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

Percentage Accurate: 97.5% → 98.4%

Time: 12.6s

Alternatives: 14

Speedup: 0.5×

• 32.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 0.5× speedup

Math

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

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 (* x y)))))

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 + (x * y);
	}
	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 + (x * y);
	}
	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 + (x * y)
	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(x * y));
	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 + (x * y);
	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[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in a around 0 16.7%

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

   4. Taylor expanded in t around 0 68.3%

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

4. Final simplification 99.2%

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

Alternative 2: 98.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-+l- 97.6%

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

   2. associate--l+ 97.6%

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

   3. fma-def 97.6%

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

   4. associate-*l/ 97.6%

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

   5. fma-neg 98.0%

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

   6. sub-neg 98.0%

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

   7. distribute-neg-in 98.0%

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

   8. remove-double-neg 98.0%

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

   9. associate-/l* 98.4%

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

   10. distribute-frac-neg 98.4%

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

   11. associate-/r/ 98.4%

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

   12. fma-def 98.4%

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

   13. neg-mul-1 98.4%

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

   14. *-commutative 98.4%

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

   15. associate-/l* 98.4%

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

   16. metadata-eval 98.4%

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

3. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 3: 98.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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. Step-by-step derivation

   1. associate-+l- 97.6%

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

   2. *-commutative 97.6%

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

   3. associate-+l- 97.6%

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

   4. fma-def 97.6%

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

   5. *-commutative 97.6%

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

   6. associate-/l* 97.6%

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

   7. associate-/l* 97.9%

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

3. Simplified 97.9%

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

5. Final simplification 97.9%

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

Alternative 4: 41.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;x \cdot y \leq -0.0125:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{+212}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= (* x y) -0.0125)
     (* x y)
     (if (<= (* x y) -1.25e-154)
       t_1
       (if (<= (* x y) 1.4e-89)
         c
         (if (<= (* x y) 4.8e+123)
           t_1
           (if (<= (* x y) 1.25e+212) c (* x y))))))))

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) <= -0.0125) {
		tmp = x * y;
	} else if ((x * y) <= -1.25e-154) {
		tmp = t_1;
	} else if ((x * y) <= 1.4e-89) {
		tmp = c;
	} else if ((x * y) <= 4.8e+123) {
		tmp = t_1;
	} else if ((x * y) <= 1.25e+212) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * (-0.25d0))
    if ((x * y) <= (-0.0125d0)) then
        tmp = x * y
    else if ((x * y) <= (-1.25d-154)) then
        tmp = t_1
    else if ((x * y) <= 1.4d-89) then
        tmp = c
    else if ((x * y) <= 4.8d+123) then
        tmp = t_1
    else if ((x * y) <= 1.25d+212) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if ((x * y) <= -0.0125) {
		tmp = x * y;
	} else if ((x * y) <= -1.25e-154) {
		tmp = t_1;
	} else if ((x * y) <= 1.4e-89) {
		tmp = c;
	} else if ((x * y) <= 4.8e+123) {
		tmp = t_1;
	} else if ((x * y) <= 1.25e+212) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if (x * y) <= -0.0125:
		tmp = x * y
	elif (x * y) <= -1.25e-154:
		tmp = t_1
	elif (x * y) <= 1.4e-89:
		tmp = c
	elif (x * y) <= 4.8e+123:
		tmp = t_1
	elif (x * y) <= 1.25e+212:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (Float64(x * y) <= -0.0125)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -1.25e-154)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.4e-89)
		tmp = c;
	elseif (Float64(x * y) <= 4.8e+123)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.25e+212)
		tmp = c;
	else
		tmp = Float64(x * y);
	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) <= -0.0125)
		tmp = x * y;
	elseif ((x * y) <= -1.25e-154)
		tmp = t_1;
	elseif ((x * y) <= 1.4e-89)
		tmp = c;
	elseif ((x * y) <= 4.8e+123)
		tmp = t_1;
	elseif ((x * y) <= 1.25e+212)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -0.0125], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1.25e-154], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.4e-89], c, If[LessEqual[N[(x * y), $MachinePrecision], 4.8e+123], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.25e+212], c, N[(x * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.012500000000000001 or 1.24999999999999998e212 < (*.f64 x y)

