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

Percentage Accurate: 97.7% → 99.3%

Time: 10.6s

Alternatives: 13

Speedup: 0.5×

• 32.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t \cdot 0.0625, b \cdot \left(a \cdot -0.25\right)\right)\right) + c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - -0.0625 \cdot \left(t \cdot \frac{z}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) INFINITY)
   (+ (fma x y (fma z (* t 0.0625) (* b (* a -0.25)))) c)
   (* x (- y (* -0.0625 (* t (/ z x)))))))

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 = fma(x, y, fma(z, (t * 0.0625), (b * (a * -0.25)))) + c;
	} else {
		tmp = x * (y - (-0.0625 * (t * (z / x))));
	}
	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(fma(x, y, fma(z, Float64(t * 0.0625), Float64(b * Float64(a * -0.25)))) + c);
	else
		tmp = Float64(x * Float64(y - Float64(-0.0625 * Float64(t * Float64(z / x)))));
	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[(N[(x * y + N[(z * N[(t * 0.0625), $MachinePrecision] + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], N[(x * N[(y - N[(-0.0625 * N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $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 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%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t \cdot 0.0625, b \cdot \left(a \cdot -0.25\right)\right)\right) + c} \]
   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 a around 0 83.3%

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

   4. Taylor expanded in c around 0 83.3%

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

   5. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right) \]

      3. neg-mul-1 100.0%

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

      4. +-commutative 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, y, \mathsf{fma}\left(z, t \cdot 0.0625, b \cdot \left(a \cdot -0.25\right)\right)\right) + c\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - -0.0625 \cdot \left(t \cdot \frac{z}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := c + t\_1\\ t_3 := c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.46 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-144}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq -3.8 \cdot 10^{-287}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+157}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (+ c t_1)) (t_3 (+ c (* a (* b -0.25)))))
   (if (<= (* x y) -8.5e+204)
     (* x y)
     (if (<= (* x y) -1.46e+184)
       t_1
       (if (<= (* x y) -2.2e+146)
         (* x y)
         (if (<= (* x y) -1.25e-144)
           t_2
           (if (<= (* x y) -3.8e-287)
             t_3
             (if (<= (* x y) 2e-147)
               t_2
               (if (<= (* x y) 6e+157) t_3 (* x y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = c + t_1;
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -8.5e+204) {
		tmp = x * y;
	} else if ((x * y) <= -1.46e+184) {
		tmp = t_1;
	} else if ((x * y) <= -2.2e+146) {
		tmp = x * y;
	} else if ((x * y) <= -1.25e-144) {
		tmp = t_2;
	} else if ((x * y) <= -3.8e-287) {
		tmp = t_3;
	} else if ((x * y) <= 2e-147) {
		tmp = t_2;
	} else if ((x * y) <= 6e+157) {
		tmp = t_3;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    t_2 = c + t_1
    t_3 = c + (a * (b * (-0.25d0)))
    if ((x * y) <= (-8.5d+204)) then
        tmp = x * y
    else if ((x * y) <= (-1.46d+184)) then
        tmp = t_1
    else if ((x * y) <= (-2.2d+146)) then
        tmp = x * y
    else if ((x * y) <= (-1.25d-144)) then
        tmp = t_2
    else if ((x * y) <= (-3.8d-287)) then
        tmp = t_3
    else if ((x * y) <= 2d-147) then
        tmp = t_2
    else if ((x * y) <= 6d+157) then
        tmp = t_3
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double t_2 = c + t_1;
	double t_3 = c + (a * (b * -0.25));
	double tmp;
	if ((x * y) <= -8.5e+204) {
		tmp = x * y;
	} else if ((x * y) <= -1.46e+184) {
		tmp = t_1;
	} else if ((x * y) <= -2.2e+146) {
		tmp = x * y;
	} else if ((x * y) <= -1.25e-144) {
		tmp = t_2;
	} else if ((x * y) <= -3.8e-287) {
		tmp = t_3;
	} else if ((x * y) <= 2e-147) {
		tmp = t_2;
	} else if ((x * y) <= 6e+157) {
		tmp = t_3;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = c + t_1
	t_3 = c + (a * (b * -0.25))
	tmp = 0
	if (x * y) <= -8.5e+204:
		tmp = x * y
	elif (x * y) <= -1.46e+184:
		tmp = t_1
	elif (x * y) <= -2.2e+146:
		tmp = x * y
	elif (x * y) <= -1.25e-144:
		tmp = t_2
	elif (x * y) <= -3.8e-287:
		tmp = t_3
	elif (x * y) <= 2e-147:
		tmp = t_2
	elif (x * y) <= 6e+157:
		tmp = t_3
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(c + t_1)
	t_3 = Float64(c + Float64(a * Float64(b * -0.25)))
	tmp = 0.0
	if (Float64(x * y) <= -8.5e+204)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.46e+184)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.2e+146)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.25e-144)
		tmp = t_2;
	elseif (Float64(x * y) <= -3.8e-287)
		tmp = t_3;
	elseif (Float64(x * y) <= 2e-147)
		tmp = t_2;
	elseif (Float64(x * y) <= 6e+157)
		tmp = t_3;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = c + t_1;
	t_3 = c + (a * (b * -0.25));
	tmp = 0.0;
	if ((x * y) <= -8.5e+204)
		tmp = x * y;
	elseif ((x * y) <= -1.46e+184)
		tmp = t_1;
	elseif ((x * y) <= -2.2e+146)
		tmp = x * y;
	elseif ((x * y) <= -1.25e-144)
		tmp = t_2;
	elseif ((x * y) <= -3.8e-287)
		tmp = t_3;
	elseif ((x * y) <= 2e-147)
		tmp = t_2;
	elseif ((x * y) <= 6e+157)
		tmp = t_3;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.5e+204], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.46e+184], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.2e+146], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.25e-144], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], -3.8e-287], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 2e-147], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 6e+157], t$95$3, N[(x * y), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -8.5e204 or -1.46e184 < (*.f64 x y) < -2.1999999999999998e146 or 6.00000000000000021e157 < (*.f64 x y)

