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

Percentage Accurate: 97.6% → 98.5%

Time: 8.0s

Alternatives: 13

Speedup: 0.5×

• 32.9% 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: 97.6% 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: 98.5% 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%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x around inf 50.4%

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

4. Final simplification 98.4%

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

Alternative 2: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. associate-+l- 96.9%

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

   2. associate--l+ 96.9%

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

   3. fma-def 97.3%

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

   4. associate-*l/ 97.3%

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

   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* 98.0%

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

   10. distribute-frac-neg 98.0%

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

   11. associate-/r/ 98.0%

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

   12. fma-def 98.0%

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

   13. neg-mul-1 98.0%

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

   14. *-commutative 98.0%

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

   15. associate-/l* 98.0%

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

   16. metadata-eval 98.0%

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

3. Simplified 98.0%

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

4. Final simplification 98.0%

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

Alternative 3: 43.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-323}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.55 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -6e-5)
     (* x y)
     (if (<= (* x y) -4e-323)
       t_1
       (if (<= (* x y) 3.5e-196)
         c
         (if (<= (* x y) 2e-186)
           t_1
           (if (<= (* x y) 3.55e-62)
             (* a (* b -0.25))
             (if (<= (* x y) 2.15e+89) t_1 (* 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) <= -6e-5) {
		tmp = x * y;
	} else if ((x * y) <= -4e-323) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e-196) {
		tmp = c;
	} else if ((x * y) <= 2e-186) {
		tmp = t_1;
	} else if ((x * y) <= 3.55e-62) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 2.15e+89) {
		tmp = t_1;
	} 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) <= (-6d-5)) then
        tmp = x * y
    else if ((x * y) <= (-4d-323)) then
        tmp = t_1
    else if ((x * y) <= 3.5d-196) then
        tmp = c
    else if ((x * y) <= 2d-186) then
        tmp = t_1
    else if ((x * y) <= 3.55d-62) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 2.15d+89) then
        tmp = t_1
    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) <= -6e-5) {
		tmp = x * y;
	} else if ((x * y) <= -4e-323) {
		tmp = t_1;
	} else if ((x * y) <= 3.5e-196) {
		tmp = c;
	} else if ((x * y) <= 2e-186) {
		tmp = t_1;
	} else if ((x * y) <= 3.55e-62) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 2.15e+89) {
		tmp = t_1;
	} 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) <= -6e-5:
		tmp = x * y
	elif (x * y) <= -4e-323:
		tmp = t_1
	elif (x * y) <= 3.5e-196:
		tmp = c
	elif (x * y) <= 2e-186:
		tmp = t_1
	elif (x * y) <= 3.55e-62:
		tmp = a * (b * -0.25)
	elif (x * y) <= 2.15e+89:
		tmp = t_1
	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) <= -6e-5)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4e-323)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.5e-196)
		tmp = c;
	elseif (Float64(x * y) <= 2e-186)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.55e-62)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 2.15e+89)
		tmp = t_1;
	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) <= -6e-5)
		tmp = x * y;
	elseif ((x * y) <= -4e-323)
		tmp = t_1;
	elseif ((x * y) <= 3.5e-196)
		tmp = c;
	elseif ((x * y) <= 2e-186)
		tmp = t_1;
	elseif ((x * y) <= 3.55e-62)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 2.15e+89)
		tmp = t_1;
	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], -6e-5], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-323], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.5e-196], c, If[LessEqual[N[(x * y), $MachinePrecision], 2e-186], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.55e-62], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2.15e+89], t$95$1, N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -6.00000000000000015e-5 or 2.1500000000000001e89 < (*.f64 x y)

