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

Percentage Accurate: 97.7% → 98.6%

Time: 10.1s

Alternatives: 14

Speedup: 0.5×

• 32.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) INFINITY)
   (+ c (- (fma x y (* z (/ t 16.0))) (* a (/ b 4.0))))
   (+ c (* t (* z 0.0625)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) <= ((double) INFINITY)) {
		tmp = c + (fma(x, y, (z * (t / 16.0))) - (a * (b / 4.0)));
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) <= Inf)
		tmp = Float64(c + Float64(fma(x, y, Float64(z * Float64(t / 16.0))) - Float64(a * Float64(b / 4.0))));
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(c + N[(N[(x * y + N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(b / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 99.7%

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

      1. associate-+l- 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-+l- 99.7%

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

      4. fma-define 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/l* 100.0%

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

      7. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 46.1%

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

      1. associate-*r* 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*r* 46.1%

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

   5. Simplified 46.1%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\mathsf{fma}\left(x, y, z \cdot \frac{t}{16}\right) - a \cdot \frac{b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

   1. associate--l+ 95.4%

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

   2. fma-define 96.2%

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

   3. associate-/l* 96.5%

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

   4. fma-neg 97.3%

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

   5. distribute-neg-frac2 97.3%

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

   6. metadata-eval 97.3%

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

3. Simplified 97.3%

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

Alternative 3: 65.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := x \cdot y - t\_1\\ t_3 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_4 := c + x \cdot y\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+94}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \cdot b \leq -200000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-277}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-197}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \cdot b \leq 10^{+140}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25))
        (t_2 (- (* x y) t_1))
        (t_3 (+ c (* t (* z 0.0625))))
        (t_4 (+ c (* x y))))
   (if (<= (* a b) -2e+186)
     t_2
     (if (<= (* a b) -1e+94)
       t_3
       (if (<= (* a b) -2e+72)
         t_2
         (if (<= (* a b) -200000.0)
           t_3
           (if (<= (* a b) -2e-277)
             t_4
             (if (<= (* a b) 5e-197)
               t_3
               (if (<= (* a b) 1e+140) t_4 (- (* (* z t) 0.0625) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = (x * y) - t_1;
	double t_3 = c + (t * (z * 0.0625));
	double t_4 = c + (x * y);
	double tmp;
	if ((a * b) <= -2e+186) {
		tmp = t_2;
	} else if ((a * b) <= -1e+94) {
		tmp = t_3;
	} else if ((a * b) <= -2e+72) {
		tmp = t_2;
	} else if ((a * b) <= -200000.0) {
		tmp = t_3;
	} else if ((a * b) <= -2e-277) {
		tmp = t_4;
	} else if ((a * b) <= 5e-197) {
		tmp = t_3;
	} else if ((a * b) <= 1e+140) {
		tmp = t_4;
	} else {
		tmp = ((z * t) * 0.0625) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = (x * y) - t_1
    t_3 = c + (t * (z * 0.0625d0))
    t_4 = c + (x * y)
    if ((a * b) <= (-2d+186)) then
        tmp = t_2
    else if ((a * b) <= (-1d+94)) then
        tmp = t_3
    else if ((a * b) <= (-2d+72)) then
        tmp = t_2
    else if ((a * b) <= (-200000.0d0)) then
        tmp = t_3
    else if ((a * b) <= (-2d-277)) then
        tmp = t_4
    else if ((a * b) <= 5d-197) then
        tmp = t_3
    else if ((a * b) <= 1d+140) then
        tmp = t_4
    else
        tmp = ((z * t) * 0.0625d0) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double t_2 = (x * y) - t_1;
	double t_3 = c + (t * (z * 0.0625));
	double t_4 = c + (x * y);
	double tmp;
	if ((a * b) <= -2e+186) {
		tmp = t_2;
	} else if ((a * b) <= -1e+94) {