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 85.3%

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

   if -8.5e204 < (*.f64 x y) < -1.46e184

   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 z around inf 100.0%

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

   if -2.1999999999999998e146 < (*.f64 x y) < -1.2499999999999999e-144 or -3.79999999999999982e-287 < (*.f64 x y) < 1.9999999999999999e-147

   1. Initial program 98.1%

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

   3. Taylor expanded in z around inf 68.2%

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

   if -1.2499999999999999e-144 < (*.f64 x y) < -3.79999999999999982e-287 or 1.9999999999999999e-147 < (*.f64 x y) < 6.00000000000000021e157

   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 68.9%

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

      1. metadata-eval 68.9%

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

      2. distribute-lft-neg-in 68.9%

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

      3. *-commutative 68.9%

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

      4. associate-*r* 68.9%

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

      5. *-commutative 68.9%

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

      6. distribute-rgt-neg-in 68.9%

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

      7. *-commutative 68.9%

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

      8. distribute-rgt-neg-in 68.9%

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

      9. metadata-eval 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.46 \cdot 10^{+184}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-144}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -3.8 \cdot 10^{-287}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-147}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 6 \cdot 10^{+157}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := c + t\_2\\ t_4 := x \cdot y + t\_2\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+144}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-144}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-158}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* a (* b -0.25))))
        (t_2 (* 0.0625 (* z t)))
        (t_3 (+ c t_2))
        (t_4 (+ (* x y) t_2)))
   (if (<= (* x y) -1e+144)
     t_4
     (if (<= (* x y) -1e-144)
       t_3
       (if (<= (* x y) -5e-287)
         t_1
         (if (<= (* x y) 2e-158) t_3 (if (<= (* x y) 5e+156) t_1 t_4)))))))