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. associate--l+ 95.3%

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

      3. fma-def 96.3%

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

      4. associate-*l/ 96.3%

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

      5. fma-neg 96.3%

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

      6. sub-neg 96.3%

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

      7. distribute-neg-in 96.3%

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

      8. remove-double-neg 96.3%

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

      9. associate-/l* 96.3%

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

      10. distribute-frac-neg 96.3%

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

      11. associate-/r/ 96.3%

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

      12. fma-def 96.3%

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

      13. neg-mul-1 96.3%

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

      14. *-commutative 96.3%

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

      15. associate-/l* 96.3%

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

      16. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in a around 0 87.0%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*r* 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in x around inf 63.0%

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

   if -6.00000000000000015e-5 < (*.f64 x y) < -3.95253e-323 or 3.50000000000000004e-196 < (*.f64 x y) < 1.9999999999999998e-186 or 3.5500000000000001e-62 < (*.f64 x y) < 2.1500000000000001e89

   1. Initial program 97.5%

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

      1. associate-+l- 97.5%

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

      2. associate--l+ 97.5%

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

      3. fma-def 97.5%

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

      4. associate-*l/ 97.5%

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

      5. fma-neg 98.8%

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

      6. sub-neg 98.8%

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

      7. distribute-neg-in 98.8%

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

      8. remove-double-neg 98.8%

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

      9. associate-/l* 98.7%

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

      10. distribute-frac-neg 98.7%

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

      11. associate-/r/ 98.8%

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

      12. fma-def 98.8%

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

      13. neg-mul-1 98.8%

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

      14. *-commutative 98.8%

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

      15. associate-/l* 98.8%

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

      16. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in a around 0 73.5%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 73.5%

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

      2. *-commutative 73.5%

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

      3. associate-*r* 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in t around inf 43.1%

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

   if -3.95253e-323 < (*.f64 x y) < 3.50000000000000004e-196

   1. Initial program 97.7%

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

   2. Taylor expanded in c around inf 41.2%

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

   if 1.9999999999999998e-186 < (*.f64 x y) < 3.5500000000000001e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.3%

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

   3. Taylor expanded in a around inf 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-*l* 73.2%

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

   5. Simplified 73.2%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -6 \cdot 10^{-5}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-323}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.5 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-186}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.55 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 2.15 \cdot 10^{+89}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + \left(a \cdot b\right) \cdot -0.25\\ t_3 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -0.000145:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.65 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (+ c (* (* a b) -0.25)))
        (t_3 (+ c (* x y))))
   (if (<= (* x y) -0.000145)
     t_3
     (if (<= (* x y) -1.2e-252)
       t_1
       (if (<= (* x y) 2.65e-62)
         t_2
         (if (<= (* x y) 9e+38) t_1 (if (<= (* x y) 2.8e+62) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + ((a * b) * -0.25);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -0.000145) {
		tmp = t_3;
	} else if ((x * y) <= -1.2e-252) {
		tmp = t_1;
	} else if ((x * y) <= 2.65e-62) {
		tmp = t_2;
	} else if ((x * y) <= 9e+38) {
		tmp = t_1;
	} else if ((x * y) <= 2.8e+62) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = c + ((a * b) * (-0.25d0))
    t_3 = c + (x * y)
    if ((x * y) <= (-0.000145d0)) then
        tmp = t_3
    else if ((x * y) <= (-1.2d-252)) then
        tmp = t_1
    else if ((x * y) <= 2.65d-62) then
        tmp = t_2
    else if ((x * y) <= 9d+38) then
        tmp = t_1
    else if ((x * y) <= 2.8d+62) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + ((a * b) * -0.25);
	double t_3 = c + (x * y);
	double tmp;
	if ((x * y) <= -0.000145) {
		tmp = t_3;
	} else if ((x * y) <= -1.2e-252) {
		tmp = t_1;
	} else if ((x * y) <= 2.65e-62) {
		tmp = t_2;
	} else if ((x * y) <= 9e+38) {
		tmp = t_1;
	} else if ((x * y) <= 2.8e+62) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + ((a * b) * -0.25)
	t_3 = c + (x * y)
	tmp = 0
	if (x * y) <= -0.000145:
		tmp = t_3
	elif (x * y) <= -1.2e-252:
		tmp = t_1
	elif (x * y) <= 2.65e-62:
		tmp = t_2
	elif (x * y) <= 9e+38:
		tmp = t_1
	elif (x * y) <= 2.8e+62:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(Float64(a * b) * -0.25))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -0.000145)
		tmp = t_3;
	elseif (Float64(x * y) <= -1.2e-252)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.65e-62)
		tmp = t_2;
	elseif (Float64(x * y) <= 9e+38)
		tmp = t_1;
	elseif (Float64(x * y) <= 2.8e+62)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (t * (z * 0.0625));
	t_2 = c + ((a * b) * -0.25);
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -0.000145)
		tmp = t_3;
	elseif ((x * y) <= -1.2e-252)
		tmp = t_1;
	elseif ((x * y) <= 2.65e-62)
		tmp = t_2;
	elseif ((x * y) <= 9e+38)
		tmp = t_1;
	elseif ((x * y) <= 2.8e+62)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -0.000145], t$95$3, If[LessEqual[N[(x * y), $MachinePrecision], -1.2e-252], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.65e-62], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 9e+38], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2.8e+62], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.45e-4 or 2.80000000000000014e62 < (*.f64 x y)