		tmp = t_3;
	} else if ((a * b) <= -2e+72) {
		tmp = t_2;
	} else if ((a * b) <= -200000.0) {
		tmp = t_3;
	} else if ((a * b) <= -2e-277) {
		tmp = t_4;
	} else if ((a * b) <= 5e-197) {
		tmp = t_3;
	} else if ((a * b) <= 1e+140) {
		tmp = t_4;
	} else {
		tmp = ((z * t) * 0.0625) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = (x * y) - t_1
	t_3 = c + (t * (z * 0.0625))
	t_4 = c + (x * y)
	tmp = 0
	if (a * b) <= -2e+186:
		tmp = t_2
	elif (a * b) <= -1e+94:
		tmp = t_3
	elif (a * b) <= -2e+72:
		tmp = t_2
	elif (a * b) <= -200000.0:
		tmp = t_3
	elif (a * b) <= -2e-277:
		tmp = t_4
	elif (a * b) <= 5e-197:
		tmp = t_3
	elif (a * b) <= 1e+140:
		tmp = t_4
	else:
		tmp = ((z * t) * 0.0625) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	t_2 = Float64(Float64(x * y) - t_1)
	t_3 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_4 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(a * b) <= -2e+186)
		tmp = t_2;
	elseif (Float64(a * b) <= -1e+94)
		tmp = t_3;
	elseif (Float64(a * b) <= -2e+72)
		tmp = t_2;
	elseif (Float64(a * b) <= -200000.0)
		tmp = t_3;
	elseif (Float64(a * b) <= -2e-277)
		tmp = t_4;
	elseif (Float64(a * b) <= 5e-197)
		tmp = t_3;
	elseif (Float64(a * b) <= 1e+140)
		tmp = t_4;
	else
		tmp = Float64(Float64(Float64(z * t) * 0.0625) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	t_2 = (x * y) - t_1;
	t_3 = c + (t * (z * 0.0625));
	t_4 = c + (x * y);
	tmp = 0.0;
	if ((a * b) <= -2e+186)
		tmp = t_2;
	elseif ((a * b) <= -1e+94)
		tmp = t_3;
	elseif ((a * b) <= -2e+72)
		tmp = t_2;
	elseif ((a * b) <= -200000.0)
		tmp = t_3;
	elseif ((a * b) <= -2e-277)
		tmp = t_4;
	elseif ((a * b) <= 5e-197)
		tmp = t_3;
	elseif ((a * b) <= 1e+140)
		tmp = t_4;
	else
		tmp = ((z * t) * 0.0625) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+186], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -1e+94], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -2e+72], t$95$2, If[LessEqual[N[(a * b), $MachinePrecision], -200000.0], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], -2e-277], t$95$4, If[LessEqual[N[(a * b), $MachinePrecision], 5e-197], t$95$3, If[LessEqual[N[(a * b), $MachinePrecision], 1e+140], t$95$4, N[(N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.99999999999999996e186 or -1e94 < (*.f64 a b) < -1.99999999999999989e72

   1. Initial program 86.7%

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

   3. Taylor expanded in z around 0 87.3%

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

   4. Taylor expanded in c around 0 83.2%

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

   if -1.99999999999999996e186 < (*.f64 a b) < -1e94 or -1.99999999999999989e72 < (*.f64 a b) < -2e5 or -1.99999999999999994e-277 < (*.f64 a b) < 5.0000000000000002e-197

   1. Initial program 98.6%

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

   3. Taylor expanded in z around inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*r* 76.3%

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

   5. Simplified 76.3%

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

   if -2e5 < (*.f64 a b) < -1.99999999999999994e-277 or 5.0000000000000002e-197 < (*.f64 a b) < 1.00000000000000006e140

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 70.7%

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

   if 1.00000000000000006e140 < (*.f64 a b)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0 95.3%

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

   4. Taylor expanded in c around 0 90.9%

      \[\leadsto \color{blue}{0.0625 \cdot \left(t \cdot z\right) - 0.25 \cdot \left(a \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+186}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -1 \cdot 10^{+94}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{+72}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq -200000:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq -2 \cdot 10^{-277}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-197}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 10^{+140}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (+ c (* t (* z 0.0625))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = c + (t * (z * 0.0625));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = c + (t * (z * 0.0625))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = c + (t * (z * 0.0625));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) < +inf.0