   1. Initial program 93.8%

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

   3. Taylor expanded in a around 0 84.0%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in c around 0 60.0%

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

   if -0.012500000000000001 < (*.f64 x y) < -1.25000000000000005e-154 or 1.3999999999999999e-89 < (*.f64 x y) < 4.79999999999999978e123

   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 x around 0 89.9%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 89.9%

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

      2. sub-neg 89.9%

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

      3. +-commutative 89.9%

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

      4. associate-+r+ 89.9%

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

      5. +-commutative 89.9%

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

      6. distribute-lft-neg-in 89.9%

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

      7. metadata-eval 89.9%

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

      8. associate-*r* 89.9%

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

      9. *-commutative 89.9%

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

      10. fma-udef 89.9%

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

      11. *-commutative 89.9%

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

      12. *-commutative 89.9%

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

      13. associate-*r* 89.9%

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

      14. +-commutative 89.9%

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

      15. fma-def 91.3%

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

      16. *-commutative 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in a around inf 47.2%

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

      1. associate-*r* 47.2%

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

      2. *-commutative 47.2%

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

      3. associate-*l* 47.2%

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

   8. Simplified 47.2%

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

   if -1.25000000000000005e-154 < (*.f64 x y) < 1.3999999999999999e-89 or 4.79999999999999978e123 < (*.f64 x y) < 1.24999999999999998e212

   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 50.6%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0125:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.25 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.4 \cdot 10^{-89}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 4.8 \cdot 10^{+123}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{+212}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -0.42:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 4800000:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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) -0.42)
     t_2
     (if (<= (* x y) 8.8e-229)
       t_1
       (if (<= (* x y) 4800000.0)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* x y) 5.8e+176) 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) <= -0.42) {
		tmp = t_2;
	} else if ((x * y) <= 8.8e-229) {
		tmp = t_1;
	} else if ((x * y) <= 4800000.0) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 5.8e+176) {
		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) <= (-0.42d0)) then
        tmp = t_2
    else if ((x * y) <= 8.8d-229) then
        tmp = t_1
    else if ((x * y) <= 4800000.0d0) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 5.8d+176) 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) <= -0.42) {
		tmp = t_2;
	} else if ((x * y) <= 8.8e-229) {
		tmp = t_1;
	} else if ((x * y) <= 4800000.0) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 5.8e+176) {
		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) <= -0.42:
		tmp = t_2
	elif (x * y) <= 8.8e-229:
		tmp = t_1
	elif (x * y) <= 4800000.0:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 5.8e+176:
		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) <= -0.42)
		tmp = t_2;
	elseif (Float64(x * y) <= 8.8e-229)
		tmp = t_1;
	elseif (Float64(x * y) <= 4800000.0)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 5.8e+176)
		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) <= -0.42)
		tmp = t_2;
	elseif ((x * y) <= 8.8e-229)
		tmp = t_1;
	elseif ((x * y) <= 4800000.0)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 5.8e+176)
		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], -0.42], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 8.8e-229], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4800000.0], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.8e+176], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.419999999999999984 or 5.8000000000000003e176 < (*.f64 x y)

   1. Initial program 94.0%

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

   3. Taylor expanded in a around 0 84.7%

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

   4. Taylor expanded in t around 0 73.5%

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

   if -0.419999999999999984 < (*.f64 x y) < 8.7999999999999996e-229 or 4.8e6 < (*.f64 x y) < 5.8000000000000003e176

   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 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*r* 73.4%

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

   5. Simplified 73.4%

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

   if 8.7999999999999996e-229 < (*.f64 x y) < 4.8e6

   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 x around 0 88.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 88.8%