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 = 0.0625 * (z * t);
	double t_3 = c + t_2;
	double t_4 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1e+144) {
		tmp = t_4;
	} else if ((x * y) <= -1e-144) {
		tmp = t_3;
	} else if ((x * y) <= -5e-287) {
		tmp = t_1;
	} else if ((x * y) <= 2e-158) {
		tmp = t_3;
	} else if ((x * y) <= 5e+156) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	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 = c + (a * (b * (-0.25d0)))
    t_2 = 0.0625d0 * (z * t)
    t_3 = c + t_2
    t_4 = (x * y) + t_2
    if ((x * y) <= (-1d+144)) then
        tmp = t_4
    else if ((x * y) <= (-1d-144)) then
        tmp = t_3
    else if ((x * y) <= (-5d-287)) then
        tmp = t_1
    else if ((x * y) <= 2d-158) then
        tmp = t_3
    else if ((x * y) <= 5d+156) then
        tmp = t_1
    else
        tmp = t_4
    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 = 0.0625 * (z * t);
	double t_3 = c + t_2;
	double t_4 = (x * y) + t_2;
	double tmp;
	if ((x * y) <= -1e+144) {
		tmp = t_4;
	} else if ((x * y) <= -1e-144) {
		tmp = t_3;
	} else if ((x * y) <= -5e-287) {
		tmp = t_1;
	} else if ((x * y) <= 2e-158) {
		tmp = t_3;
	} else if ((x * y) <= 5e+156) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (a * (b * -0.25))
	t_2 = 0.0625 * (z * t)
	t_3 = c + t_2
	t_4 = (x * y) + t_2
	tmp = 0
	if (x * y) <= -1e+144:
		tmp = t_4
	elif (x * y) <= -1e-144:
		tmp = t_3
	elif (x * y) <= -5e-287:
		tmp = t_1
	elif (x * y) <= 2e-158:
		tmp = t_3
	elif (x * y) <= 5e+156:
		tmp = t_1
	else:
		tmp = t_4
	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(0.0625 * Float64(z * t))
	t_3 = Float64(c + t_2)
	t_4 = Float64(Float64(x * y) + t_2)
	tmp = 0.0
	if (Float64(x * y) <= -1e+144)
		tmp = t_4;
	elseif (Float64(x * y) <= -1e-144)
		tmp = t_3;
	elseif (Float64(x * y) <= -5e-287)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-158)
		tmp = t_3;
	elseif (Float64(x * y) <= 5e+156)
		tmp = t_1;
	else
		tmp = t_4;
	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 = 0.0625 * (z * t);
	t_3 = c + t_2;
	t_4 = (x * y) + t_2;
	tmp = 0.0;
	if ((x * y) <= -1e+144)
		tmp = t_4;
	elseif ((x * y) <= -1e-144)
		tmp = t_3;
	elseif ((x * y) <= -5e-287)
		tmp = t_1;
	elseif ((x * y) <= 2e-158)
		tmp = t_3;
	elseif ((x * y) <= 5e+156)
		tmp = t_1;
	else
		tmp = t_4;
	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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+144], t$95$4, If[LessEqual[N[(x * y), $MachinePrecision], -1e-144], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -5e-287], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-158], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], 5e+156], t$95$1, t$95$4]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.00000000000000002e144 or 4.99999999999999992e156 < (*.f64 x y)

   1. Initial program 95.0%

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

   3. Taylor expanded in a around 0 91.7%

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

   4. Taylor expanded in c around 0 91.7%

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

   if -1.00000000000000002e144 < (*.f64 x y) < -9.9999999999999995e-145 or -5.00000000000000025e-287 < (*.f64 x y) < 2.00000000000000013e-158

   1. Initial program 98.0%

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

   3. Taylor expanded in z around inf 68.5%

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

   if -9.9999999999999995e-145 < (*.f64 x y) < -5.00000000000000025e-287 or 2.00000000000000013e-158 < (*.f64 x y) < 4.99999999999999992e156