   1. Initial program 99.7%

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

   if +inf.0 < (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64)))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 46.1%

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

      1. associate-*r* 46.1%

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

      2. *-commutative 46.1%

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

      3. associate-*r* 46.1%

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

   5. Simplified 46.1%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;c + \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right)\\ \mathbf{else}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -0.0205:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-112}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.3 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -0.0205)
     t_2
     (if (<= (* x y) 7e-161)
       t_1
       (if (<= (* x y) 6e-112)
         (+ c (* a (* b -0.25)))
         (if (<= (* x y) 6.3e+100) 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 tmp;
	if ((x * y) <= -0.0205) {
		tmp = t_2;
	} else if ((x * y) <= 7e-161) {
		tmp = t_1;
	} else if ((x * y) <= 6e-112) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 6.3e+100) {
		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 + (t * (z * 0.0625d0))
    t_2 = c + (x * y)
    if ((x * y) <= (-0.0205d0)) then
        tmp = t_2
    else if ((x * y) <= 7d-161) then
        tmp = t_1
    else if ((x * y) <= 6d-112) then
        tmp = c + (a * (b * (-0.25d0)))
    else if ((x * y) <= 6.3d+100) 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 tmp;
	if ((x * y) <= -0.0205) {
		tmp = t_2;
	} else if ((x * y) <= 7e-161) {
		tmp = t_1;
	} else if ((x * y) <= 6e-112) {
		tmp = c + (a * (b * -0.25));
	} else if ((x * y) <= 6.3e+100) {
		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)
	tmp = 0
	if (x * y) <= -0.0205:
		tmp = t_2
	elif (x * y) <= 7e-161:
		tmp = t_1
	elif (x * y) <= 6e-112:
		tmp = c + (a * (b * -0.25))
	elif (x * y) <= 6.3e+100:
		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))
	tmp = 0.0
	if (Float64(x * y) <= -0.0205)
		tmp = t_2;
	elseif (Float64(x * y) <= 7e-161)
		tmp = t_1;
	elseif (Float64(x * y) <= 6e-112)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	elseif (Float64(x * y) <= 6.3e+100)
		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);
	tmp = 0.0;
	if ((x * y) <= -0.0205)
		tmp = t_2;
	elseif ((x * y) <= 7e-161)
		tmp = t_1;
	elseif ((x * y) <= 6e-112)
		tmp = c + (a * (b * -0.25));
	elseif ((x * y) <= 6.3e+100)
		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]}, If[LessEqual[N[(x * y), $MachinePrecision], -0.0205], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 7e-161], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6e-112], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.3e+100], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.0205000000000000009 or 6.3000000000000004e100 < (*.f64 x y)

   1. Initial program 94.3%

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

   3. Taylor expanded in x around inf 71.0%

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

   if -0.0205000000000000009 < (*.f64 x y) < 7.00000000000000039e-161 or 6.0000000000000002e-112 < (*.f64 x y) < 6.3000000000000004e100

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 65.0%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*r* 65.7%