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

      2. sub-neg 88.8%

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

      3. +-commutative 88.8%

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

      4. associate-+r+ 88.8%

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

      5. +-commutative 88.8%

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

      6. distribute-lft-neg-in 88.8%

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

      7. metadata-eval 88.8%

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

      8. associate-*r* 88.8%

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

      9. *-commutative 88.8%

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

      10. fma-udef 88.8%

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

      11. *-commutative 88.8%

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

      12. *-commutative 88.8%

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

      13. associate-*r* 88.8%

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

      14. +-commutative 88.8%

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

      15. fma-def 90.8%

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

      16. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in a around 0 70.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.42:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 8.8 \cdot 10^{-229}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 4800000:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 5.8 \cdot 10^{+176}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -260000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-229}:\\ \;\;\;\;c - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 1600000:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{+165}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -260000.0)
     t_1
     (if (<= (* x y) 1.55e-229)
       (- c (* (* a b) 0.25))
       (if (<= (* x y) 1600000.0)
         (+ c (* 0.0625 (* z t)))
         (if (<= (* x y) 7.6e+165) (+ c (* a (* b -0.25))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -260000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e-229) {
		tmp = c - ((a * b) * 0.25);
	} else if ((x * y) <= 1600000.0) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 7.6e+165) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if ((x * y) <= (-260000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 1.55d-229) then
        tmp = c - ((a * b) * 0.25d0)
    else if ((x * y) <= 1600000.0d0) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 7.6d+165) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -260000.0) {
		tmp = t_1;
	} else if ((x * y) <= 1.55e-229) {
		tmp = c - ((a * b) * 0.25);
	} else if ((x * y) <= 1600000.0) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 7.6e+165) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -260000.0:
		tmp = t_1
	elif (x * y) <= 1.55e-229:
		tmp = c - ((a * b) * 0.25)
	elif (x * y) <= 1600000.0:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 7.6e+165:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -260000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 1.55e-229)
		tmp = Float64(c - Float64(Float64(a * b) * 0.25));
	elseif (Float64(x * y) <= 1600000.0)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 7.6e+165)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -260000.0)
		tmp = t_1;
	elseif ((x * y) <= 1.55e-229)
		tmp = c - ((a * b) * 0.25);
	elseif ((x * y) <= 1600000.0)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 7.6e+165)
		tmp = c + (a * (b * -0.25));
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(x * y), $MachinePrecision], -260000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1.55e-229], N[(c - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1600000.0], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 7.6e+165], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -2.6e5 or 7.59999999999999981e165 < (*.f64 x y)

   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 a around 0 85.1%

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

   4. Taylor expanded in t around 0 73.9%

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

   if -2.6e5 < (*.f64 x y) < 1.55e-229

   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 x around 0 100.0%

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

   4. Taylor expanded in t around 0 72.5%

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

   if 1.55e-229 < (*.f64 x y) < 1.6e6

   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 x around 0 88.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 88.8%

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

      2. sub-neg 88.8%

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

      3. +-commutative 88.8%

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

      4. associate-+r+ 88.8%

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

      5. +-commutative 88.8%

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

      6. distribute-lft-neg-in 88.8%

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

      7. metadata-eval 88.8%

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

      8. associate-*r* 88.8%

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

      9. *-commutative 88.8%

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

      10. fma-udef 88.8%

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

      11. *-commutative 88.8%

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

      12. *-commutative 88.8%

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

      13. associate-*r* 88.8%

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

      14. +-commutative 88.8%

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

      15. fma-def 90.8%

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

      16. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in a around 0 70.6%

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

   if 1.6e6 < (*.f64 x y) < 7.59999999999999981e165

   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 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*r* 74.4%