   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 68.9%

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

      1. metadata-eval 68.9%

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

      2. distribute-lft-neg-in 68.9%

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

      3. *-commutative 68.9%

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

      4. associate-*r* 68.9%

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

      5. *-commutative 68.9%

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

      6. distribute-rgt-neg-in 68.9%

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

      7. *-commutative 68.9%

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

      8. distribute-rgt-neg-in 68.9%

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

      9. metadata-eval 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+144}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-144}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-287}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-158}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+156}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 44.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.45 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -2.95 \cdot 10^{+54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 8.4 \cdot 10^{+130}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -8.5e+204)
     (* x y)
     (if (<= (* x y) -1.45e+184)
       t_1
       (if (<= (* x y) -2.95e+54)
         (* x y)
         (if (<= (* x y) -3.6e-146)
           t_1
           (if (<= (* x y) 8.4e+130) (* (* a b) -0.25) (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -8.5e+204) {
		tmp = x * y;
	} else if ((x * y) <= -1.45e+184) {
		tmp = t_1;
	} else if ((x * y) <= -2.95e+54) {
		tmp = x * y;
	} else if ((x * y) <= -3.6e-146) {
		tmp = t_1;
	} else if ((x * y) <= 8.4e+130) {
		tmp = (a * b) * -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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((x * y) <= (-8.5d+204)) then
        tmp = x * y
    else if ((x * y) <= (-1.45d+184)) then
        tmp = t_1
    else if ((x * y) <= (-2.95d+54)) then
        tmp = x * y
    else if ((x * y) <= (-3.6d-146)) then
        tmp = t_1
    else if ((x * y) <= 8.4d+130) then
        tmp = (a * b) * (-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 t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -8.5e+204) {
		tmp = x * y;
	} else if ((x * y) <= -1.45e+184) {
		tmp = t_1;
	} else if ((x * y) <= -2.95e+54) {
		tmp = x * y;
	} else if ((x * y) <= -3.6e-146) {
		tmp = t_1;
	} else if ((x * y) <= 8.4e+130) {
		tmp = (a * b) * -0.25;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (x * y) <= -8.5e+204:
		tmp = x * y
	elif (x * y) <= -1.45e+184:
		tmp = t_1
	elif (x * y) <= -2.95e+54:
		tmp = x * y
	elif (x * y) <= -3.6e-146:
		tmp = t_1
	elif (x * y) <= 8.4e+130:
		tmp = (a * b) * -0.25
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -8.5e+204)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.45e+184)
		tmp = t_1;
	elseif (Float64(x * y) <= -2.95e+54)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -3.6e-146)
		tmp = t_1;
	elseif (Float64(x * y) <= 8.4e+130)
		tmp = Float64(Float64(a * b) * -0.25);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -8.5e+204)
		tmp = x * y;
	elseif ((x * y) <= -1.45e+184)
		tmp = t_1;
	elseif ((x * y) <= -2.95e+54)
		tmp = x * y;
	elseif ((x * y) <= -3.6e-146)
		tmp = t_1;
	elseif ((x * y) <= 8.4e+130)
		tmp = (a * b) * -0.25;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -8.5e+204], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.45e+184], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2.95e+54], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -3.6e-146], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 8.4e+130], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -8.5e204 or -1.4499999999999999e184 < (*.f64 x y) < -2.9499999999999999e54 or 8.39999999999999962e130 < (*.f64 x y)

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 72.6%

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

   if -8.5e204 < (*.f64 x y) < -1.4499999999999999e184 or -2.9499999999999999e54 < (*.f64 x y) < -3.59999999999999978e-146

   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 z around inf 53.9%

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

   if -3.59999999999999978e-146 < (*.f64 x y) < 8.39999999999999962e130

   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 a around inf 39.5%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -8.5 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.45 \cdot 10^{+184}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -2.95 \cdot 10^{+54}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 8.4 \cdot 10^{+130}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.2% accurate, 0.5× speedup

Math

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

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) (+ t_1 c) (* x (- y (* -0.0625 (* t (/ z x))))))))

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 = t_1 + c;
	} else {
		tmp = x * (y - (-0.0625 * (t * (z / x))));
	}
	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 = t_1 + c;
	} else {
		tmp = x * (y - (-0.0625 * (t * (z / x))));
	}
	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 = t_1 + c
	else:
		tmp = x * (y - (-0.0625 * (t * (z / x))))
	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(t_1 + c);
	else
		tmp = Float64(x * Float64(y - Float64(-0.0625 * Float64(t * Float64(z / x)))));
	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 = t_1 + c;
	else
		tmp = x * (y - (-0.0625 * (t * (z / x))));
	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[(t$95$1 + c), $MachinePrecision], N[(x * N[(y - N[(-0.0625 * N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $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 100.0%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   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 a around 0 83.3%

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

   4. Taylor expanded in c around 0 83.3%

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

   5. Taylor expanded in x around -inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right)} \]

      2. mul-1-neg 100.0%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right) \]