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

   5. Simplified 65.7%

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

   if 7.00000000000000039e-161 < (*.f64 x y) < 6.0000000000000002e-112

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*r* 85.3%

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

   5. Simplified 85.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0205:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 7 \cdot 10^{-161}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{-112}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 6.3 \cdot 10^{+100}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -5e-51)
     t_2
     (if (<= (* x y) 5e-99)
       t_1
       (if (<= (* x y) 4.1e-72)
         (* t (* z 0.0625))
         (if (<= (* x y) 6.8e+139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -5e-51) {
		tmp = t_2;
	} else if ((x * y) <= 5e-99) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e-72) {
		tmp = t * (z * 0.0625);
	} else if ((x * y) <= 6.8e+139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (a * (b * (-0.25d0)))
    t_2 = c + (x * y)
    if ((x * y) <= (-5d-51)) then
        tmp = t_2
    else if ((x * y) <= 5d-99) then
        tmp = t_1
    else if ((x * y) <= 4.1d-72) then
        tmp = t * (z * 0.0625d0)
    else if ((x * y) <= 6.8d+139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (a * (b * -0.25));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -5e-51) {
		tmp = t_2;
	} else if ((x * y) <= 5e-99) {
		tmp = t_1;
	} else if ((x * y) <= 4.1e-72) {
		tmp = t * (z * 0.0625);
	} else if ((x * y) <= 6.8e+139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -5e-51:
		tmp = t_2
	elif (x * y) <= 5e-99:
		tmp = t_1
	elif (x * y) <= 4.1e-72:
		tmp = t * (z * 0.0625)
	elif (x * y) <= 6.8e+139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(a * Float64(b * -0.25)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -5e-51)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-99)
		tmp = t_1;
	elseif (Float64(x * y) <= 4.1e-72)
		tmp = Float64(t * Float64(z * 0.0625));
	elseif (Float64(x * y) <= 6.8e+139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (a * (b * -0.25));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -5e-51)
		tmp = t_2;
	elseif ((x * y) <= 5e-99)
		tmp = t_1;
	elseif ((x * y) <= 4.1e-72)
		tmp = t * (z * 0.0625);
	elseif ((x * y) <= 6.8e+139)
		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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e-51], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-99], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4.1e-72], N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 6.8e+139], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.00000000000000004e-51 or 6.8000000000000005e139 < (*.f64 x y)

   1. Initial program 93.7%

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

   3. Taylor expanded in x around inf 69.6%

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

   if -5.00000000000000004e-51 < (*.f64 x y) < 4.99999999999999969e-99 or 4.10000000000000003e-72 < (*.f64 x y) < 6.8000000000000005e139

   1. Initial program 97.2%

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

   3. Taylor expanded in a around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-*r* 61.0%

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

   5. Simplified 61.0%

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

   if 4.99999999999999969e-99 < (*.f64 x y) < 4.10000000000000003e-72

   1. Initial program 83.3%

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

   3. Taylor expanded in b around inf 52.8%

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

   4. Taylor expanded in t around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-51}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-99}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4.1 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6.8 \cdot 10^{+139}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := b \cdot \left(a \cdot -0.25\right)\\ t_3 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+114}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* b (* a -0.25))) (t_3 (* t (* z 0.0625))))
   (if (<= t -9.2e+73)
     t_3
     (if (<= t 7.2e-230)
       t_1
       (if (<= t 6.2e-172)
         t_2
         (if (<= t 3.1e+81) t_1 (if (<= t 2e+114) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = b * (a * -0.25);
	double t_3 = t * (z * 0.0625);
	double tmp;
	if (t <= -9.2e+73) {
		tmp = t_3;
	} else if (t <= 7.2e-230) {
		tmp = t_1;
	} else if (t <= 6.2e-172) {
		tmp = t_2;
	} else if (t <= 3.1e+81) {
		tmp = t_1;
	} else if (t <= 2e+114) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = b * (a * (-0.25d0))
    t_3 = t * (z * 0.0625d0)
    if (t <= (-9.2d+73)) then
        tmp = t_3
    else if (t <= 7.2d-230) then
        tmp = t_1
    else if (t <= 6.2d-172) then
        tmp = t_2
    else if (t <= 3.1d+81) then
        tmp = t_1
    else if (t <= 2d+114) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = b * (a * -0.25);
	double t_3 = t * (z * 0.0625);
	double tmp;
	if (t <= -9.2e+73) {
		tmp = t_3;
	} else if (t <= 7.2e-230) {
		tmp = t_1;
	} else if (t <= 6.2e-172) {
		tmp = t_2;
	} else if (t <= 3.1e+81) {
		tmp = t_1;
	} else if (t <= 2e+114) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = b * (a * -0.25)
	t_3 = t * (z * 0.0625)
	tmp = 0
	if t <= -9.2e+73:
		tmp = t_3
	elif t <= 7.2e-230:
		tmp = t_1
	elif t <= 6.2e-172:
		tmp = t_2
	elif t <= 3.1e+81:
		tmp = t_1
	elif t <= 2e+114:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(b * Float64(a * -0.25))
	t_3 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (t <= -9.2e+73)
		tmp = t_3;
	elseif (t <= 7.2e-230)
		tmp = t_1;
	elseif (t <= 6.2e-172)
		tmp = t_2;
	elseif (t <= 3.1e+81)
		tmp = t_1;
	elseif (t <= 2e+114)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = b * (a * -0.25);
	t_3 = t * (z * 0.0625);
	tmp = 0.0;
	if (t <= -9.2e+73)
		tmp = t_3;
	elseif (t <= 7.2e-230)
		tmp = t_1;
	elseif (t <= 6.2e-172)
		tmp = t_2;
	elseif (t <= 3.1e+81)
		tmp = t_1;
	elseif (t <= 2e+114)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+73], t$95$3, If[LessEqual[t, 7.2e-230], t$95$1, If[LessEqual[t, 6.2e-172], t$95$2, If[LessEqual[t, 3.1e+81], t$95$1, If[LessEqual[t, 2e+114], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.199999999999999e73 or 2e114 < t