   1. Initial program 95.5%

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

   2. Taylor expanded in x around inf 74.6%

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

   if -1.45e-4 < (*.f64 x y) < -1.2000000000000001e-252 or 2.6499999999999998e-62 < (*.f64 x y) < 8.99999999999999961e38

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 69.1%

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

      1. associate-*r* 69.1%

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

      2. *-commutative 69.1%

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

      3. associate-*r* 69.1%

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

   4. Simplified 69.1%

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

   if -1.2000000000000001e-252 < (*.f64 x y) < 2.6499999999999998e-62 or 8.99999999999999961e38 < (*.f64 x y) < 2.80000000000000014e62

   1. Initial program 98.8%

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

   2. Taylor expanded in a around inf 72.3%

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

      1. *-commutative 72.3%

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

   4. Simplified 72.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.000145:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -1.2 \cdot 10^{-252}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.65 \cdot 10^{-62}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;x \cdot y \leq 9 \cdot 10^{+38}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 2.8 \cdot 10^{+62}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 5: 65.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-224}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-151}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* (* a b) -0.25))))
   (if (<= (* a b) -2e+89)
     t_1
     (if (<= (* a b) 5e-224)
       (+ c (* x y))
       (if (<= (* a b) 2e-151)
         (+ c (* t (* z 0.0625)))
         (if (<= (* a b) 5e+108) (+ (* x y) (* 0.0625 (* z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + ((a * b) * -0.25);
	double tmp;
	if ((a * b) <= -2e+89) {
		tmp = t_1;
	} else if ((a * b) <= 5e-224) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e-151) {
		tmp = c + (t * (z * 0.0625));
	} else if ((a * b) <= 5e+108) {
		tmp = (x * y) + (0.0625 * (z * t));
	} 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 + ((a * b) * (-0.25d0))
    if ((a * b) <= (-2d+89)) then
        tmp = t_1
    else if ((a * b) <= 5d-224) then
        tmp = c + (x * y)
    else if ((a * b) <= 2d-151) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((a * b) <= 5d+108) then
        tmp = (x * y) + (0.0625d0 * (z * t))
    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 + ((a * b) * -0.25);
	double tmp;
	if ((a * b) <= -2e+89) {
		tmp = t_1;
	} else if ((a * b) <= 5e-224) {
		tmp = c + (x * y);
	} else if ((a * b) <= 2e-151) {
		tmp = c + (t * (z * 0.0625));
	} else if ((a * b) <= 5e+108) {
		tmp = (x * y) + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + ((a * b) * -0.25)
	tmp = 0
	if (a * b) <= -2e+89:
		tmp = t_1
	elif (a * b) <= 5e-224:
		tmp = c + (x * y)
	elif (a * b) <= 2e-151:
		tmp = c + (t * (z * 0.0625))
	elif (a * b) <= 5e+108:
		tmp = (x * y) + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(Float64(a * b) * -0.25))
	tmp = 0.0
	if (Float64(a * b) <= -2e+89)
		tmp = t_1;
	elseif (Float64(a * b) <= 5e-224)
		tmp = Float64(c + Float64(x * y));
	elseif (Float64(a * b) <= 2e-151)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(a * b) <= 5e+108)
		tmp = Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + ((a * b) * -0.25);
	tmp = 0.0;
	if ((a * b) <= -2e+89)
		tmp = t_1;
	elseif ((a * b) <= 5e-224)
		tmp = c + (x * y);
	elseif ((a * b) <= 2e-151)
		tmp = c + (t * (z * 0.0625));
	elseif ((a * b) <= 5e+108)
		tmp = (x * y) + (0.0625 * (z * t));
	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[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -2e+89], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 5e-224], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 2e-151], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+108], N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.99999999999999999e89 or 4.99999999999999991e108 < (*.f64 a b)