      3. neg-mul-1 100.0%

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

      4. +-commutative 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 6: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -9.4 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.8 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{+146} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+158}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -9.4e+204)
     (* x y)
     (if (<= (* x y) -4.8e+183)
       t_1
       (if (or (<= (* x y) -3.3e+146) (not (<= (* x y) 4.8e+158)))
         (* x y)
         (+ c t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -9.4e+204) {
		tmp = x * y;
	} else if ((x * y) <= -4.8e+183) {
		tmp = t_1;
	} else if (((x * y) <= -3.3e+146) || !((x * y) <= 4.8e+158)) {
		tmp = x * y;
	} else {
		tmp = c + 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 = 0.0625d0 * (z * t)
    if ((x * y) <= (-9.4d+204)) then
        tmp = x * y
    else if ((x * y) <= (-4.8d+183)) then
        tmp = t_1
    else if (((x * y) <= (-3.3d+146)) .or. (.not. ((x * y) <= 4.8d+158))) then
        tmp = x * y
    else
        tmp = c + 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 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -9.4e+204) {
		tmp = x * y;
	} else if ((x * y) <= -4.8e+183) {
		tmp = t_1;
	} else if (((x * y) <= -3.3e+146) || !((x * y) <= 4.8e+158)) {
		tmp = x * y;
	} else {
		tmp = c + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (x * y) <= -9.4e+204:
		tmp = x * y
	elif (x * y) <= -4.8e+183:
		tmp = t_1
	elif ((x * y) <= -3.3e+146) or not ((x * y) <= 4.8e+158):
		tmp = x * y
	else:
		tmp = c + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -9.4e+204)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4.8e+183)
		tmp = t_1;
	elseif ((Float64(x * y) <= -3.3e+146) || !(Float64(x * y) <= 4.8e+158))
		tmp = Float64(x * y);
	else
		tmp = Float64(c + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -9.4e+204)
		tmp = x * y;
	elseif ((x * y) <= -4.8e+183)
		tmp = t_1;
	elseif (((x * y) <= -3.3e+146) || ~(((x * y) <= 4.8e+158)))
		tmp = x * y;
	else
		tmp = c + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -9.4e+204], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4.8e+183], t$95$1, If[Or[LessEqual[N[(x * y), $MachinePrecision], -3.3e+146], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.8e+158]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(c + t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.4000000000000003e204 or -4.8000000000000003e183 < (*.f64 x y) < -3.30000000000000016e146 or 4.80000000000000016e158 < (*.f64 x y)

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 85.3%

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

   if -9.4000000000000003e204 < (*.f64 x y) < -4.8000000000000003e183

   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 z around inf 100.0%

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

   if -3.30000000000000016e146 < (*.f64 x y) < 4.80000000000000016e158

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 61.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -9.4 \cdot 10^{+204}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4.8 \cdot 10^{+183}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq -3.3 \cdot 10^{+146} \lor \neg \left(x \cdot y \leq 4.8 \cdot 10^{+158}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+71}:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+156}:\\ \;\;\;\;\left(c + t\_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - -0.0625 \cdot \left(t \cdot \frac{z}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -2e+71)
     (+ c (+ (* x y) t_1))
     (if (<= (* x y) 5e+156)
       (- (+ c t_1) (* (* a b) 0.25))
       (* x (- y (* -0.0625 (* t (/ z x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -2e+71) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 5e+156) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} else {
		tmp = x * (y - (-0.0625 * (t * (z / x))));
	}
	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 = 0.0625d0 * (z * t)
    if ((x * y) <= (-2d+71)) then
        tmp = c + ((x * y) + t_1)
    else if ((x * y) <= 5d+156) then
        tmp = (c + t_1) - ((a * b) * 0.25d0)
    else
        tmp = x * (y - ((-0.0625d0) * (t * (z / x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -2e+71) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 5e+156) {
		tmp = (c + t_1) - ((a * b) * 0.25);
	} else {
		tmp = x * (y - (-0.0625 * (t * (z / x))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (x * y) <= -2e+71:
		tmp = c + ((x * y) + t_1)
	elif (x * y) <= 5e+156:
		tmp = (c + t_1) - ((a * b) * 0.25)
	else:
		tmp = x * (y - (-0.0625 * (t * (z / x))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(x * y) <= -2e+71)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	elseif (Float64(x * y) <= 5e+156)
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(x * Float64(y - Float64(-0.0625 * Float64(t * Float64(z / x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -2e+71)
		tmp = c + ((x * y) + t_1);
	elseif ((x * y) <= 5e+156)
		tmp = (c + t_1) - ((a * b) * 0.25);
	else
		tmp = x * (y - (-0.0625 * (t * (z / x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+71], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+156], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(x * N[(y - N[(-0.0625 * N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e71