   1. Initial program 89.4%

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

   3. Taylor expanded in b around inf 80.2%

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

   4. Taylor expanded in t around inf 58.2%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-*r* 59.1%

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

   6. Simplified 59.1%

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

   if -9.199999999999999e73 < t < 7.1999999999999997e-230 or 6.2000000000000005e-172 < t < 3.1e81

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 60.3%

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

   if 7.1999999999999997e-230 < t < 6.2000000000000005e-172 or 3.1e81 < t < 2e114

   1. Initial program 93.3%

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

   3. Taylor expanded in b around inf 93.3%

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

   4. Taylor expanded in b around inf 66.8%

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

      1. associate-*r* 66.8%

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

      2. *-commutative 66.8%

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

   6. Simplified 66.8%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-230}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-172}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+81}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot -0.25\right)\\ t_2 := t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-230}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+117}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* b (* a -0.25))) (t_2 (* t (* z 0.0625))))
   (if (<= t -5.2e-75)
     t_2
     (if (<= t 5.5e-230)
       (* x y)
       (if (<= t 1e-160)
         t_1
         (if (<= t 1.3e+82) (* x y) (if (<= t 4.2e+117) t_1 t_2)))))))

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 = t * (z * 0.0625);
	double tmp;
	if (t <= -5.2e-75) {
		tmp = t_2;
	} else if (t <= 5.5e-230) {
		tmp = x * y;
	} else if (t <= 1e-160) {
		tmp = t_1;
	} else if (t <= 1.3e+82) {
		tmp = x * y;
	} else if (t <= 4.2e+117) {
		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 = b * (a * (-0.25d0))
    t_2 = t * (z * 0.0625d0)
    if (t <= (-5.2d-75)) then
        tmp = t_2
    else if (t <= 5.5d-230) then
        tmp = x * y
    else if (t <= 1d-160) then
        tmp = t_1
    else if (t <= 1.3d+82) then
        tmp = x * y
    else if (t <= 4.2d+117) 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 = b * (a * -0.25);
	double t_2 = t * (z * 0.0625);
	double tmp;
	if (t <= -5.2e-75) {
		tmp = t_2;
	} else if (t <= 5.5e-230) {
		tmp = x * y;
	} else if (t <= 1e-160) {
		tmp = t_1;
	} else if (t <= 1.3e+82) {
		tmp = x * y;
	} else if (t <= 4.2e+117) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b * (a * -0.25)
	t_2 = t * (z * 0.0625)
	tmp = 0
	if t <= -5.2e-75:
		tmp = t_2
	elif t <= 5.5e-230:
		tmp = x * y
	elif t <= 1e-160:
		tmp = t_1
	elif t <= 1.3e+82:
		tmp = x * y
	elif t <= 4.2e+117:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b * Float64(a * -0.25))
	t_2 = Float64(t * Float64(z * 0.0625))
	tmp = 0.0
	if (t <= -5.2e-75)
		tmp = t_2;
	elseif (t <= 5.5e-230)
		tmp = Float64(x * y);
	elseif (t <= 1e-160)
		tmp = t_1;
	elseif (t <= 1.3e+82)
		tmp = Float64(x * y);
	elseif (t <= 4.2e+117)
		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 = b * (a * -0.25);
	t_2 = t * (z * 0.0625);
	tmp = 0.0;
	if (t <= -5.2e-75)
		tmp = t_2;
	elseif (t <= 5.5e-230)
		tmp = x * y;
	elseif (t <= 1e-160)
		tmp = t_1;
	elseif (t <= 1.3e+82)
		tmp = x * y;
	elseif (t <= 4.2e+117)
		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[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e-75], t$95$2, If[LessEqual[t, 5.5e-230], N[(x * y), $MachinePrecision], If[LessEqual[t, 1e-160], t$95$1, If[LessEqual[t, 1.3e+82], N[(x * y), $MachinePrecision], If[LessEqual[t, 4.2e+117], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.2e-75 or 4.2000000000000002e117 < t