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

   5. Simplified 74.4%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -260000:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 1.55 \cdot 10^{-229}:\\ \;\;\;\;c - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 1600000:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 7.6 \cdot 10^{+165}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -750000000:\\ \;\;\;\;x \cdot y + t\_1\\ \mathbf{elif}\;x \cdot y \leq 2.45 \cdot 10^{-224}:\\ \;\;\;\;c - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 16200000:\\ \;\;\;\;c + t\_1\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+166}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -750000000.0)
     (+ (* x y) t_1)
     (if (<= (* x y) 2.45e-224)
       (- c (* (* a b) 0.25))
       (if (<= (* x y) 16200000.0)
         (+ c t_1)
         (if (<= (* x y) 3.5e+166) (+ c (* a (* b -0.25))) (+ c (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -750000000.0) {
		tmp = (x * y) + t_1;
	} else if ((x * y) <= 2.45e-224) {
		tmp = c - ((a * b) * 0.25);
	} else if ((x * y) <= 16200000.0) {
		tmp = c + t_1;
	} else if ((x * y) <= 3.5e+166) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((x * y) <= (-750000000.0d0)) then
        tmp = (x * y) + t_1
    else if ((x * y) <= 2.45d-224) then
        tmp = c - ((a * b) * 0.25d0)
    else if ((x * y) <= 16200000.0d0) then
        tmp = c + t_1
    else if ((x * y) <= 3.5d+166) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((x * y) <= -750000000.0) {
		tmp = (x * y) + t_1;
	} else if ((x * y) <= 2.45e-224) {
		tmp = c - ((a * b) * 0.25);
	} else if ((x * y) <= 16200000.0) {
		tmp = c + t_1;
	} else if ((x * y) <= 3.5e+166) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = c + (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) <= -750000000.0:
		tmp = (x * y) + t_1
	elif (x * y) <= 2.45e-224:
		tmp = c - ((a * b) * 0.25)
	elif (x * y) <= 16200000.0:
		tmp = c + t_1
	elif (x * y) <= 3.5e+166:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = c + (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) <= -750000000.0)
		tmp = Float64(Float64(x * y) + t_1);
	elseif (Float64(x * y) <= 2.45e-224)
		tmp = Float64(c - Float64(Float64(a * b) * 0.25));
	elseif (Float64(x * y) <= 16200000.0)
		tmp = Float64(c + t_1);
	elseif (Float64(x * y) <= 3.5e+166)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((x * y) <= -750000000.0)
		tmp = (x * y) + t_1;
	elseif ((x * y) <= 2.45e-224)
		tmp = c - ((a * b) * 0.25);
	elseif ((x * y) <= 16200000.0)
		tmp = c + t_1;
	elseif ((x * y) <= 3.5e+166)
		tmp = c + (a * (b * -0.25));
	else
		tmp = c + (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], -750000000.0], N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.45e-224], N[(c - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 16200000.0], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.5e+166], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -7.5e8

   1. Initial program 92.9%

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

   3. Taylor expanded in a around 0 82.3%

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

   4. Taylor expanded in c around 0 70.0%

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

   if -7.5e8 < (*.f64 x y) < 2.4499999999999998e-224

   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 x around 0 99.6%

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

   4. Taylor expanded in t around 0 72.3%

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

   if 2.4499999999999998e-224 < (*.f64 x y) < 1.62e7

   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 x around 0 88.8%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 88.8%

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

      2. sub-neg 88.8%

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

      3. +-commutative 88.8%

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

      4. associate-+r+ 88.8%

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

      5. +-commutative 88.8%

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

      6. distribute-lft-neg-in 88.8%

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

      7. metadata-eval 88.8%

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

      8. associate-*r* 88.8%

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

      9. *-commutative 88.8%

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

      10. fma-udef 88.8%

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

      11. *-commutative 88.8%

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

      12. *-commutative 88.8%

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

      13. associate-*r* 88.8%

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

      14. +-commutative 88.8%

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

      15. fma-def 90.8%

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

      16. *-commutative 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in a around 0 70.6%

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

   if 1.62e7 < (*.f64 x y) < 3.4999999999999999e166

   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 74.4%

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

      1. *-commutative 74.4%

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

      2. associate-*r* 74.4%

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

   5. Simplified 74.4%

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

   if 3.4999999999999999e166 < (*.f64 x y)

   1. Initial program 96.3%

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

   3. Taylor expanded in a around 0 89.2%

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

   4. Taylor expanded in t around 0 85.3%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -750000000:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 2.45 \cdot 10^{-224}:\\ \;\;\;\;c - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;x \cdot y \leq 16200000:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{+166}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ t_2 := \left(a \cdot b\right) \cdot 0.25\\ \mathbf{if}\;x \cdot y \leq -520000:\\ \;\;\;\;c + \left(x \cdot y + t\_1\right)\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+39}:\\ \;\;\;\;\left(c + t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))) (t_2 (* (* a b) 0.25)))
   (if (<= (* x y) -520000.0)
     (+ c (+ (* x y) t_1))
     (if (<= (* x y) 5.5e+39) (- (+ c t_1) t_2) (- (+ c (* x y)) t_2)))))