   1. Initial program 95.9%

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

   3. Taylor expanded in a around 0 92.3%

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

   if -2.0000000000000001e71 < (*.f64 x y) < 4.99999999999999992e156

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 94.8%

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

   if 4.99999999999999992e156 < (*.f64 x y)

   1. Initial program 93.0%

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

   3. Taylor expanded in a around 0 88.8%

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

   4. Taylor expanded in c around 0 88.8%

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

   5. Taylor expanded in x around -inf 91.1%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 91.1%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right)} \]

      2. mul-1-neg 91.1%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(-1 \cdot y + -0.0625 \cdot \frac{t \cdot z}{x}\right) \]

      3. neg-mul-1 91.1%

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

      4. +-commutative 91.1%

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

      5. unsub-neg 91.1%

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

      6. associate-/l* 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+71}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+156}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y - -0.0625 \cdot \left(t \cdot \frac{z}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+132} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -5e+132) (not (<= (* a b) 2e+147)))
   (- (* x y) (* (* a b) 0.25))
   (+ c (+ (* x y) (* 0.0625 (* z t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+132) || !((a * b) <= 2e+147)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((a * b) <= (-5d+132)) .or. (.not. ((a * b) <= 2d+147))) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((a * b) <= -5e+132) || !((a * b) <= 2e+147)) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((a * b) <= -5e+132) or not ((a * b) <= 2e+147):
		tmp = (x * y) - ((a * b) * 0.25)
	else:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(a * b) <= -5e+132) || !(Float64(a * b) <= 2e+147))
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	else
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((a * b) <= -5e+132) || ~(((a * b) <= 2e+147)))
		tmp = (x * y) - ((a * b) * 0.25);
	else
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(a * b), $MachinePrecision], -5e+132], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+147]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -5.0000000000000001e132 or 2e147 < (*.f64 a b)

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 81.1%

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

   4. Taylor expanded in c around 0 78.9%

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

   if -5.0000000000000001e132 < (*.f64 a b) < 2e147

   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 0 94.1%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+132} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+147}\right):\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+76}:\\ \;\;\;\;\left(x \cdot y + c\right) - t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+148}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+76)
     (- (+ (* x y) c) t_1)
     (if (<= (* a b) 5e+148) (+ c (+ (* x y) t_2)) (- t_2 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 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+76) {
		tmp = ((x * y) + c) - t_1;
	} else if ((a * b) <= 5e+148) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+76)) then
        tmp = ((x * y) + c) - t_1
    else if ((a * b) <= 5d+148) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = t_2 - 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 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+76) {
		tmp = ((x * y) + c) - t_1;
	} else if ((a * b) <= 5e+148) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+76:
		tmp = ((x * y) + c) - t_1
	elif (a * b) <= 5e+148:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = t_2 - 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(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+76)
		tmp = Float64(Float64(Float64(x * y) + c) - t_1);
	elseif (Float64(a * b) <= 5e+148)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(t_2 - 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 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+76)
		tmp = ((x * y) + c) - t_1;
	elseif ((a * b) <= 5e+148)
		tmp = c + ((x * y) + t_2);
	else
		tmp = t_2 - 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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+76], N[(N[(N[(x * y), $MachinePrecision] + c), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+148], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.99999999999999991e76

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 79.0%

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

   if -4.99999999999999991e76 < (*.f64 a b) < 5.00000000000000024e148

   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 0 95.1%

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

   if 5.00000000000000024e148 < (*.f64 a b)