   1. Initial program 92.2%

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

   3. Taylor expanded in b around inf 79.7%

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

   4. Taylor expanded in t around inf 50.4%

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

      1. associate-*r* 51.0%

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

      2. *-commutative 51.0%

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

      3. associate-*r* 51.0%

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

   6. Simplified 51.0%

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

   if -5.2e-75 < t < 5.4999999999999997e-230 or 9.9999999999999999e-161 < t < 1.2999999999999999e82

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf 77.7%

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

   4. Taylor expanded in x around inf 43.5%

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

   if 5.4999999999999997e-230 < t < 9.9999999999999999e-161 or 1.2999999999999999e82 < t < 4.2000000000000002e117

   1. Initial program 93.3%

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

   3. Taylor expanded in b around inf 93.3%

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

   4. Taylor expanded in b around inf 66.8%

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

      1. associate-*r* 66.8%

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

      2. *-commutative 66.8%

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

   6. Simplified 66.8%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-230}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 10^{-160}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+117}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(z \cdot 0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+134} \lor \neg \left(z \leq -2.2 \cdot 10^{+63}\right) \land \left(z \leq -1100 \lor \neg \left(z \leq 2.3 \cdot 10^{-102}\right)\right):\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -3.3e+134)
         (and (not (<= z -2.2e+63)) (or (<= z -1100.0) (not (<= z 2.3e-102)))))
   (+ c (* t (* z 0.0625)))
   (- (* x y) (* (* a b) 0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.3e+134) || (!(z <= -2.2e+63) && ((z <= -1100.0) || !(z <= 2.3e-102)))) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-3.3d+134)) .or. (.not. (z <= (-2.2d+63))) .and. (z <= (-1100.0d0)) .or. (.not. (z <= 2.3d-102))) then
        tmp = c + (t * (z * 0.0625d0))
    else
        tmp = (x * y) - ((a * b) * 0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -3.3e+134) || (!(z <= -2.2e+63) && ((z <= -1100.0) || !(z <= 2.3e-102)))) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = (x * y) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -3.3e+134) or (not (z <= -2.2e+63) and ((z <= -1100.0) or not (z <= 2.3e-102))):
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = (x * y) - ((a * b) * 0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -3.3e+134) || (!(z <= -2.2e+63) && ((z <= -1100.0) || !(z <= 2.3e-102))))
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -3.3e+134) || (~((z <= -2.2e+63)) && ((z <= -1100.0) || ~((z <= 2.3e-102)))))
		tmp = c + (t * (z * 0.0625));
	else
		tmp = (x * y) - ((a * b) * 0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -3.3e+134], And[N[Not[LessEqual[z, -2.2e+63]], $MachinePrecision], Or[LessEqual[z, -1100.0], N[Not[LessEqual[z, 2.3e-102]], $MachinePrecision]]]], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e134 or -2.1999999999999999e63 < z < -1100 or 2.29999999999999987e-102 < z

