate-/l* 94.7%

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

      5. div-inv 94.7%

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

      6. clear-num 94.7%

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

      7. div-inv 94.7%

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

      8. metadata-eval 94.7%

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

   5. Applied egg-rr 94.7%

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

   6. Taylor expanded in x around inf 56.6%

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

   if -64000 < y < 2.89999999999999998e-282

   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. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-lft-identity 99.8%

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

      11. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-/l* 99.7%

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

      5. div-inv 99.9%

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

      6. clear-num 99.9%

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

      7. div-inv 99.9%

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

      8. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around inf 33.9%

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

      1. *-commutative 33.9%

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

      2. *-commutative 33.9%

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

      3. associate-*l* 33.9%

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

   8. Simplified 33.9%

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

   if 2.89999999999999998e-282 < y < 2.10000000000000004e98

   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. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 100.0%

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

      9. metadata-eval 100.0%

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

      10. *-lft-identity 100.0%

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

      11. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-/l* 99.9%

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

      5. div-inv 99.9%

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

      6. clear-num 99.9%

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

      7. div-inv 99.9%

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

      8. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 31.5%

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

   if 2.10000000000000004e98 < y < 1.10000000000000002e156

   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 51.0%

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

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -64000:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-282}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+98}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+156}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 11: 37.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+97}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.45e-85)
   (* x y)
   (if (<= y 4.3e+97) (* 0.0625 (* t z)) (if (<= y 6.5e+155) c (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.45e-85) {
		tmp = x * y;
	} else if (y <= 4.3e+97) {
		tmp = 0.0625 * (t * z);
	} else if (y <= 6.5e+155) {
		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 <= (-1.45d-85)) then
        tmp = x * y
    else if (y <= 4.3d+97) then
        tmp = 0.0625d0 * (t * z)
    else if (y <= 6.5d+155) 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 <= -1.45e-85) {
		tmp = x * y;
	} else if (y <= 4.3e+97) {
		tmp = 0.0625 * (t * z);
	} else if (y <= 6.5e+155) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.45e-85:
		tmp = x * y
	elif y <= 4.3e+97:
		tmp = 0.0625 * (t * z)
	elif y <= 6.5e+155:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.45e-85)
		tmp = Float64(x * y);
	elseif (y <= 4.3e+97)
		tmp = Float64(0.0625 * Float64(t * z));
	elseif (y <= 6.5e+155)
		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 <= -1.45e-85)
		tmp = x * y;
	elseif (y <= 4.3e+97)
		tmp = 0.0625 * (t * z);
	elseif (y <= 6.5e+155)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -1.45e-85], N[(x * y), $MachinePrecision], If[LessEqual[y, 4.3e+97], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e+155], c, N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e-85 or 6.50000000000000046e155 < y

   1. Initial program 95.6%

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

      1. associate-+l- 95.6%

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

      2. sub-neg 95.6%

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

      3. neg-mul-1 95.6%

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

      4. metadata-eval 95.6%

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

      5. metadata-eval 95.6%

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

      6. cancel-sign-sub-inv 95.6%

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

      7. fma-def 95.6%

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

      8. associate-/l* 95.5%

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

      9. metadata-eval 95.5%

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

      10. *-lft-identity 95.5%

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

      11. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. fma-udef 95.5%

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

      2. associate-/l* 95.5%

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

      3. +-commutative 95.5%

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

      4. associate-/l* 95.5%

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

      5. div-inv 95.5%

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

      6. clear-num 95.5%

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

      7. div-inv 95.5%

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

      8. metadata-eval 95.5%

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

   5. Applied egg-rr 95.5%

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

   6. Taylor expanded in x around inf 48.6%

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

   if -1.4500000000000001e-85 < y < 4.2999999999999998e97

   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. sub-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. metadata-eval 100.0%

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

      5. metadata-eval 100.0%

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

      6. cancel-sign-sub-inv 100.0%

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

      7. fma-def 100.0%

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

      8. associate-/l* 99.9%

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

      9. metadata-eval 99.9%

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

      10. *-lft-identity 99.9%

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

      11. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-/l* 99.9%

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

      5. div-inv 99.9%

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

      6. clear-num 99.9%

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

      7. div-inv 99.9%

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

      8. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 35.1%

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

   if 4.2999999999999998e97 < y < 6.50000000000000046e155

   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 51.0%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+97}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+155}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12: 35.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+113}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.3e+113) (* x y) (if (<= x 2.7e-39) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.3e+113) {
		tmp = x * y;
	} else if (x <= 2.7e-39) {
		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 <= (-1.3d+113)) then
        tmp = x * y
    else if (x <= 2.7d-39) 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 <= -1.3e+113) {
		tmp = x * y;
	} else if (x <= 2.7e-39) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.3e+113:
		tmp = x * y
	elif x <= 2.7e-39:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.3e+113)
		tmp = Float64(x * y);
	elseif (x <= 2.7e-39)
		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 <= -1.3e+113)
		tmp = x * y;
	elseif (x <= 2.7e-39)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.3e+113], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.7e-39], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3e113 or 2.7000000000000001e-39 < x

   1. Initial program 95.9%

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

      1. associate-+l- 95.9%

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

      2. sub-neg 95.9%

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

      3. neg-mul-1 95.9%

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

      4. metadata-eval 95.9%

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

      5. metadata-eval 95.9%

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

      6. cancel-sign-sub-inv 95.9%

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

      7. fma-def 95.9%

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

      8. associate-/l* 95.9%

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

      9. metadata-eval 95.9%

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

      10. *-lft-identity 95.9%

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

      11. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

      1. fma-udef 95.8%

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

      2. associate-/l* 95.9%

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

      3. +-commutative 95.9%

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

      4. associate-/l* 95.8%

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

      5. div-inv 95.9%

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

      6. clear-num 95.9%

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

      7. div-inv 95.9%

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

      8. metadata-eval 95.9%

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

   5. Applied egg-rr 95.9%

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

   6. Taylor expanded in x around inf 49.1%

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

   if -1.3e113 < x < 2.7000000000000001e-39

   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 28.1%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+113}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-39}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 13: 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 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 21.1%

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

3. Final simplification 21.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023227 
(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))