   1. Initial program 94.2%

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

   3. Taylor expanded in x around 0 86.6%

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

   4. Taylor expanded in c around 0 84.8%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+76}:\\ \;\;\;\;\left(x \cdot y + c\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+148}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a \cdot b\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y - t\_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+148}:\\ \;\;\;\;c + \left(x \cdot y + t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* a b) 0.25)) (t_2 (* 0.0625 (* z t))))
   (if (<= (* a b) -5e+132)
     (- (* x y) t_1)
     (if (<= (* a b) 5e+148) (+ c (+ (* x y) t_2)) (- t_2 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 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+132) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 5e+148) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * b) * 0.25d0
    t_2 = 0.0625d0 * (z * t)
    if ((a * b) <= (-5d+132)) then
        tmp = (x * y) - t_1
    else if ((a * b) <= 5d+148) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = t_2 - 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 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -5e+132) {
		tmp = (x * y) - t_1;
	} else if ((a * b) <= 5e+148) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) * 0.25
	t_2 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -5e+132:
		tmp = (x * y) - t_1
	elif (a * b) <= 5e+148:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = t_2 - 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(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(a * b) <= -5e+132)
		tmp = Float64(Float64(x * y) - t_1);
	elseif (Float64(a * b) <= 5e+148)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(t_2 - 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 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((a * b) <= -5e+132)
		tmp = (x * y) - t_1;
	elseif ((a * b) <= 5e+148)
		tmp = c + ((x * y) + t_2);
	else
		tmp = t_2 - 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[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -5e+132], N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+148], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.0000000000000001e132

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 78.1%

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

   4. Taylor expanded in c around 0 75.2%

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

   if -5.0000000000000001e132 < (*.f64 a b) < 5.00000000000000024e148

   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 0 94.1%

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

   if 5.00000000000000024e148 < (*.f64 a b)

   1. Initial program 94.2%

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

   3. Taylor expanded in x around 0 86.6%

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

   4. Taylor expanded in c around 0 84.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -5 \cdot 10^{+132}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+148}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+70} \lor \neg \left(x \cdot y \leq 4.5 \cdot 10^{+129}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.1e+70) (not (<= (* x y) 4.5e+129)))
   (* 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 (((x * y) <= -2.1e+70) || !((x * y) <= 4.5e+129)) {
		tmp = x * y;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((x * y) <= (-2.1d+70)) .or. (.not. ((x * y) <= 4.5d+129))) then
        tmp = x * y
    else
        tmp = (a * b) * (-0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((x * y) <= -2.1e+70) || !((x * y) <= 4.5e+129)) {
		tmp = x * y;
	} else {
		tmp = (a * b) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.1e+70) or not ((x * y) <= 4.5e+129):
		tmp = x * y
	else:
		tmp = (a * b) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2.1e+70) || !(Float64(x * y) <= 4.5e+129))
		tmp = Float64(x * y);
	else
		tmp = Float64(Float64(a * b) * -0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -2.1e+70) || ~(((x * y) <= 4.5e+129)))
		tmp = x * y;
	else
		tmp = (a * b) * -0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2.1e+70], N[Not[LessEqual[N[(x * y), $MachinePrecision], 4.5e+129]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.10000000000000008e70 or 4.5000000000000001e129 < (*.f64 x y)

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf 70.4%

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

   if -2.10000000000000008e70 < (*.f64 x y) < 4.5000000000000001e129

   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 a around inf 36.1%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{+70} \lor \neg \left(x \cdot y \leq 4.5 \cdot 10^{+129}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.02 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq 5.2 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2.02e+145) (not (<= (* x y) 5.2e+84))) (* 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) <= -2.02e+145) || !((x * y) <= 5.2e+84)) {
		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) <= (-2.02d+145)) .or. (.not. ((x * y) <= 5.2d+84))) 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) <= -2.02e+145) || !((x * y) <= 5.2e+84)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2.02e+145) or not ((x * y) <= 5.2e+84):
		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) <= -2.02e+145) || !(Float64(x * y) <= 5.2e+84))
		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) <= -2.02e+145) || ~(((x * y) <= 5.2e+84)))
		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], -2.02e+145], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5.2e+84]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.01999999999999996e145 or 5.2000000000000002e84 < (*.f64 x y)

   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 x around inf 71.0%

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

   if -2.01999999999999996e145 < (*.f64 x y) < 5.2000000000000002e84

   1. Initial program 98.7%

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

   3. Taylor expanded in c around inf 29.7%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2.02 \cdot 10^{+145} \lor \neg \left(x \cdot y \leq 5.2 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 97.6%

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

3. Taylor expanded in c around inf 20.7%

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

Reproduce

herbie shell --seed 2024097 
(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))