   1. Initial program 93.7%

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

   3. Taylor expanded in z around inf 65.3%

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

      1. associate-*r* 65.9%

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

      2. *-commutative 65.9%

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

      3. associate-*r* 65.9%

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

   5. Simplified 65.9%

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

   if -3.3e134 < z < -2.1999999999999999e63 or -1100 < z < 2.29999999999999987e-102

   1. Initial program 97.4%

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

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in c around 0 70.7%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+134} \lor \neg \left(z \leq -2.2 \cdot 10^{+63}\right) \land \left(z \leq -1100 \lor \neg \left(z \leq 2.3 \cdot 10^{-102}\right)\right):\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -0.0205 \lor \neg \left(x \cdot y \leq 2.6 \cdot 10^{+109}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (or (<= (* x y) -0.0205) (not (<= (* x y) 2.6e+109)))
     (- (+ c (* x y)) t_1)
     (- (+ c (* (* z t) 0.0625)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -0.0205) || !((x * y) <= 2.6e+109)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    if (((x * y) <= (-0.0205d0)) .or. (.not. ((x * y) <= 2.6d+109))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = (c + ((z * t) * 0.0625d0)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (((x * y) <= -0.0205) || !((x * y) <= 2.6e+109)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if ((x * y) <= -0.0205) or not ((x * y) <= 2.6e+109):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = (c + ((z * t) * 0.0625)) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if ((Float64(x * y) <= -0.0205) || !(Float64(x * y) <= 2.6e+109))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(c + Float64(Float64(z * t) * 0.0625)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if (((x * y) <= -0.0205) || ~(((x * y) <= 2.6e+109)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = (c + ((z * t) * 0.0625)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[Or[LessEqual[N[(x * y), $MachinePrecision], -0.0205], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.6e+109]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(c + N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -0.0205000000000000009 or 2.5999999999999998e109 < (*.f64 x y)

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 84.7%

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

   if -0.0205000000000000009 < (*.f64 x y) < 2.5999999999999998e109

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 91.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0205 \lor \neg \left(x \cdot y \leq 2.6 \cdot 10^{+109}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + \left(z \cdot t\right) \cdot 0.0625\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 44.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+59}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-24}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* x y) -1e+59)
   (* x y)
   (if (<= (* x y) -2.9e-24)
     c
     (if (<= (* x y) 3.1e+130) (* b (* a -0.25)) (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1e+59) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e-24) {
		tmp = c;
	} else if ((x * y) <= 3.1e+130) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x * y) <= (-1d+59)) then
        tmp = x * y
    else if ((x * y) <= (-2.9d-24)) then
        tmp = c
    else if ((x * y) <= 3.1d+130) then
        tmp = b * (a * (-0.25d0))
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -1e+59) {
		tmp = x * y;
	} else if ((x * y) <= -2.9e-24) {
		tmp = c;
	} else if ((x * y) <= 3.1e+130) {
		tmp = b * (a * -0.25);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x * y) <= -1e+59:
		tmp = x * y
	elif (x * y) <= -2.9e-24:
		tmp = c
	elif (x * y) <= 3.1e+130:
		tmp = b * (a * -0.25)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -1e+59)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -2.9e-24)
		tmp = c;
	elseif (Float64(x * y) <= 3.1e+130)
		tmp = Float64(b * Float64(a * -0.25));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x * y) <= -1e+59)
		tmp = x * y;
	elseif ((x * y) <= -2.9e-24)
		tmp = c;
	elseif ((x * y) <= 3.1e+130)
		tmp = b * (a * -0.25);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+59], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2.9e-24], c, If[LessEqual[N[(x * y), $MachinePrecision], 3.1e+130], N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999972e58 or 3.1e130 < (*.f64 x y)