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 = (a * b) * 0.25;
	double tmp;
	if ((x * y) <= -520000.0) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 5.5e+39) {
		tmp = (c + t_1) - t_2;
	} else {
		tmp = (c + (x * y)) - 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 = 0.0625d0 * (z * t)
    t_2 = (a * b) * 0.25d0
    if ((x * y) <= (-520000.0d0)) then
        tmp = c + ((x * y) + t_1)
    else if ((x * y) <= 5.5d+39) then
        tmp = (c + t_1) - t_2
    else
        tmp = (c + (x * y)) - 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 = 0.0625 * (z * t);
	double t_2 = (a * b) * 0.25;
	double tmp;
	if ((x * y) <= -520000.0) {
		tmp = c + ((x * y) + t_1);
	} else if ((x * y) <= 5.5e+39) {
		tmp = (c + t_1) - t_2;
	} else {
		tmp = (c + (x * y)) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	t_2 = (a * b) * 0.25
	tmp = 0
	if (x * y) <= -520000.0:
		tmp = c + ((x * y) + t_1)
	elif (x * y) <= 5.5e+39:
		tmp = (c + t_1) - t_2
	else:
		tmp = (c + (x * y)) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	t_2 = Float64(Float64(a * b) * 0.25)
	tmp = 0.0
	if (Float64(x * y) <= -520000.0)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	elseif (Float64(x * y) <= 5.5e+39)
		tmp = Float64(Float64(c + t_1) - t_2);
	else
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	t_2 = (a * b) * 0.25;
	tmp = 0.0;
	if ((x * y) <= -520000.0)
		tmp = c + ((x * y) + t_1);
	elseif ((x * y) <= 5.5e+39)
		tmp = (c + t_1) - t_2;
	else
		tmp = (c + (x * y)) - t_2;
	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[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -520000.0], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5.5e+39], N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.2e5

   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 a around 0 83.2%

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

   if -5.2e5 < (*.f64 x y) < 5.4999999999999997e39

   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 0 95.2%

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

   if 5.4999999999999997e39 < (*.f64 x y)

   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 0 92.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -520000:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5.5 \cdot 10^{+39}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 22000000:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.82 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))))
   (if (<= (* x y) -1.1e+156)
     t_1
     (if (<= (* x y) 22000000.0)
       (+ c (* 0.0625 (* z t)))
       (if (<= (* x y) 1.82e+50) (* a (* b -0.25)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.1e+156) {
		tmp = t_1;
	} else if ((x * y) <= 22000000.0) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 1.82e+50) {
		tmp = a * (b * -0.25);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (x * y)
    if ((x * y) <= (-1.1d+156)) then
        tmp = t_1
    else if ((x * y) <= 22000000.0d0) then
        tmp = c + (0.0625d0 * (z * t))
    else if ((x * y) <= 1.82d+50) then
        tmp = a * (b * (-0.25d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double tmp;
	if ((x * y) <= -1.1e+156) {
		tmp = t_1;
	} else if ((x * y) <= 22000000.0) {
		tmp = c + (0.0625 * (z * t));
	} else if ((x * y) <= 1.82e+50) {
		tmp = a * (b * -0.25);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	tmp = 0
	if (x * y) <= -1.1e+156:
		tmp = t_1
	elif (x * y) <= 22000000.0:
		tmp = c + (0.0625 * (z * t))
	elif (x * y) <= 1.82e+50:
		tmp = a * (b * -0.25)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -1.1e+156)
		tmp = t_1;
	elseif (Float64(x * y) <= 22000000.0)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	elseif (Float64(x * y) <= 1.82e+50)
		tmp = Float64(a * Float64(b * -0.25));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -1.1e+156)
		tmp = t_1;
	elseif ((x * y) <= 22000000.0)
		tmp = c + (0.0625 * (z * t));
	elseif ((x * y) <= 1.82e+50)
		tmp = a * (b * -0.25);
	else
		tmp = t_1;
	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]}, If[LessEqual[N[(x * y), $MachinePrecision], -1.1e+156], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 22000000.0], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1.82e+50], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.10000000000000002e156 or 1.81999999999999997e50 < (*.f64 x y)