   1. Initial program 93.1%

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

   3. Taylor expanded in b around inf 77.9%

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

   4. Taylor expanded in x around inf 69.9%

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

   if -9.99999999999999972e58 < (*.f64 x y) < -2.8999999999999999e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in c around inf 45.7%

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

   if -2.8999999999999999e-24 < (*.f64 x y) < 3.1e130

   1. Initial program 96.1%

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

   3. Taylor expanded in b around inf 80.2%

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

   4. Taylor expanded in b around inf 33.3%

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

      1. associate-*r* 33.3%

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

      2. *-commutative 33.3%

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

   6. Simplified 33.3%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+59}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -2.9 \cdot 10^{-24}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 3.1 \cdot 10^{+130}:\\ \;\;\;\;b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+134}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-74}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)))
   (if (<= z -3.3e+134)
     (+ c (* t (* z 0.0625)))
     (if (<= z 1.38e-74) (- (+ c (* x y)) t_1) (- (* (* z t) 0.0625) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (z <= -3.3e+134) {
		tmp = c + (t * (z * 0.0625));
	} else if (z <= 1.38e-74) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = ((z * t) * 0.0625) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    if (z <= (-3.3d+134)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (z <= 1.38d-74) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = ((z * t) * 0.0625d0) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) * 0.25;
	double tmp;
	if (z <= -3.3e+134) {
		tmp = c + (t * (z * 0.0625));
	} else if (z <= 1.38e-74) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = ((z * t) * 0.0625) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	tmp = 0
	if z <= -3.3e+134:
		tmp = c + (t * (z * 0.0625))
	elif z <= 1.38e-74:
		tmp = (c + (x * y)) - t_1
	else:
		tmp = ((z * t) * 0.0625) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (z <= -3.3e+134)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (z <= 1.38e-74)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(Float64(Float64(z * t) * 0.0625) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) * 0.25;
	tmp = 0.0;
	if (z <= -3.3e+134)
		tmp = c + (t * (z * 0.0625));
	elseif (z <= 1.38e-74)
		tmp = (c + (x * y)) - t_1;
	else
		tmp = ((z * t) * 0.0625) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[z, -3.3e+134], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e-74], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[(z * t), $MachinePrecision] * 0.0625), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e134

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. associate-*r* 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 72.4%

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

   5. Simplified 72.4%

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

   if -3.3e134 < z < 1.38e-74

   1. Initial program 97.7%

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

   3. Taylor expanded in z around 0 87.8%

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

   if 1.38e-74 < z

   1. Initial program 91.2%

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

   3. Taylor expanded in x around 0 83.1%

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

   4. Taylor expanded in c around 0 67.2%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+134}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-74}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot t\right) \cdot 0.0625 - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 42.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.6 \cdot 10^{+58} \lor \neg \left(x \cdot y \leq 2.8 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -9.6e+58) (not (<= (* x y) 2.8e+57))) (* x y) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -9.6e+58) || !((x * y) <= 2.8e+57)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-9.6d+58)) .or. (.not. ((x * y) <= 2.8d+57))) then
        tmp = x * y
    else
        tmp = c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -9.6e+58) || !((x * y) <= 2.8e+57)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -9.6e+58) or not ((x * y) <= 2.8e+57):
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -9.6e+58) || !(Float64(x * y) <= 2.8e+57))
		tmp = Float64(x * y);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -9.6e+58) || ~(((x * y) <= 2.8e+57)))
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -9.6e+58], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.8e+57]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.5999999999999999e58 or 2.8e57 < (*.f64 x y)

   1. Initial program 93.4%

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

   3. Taylor expanded in b around inf 79.8%

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

   4. Taylor expanded in x around inf 62.4%

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

   if -9.5999999999999999e58 < (*.f64 x y) < 2.8e57

   1. Initial program 96.7%

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

   3. Taylor expanded in c around inf 30.0%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.6 \cdot 10^{+58} \lor \neg \left(x \cdot y \leq 2.8 \cdot 10^{+57}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.9% 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 95.4%

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

3. Taylor expanded in c around inf 19.8%

   \[\leadsto \color{blue}{c} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(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))