   1. Initial program 94.4%

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

   3. Taylor expanded in a around 0 81.4%

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

   4. Taylor expanded in t around 0 73.9%

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

   if -1.10000000000000002e156 < (*.f64 x y) < 2.2e7

   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 0 93.4%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 93.4%

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

      2. sub-neg 93.4%

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

      3. +-commutative 93.4%

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

      4. associate-+r+ 93.4%

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

      5. +-commutative 93.4%

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

      6. distribute-lft-neg-in 93.4%

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

      7. metadata-eval 93.4%

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

      8. associate-*r* 93.4%

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

      9. *-commutative 93.4%

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

      10. fma-udef 93.4%

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

      11. *-commutative 93.4%

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

      12. *-commutative 93.4%

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

      13. associate-*r* 93.4%

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

      14. +-commutative 93.4%

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

      15. fma-def 94.1%

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

      16. *-commutative 94.1%

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

   5. Simplified 94.1%

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

   6. Taylor expanded in a around 0 66.3%

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

   if 2.2e7 < (*.f64 x y) < 1.81999999999999997e50

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 91.9%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 91.9%

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

      2. sub-neg 91.9%

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

      3. +-commutative 91.9%

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

      4. associate-+r+ 91.9%

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

      5. +-commutative 91.9%

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

      6. distribute-lft-neg-in 91.9%

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

      7. metadata-eval 91.9%

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

      8. associate-*r* 91.9%

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

      9. *-commutative 91.9%

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

      10. fma-udef 91.9%

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

      11. *-commutative 91.9%

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

      12. *-commutative 91.9%

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

      13. associate-*r* 91.9%

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

      14. +-commutative 91.9%

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

      15. fma-def 92.0%

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

      16. *-commutative 92.0%

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

   5. Simplified 92.0%

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

   6. Taylor expanded in a around inf 67.8%

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

      1. associate-*r* 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*l* 67.8%

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

   8. Simplified 67.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.1 \cdot 10^{+156}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 22000000:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 1.82 \cdot 10^{+50}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+76} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+19}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* a b) -1e+76) (not (<= (* a b) 2e+19)))
   (- (+ c (* 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) <= -1e+76) || !((a * b) <= 2e+19)) {
		tmp = (c + (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) <= (-1d+76)) .or. (.not. ((a * b) <= 2d+19))) then
        tmp = (c + (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) <= -1e+76) || !((a * b) <= 2e+19)) {
		tmp = (c + (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) <= -1e+76) or not ((a * b) <= 2e+19):
		tmp = (c + (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) <= -1e+76) || !(Float64(a * b) <= 2e+19))
		tmp = Float64(Float64(c + 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) <= -1e+76) || ~(((a * b) <= 2e+19)))
		tmp = (c + (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], -1e+76], N[Not[LessEqual[N[(a * b), $MachinePrecision], 2e+19]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $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) < -1e76 or 2e19 < (*.f64 a b)

   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 z around 0 87.3%

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

   if -1e76 < (*.f64 a b) < 2e19

   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 0 93.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -1 \cdot 10^{+76} \lor \neg \left(a \cdot b \leq 2 \cdot 10^{+19}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+236}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+182)
   (- (* x y) (* (* a b) 0.25))
   (if (<= (* a b) 2e+236)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (+ c (* a (* b -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+182) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+236) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a * b) <= (-2d+182)) then
        tmp = (x * y) - ((a * b) * 0.25d0)
    else if ((a * b) <= 2d+236) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    else
        tmp = c + (a * (b * (-0.25d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -2e+182) {
		tmp = (x * y) - ((a * b) * 0.25);
	} else if ((a * b) <= 2e+236) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = c + (a * (b * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+182:
		tmp = (x * y) - ((a * b) * 0.25)
	elif (a * b) <= 2e+236:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = c + (a * (b * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+182)
		tmp = Float64(Float64(x * y) - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 2e+236)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a * b) <= -2e+182)
		tmp = (x * y) - ((a * b) * 0.25);
	elseif ((a * b) <= 2e+236)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = c + (a * (b * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -2e+182], N[(N[(x * y), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e+236], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e182

   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 z around 0 93.2%

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

   4. Taylor expanded in c around 0 93.2%

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

   if -2.0000000000000001e182 < (*.f64 a b) < 2.00000000000000011e236

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0 88.5%

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

   if 2.00000000000000011e236 < (*.f64 a b)

   1. Initial program 90.5%

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

   3. Taylor expanded in a around inf 95.2%

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

      1. *-commutative 95.2%

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

      2. associate-*r* 95.2%

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

   5. Simplified 95.2%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+182}:\\ \;\;\;\;x \cdot y - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{+236}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -800000000 \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+212}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -800000000.0) (not (<= (* x y) 1.25e+212))) (* 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) <= -800000000.0) || !((x * y) <= 1.25e+212)) {
		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) <= (-800000000.0d0)) .or. (.not. ((x * y) <= 1.25d+212))) 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) <= -800000000.0) || !((x * y) <= 1.25e+212)) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -800000000.0) or not ((x * y) <= 1.25e+212):
		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) <= -800000000.0) || !(Float64(x * y) <= 1.25e+212))
		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) <= -800000000.0) || ~(((x * y) <= 1.25e+212)))
		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], -800000000.0], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1.25e+212]], $MachinePrecision]], N[(x * y), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -8e8 or 1.24999999999999998e212 < (*.f64 x y)

   1. Initial program 93.5%

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

   3. Taylor expanded in a around 0 83.4%

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

   4. Taylor expanded in t around 0 72.2%

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

   5. Taylor expanded in c around 0 62.1%

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

   if -8e8 < (*.f64 x y) < 1.24999999999999998e212

   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 c around inf 37.0%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -800000000 \lor \neg \left(x \cdot y \leq 1.25 \cdot 10^{+212}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+144} \lor \neg \left(a \leq 9.5 \cdot 10^{+17}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= a -1.15e+144) (not (<= a 9.5e+17)))
   (* a (* b -0.25))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.15e+144) || !(a <= 9.5e+17)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((a <= (-1.15d+144)) .or. (.not. (a <= 9.5d+17))) then
        tmp = a * (b * (-0.25d0))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a <= -1.15e+144) || !(a <= 9.5e+17)) {
		tmp = a * (b * -0.25);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a <= -1.15e+144) or not (a <= 9.5e+17):
		tmp = a * (b * -0.25)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((a <= -1.15e+144) || !(a <= 9.5e+17))
		tmp = Float64(a * Float64(b * -0.25));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((a <= -1.15e+144) || ~((a <= 9.5e+17)))
		tmp = a * (b * -0.25);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[a, -1.15e+144], N[Not[LessEqual[a, 9.5e+17]], $MachinePrecision]], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1500000000000001e144 or 9.5e17 < a

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 81.3%

      \[\leadsto \color{blue}{\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - 0.25 \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. associate--l+ 81.3%

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

      2. sub-neg 81.3%

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

      3. +-commutative 81.3%

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

      4. associate-+r+ 81.3%

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

      5. +-commutative 81.3%

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

      6. distribute-lft-neg-in 81.3%

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

      7. metadata-eval 81.3%

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

      8. associate-*r* 81.3%

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

      9. *-commutative 81.3%

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

      10. fma-udef 81.3%

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

      11. *-commutative 81.3%

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

      12. *-commutative 81.3%

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

      13. associate-*r* 81.3%

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

      14. +-commutative 81.3%

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

      15. fma-def 82.4%

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

      16. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in a around inf 41.3%

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

      1. associate-*r* 41.3%

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

      2. *-commutative 41.3%

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

      3. associate-*l* 41.3%

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

   8. Simplified 41.3%

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

   if -1.1500000000000001e144 < a < 9.5e17

   1. Initial program 98.2%

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

   3. Taylor expanded in a around 0 79.6%

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

   4. Taylor expanded in t around 0 57.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+144} \lor \neg \left(a \leq 9.5 \cdot 10^{+17}\right):\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.2% 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 29.4%

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

4. Final simplification 29.4%

   \[\leadsto c \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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))