   1. Initial program 94.1%

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

   2. Taylor expanded in a around inf 74.3%

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

      1. *-commutative 74.3%

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

   4. Simplified 74.3%

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

   if -1.99999999999999999e89 < (*.f64 a b) < 4.9999999999999999e-224

   1. Initial program 98.1%

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

   2. Taylor expanded in x around inf 70.9%

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

   if 4.9999999999999999e-224 < (*.f64 a b) < 1.9999999999999999e-151

   1. Initial program 91.7%

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

   2. Taylor expanded in z around inf 91.7%

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

      1. associate-*r* 91.7%

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

      2. *-commutative 91.7%

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

      3. associate-*r* 91.7%

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

   4. Simplified 91.7%

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

   if 1.9999999999999999e-151 < (*.f64 a b) < 4.99999999999999991e108

   1. Initial program 99.9%

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

      1. associate-+l- 99.9%

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

      2. associate--l+ 99.9%

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

      3. fma-def 100.0%

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

      4. associate-*l/ 100.0%

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

      5. fma-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. remove-double-neg 100.0%

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

      9. associate-/l* 99.9%

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

      10. distribute-frac-neg 99.9%

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

      11. associate-/r/ 100.0%

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

      12. fma-def 100.0%

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

      13. neg-mul-1 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/l* 100.0%

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

      16. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 88.8%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 88.8%

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

      2. *-commutative 88.8%

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

      3. associate-*r* 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in c around 0 70.0%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+89}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{-224}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \cdot b \leq 2 \cdot 10^{-151}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+108}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \end{array} \]

Alternative 6: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ \mathbf{if}\;x \cdot y \leq -0.0053:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 6.1 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625)))) (t_2 (+ c (* x y))))
   (if (<= (* x y) -0.0053)
     t_2
     (if (<= (* x y) 4.2e-186)
       t_1
       (if (<= (* x y) 6.1e-62)
         (* a (* b -0.25))
         (if (<= (* x y) 3.8e+89) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -0.0053) {
		tmp = t_2;
	} else if ((x * y) <= 4.2e-186) {
		tmp = t_1;
	} else if ((x * y) <= 6.1e-62) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 3.8e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = c + (x * y)
    if ((x * y) <= (-0.0053d0)) then
        tmp = t_2
    else if ((x * y) <= 4.2d-186) then
        tmp = t_1
    else if ((x * y) <= 6.1d-62) then
        tmp = a * (b * (-0.25d0))
    else if ((x * y) <= 3.8d+89) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (t * (z * 0.0625));
	double t_2 = c + (x * y);
	double tmp;
	if ((x * y) <= -0.0053) {
		tmp = t_2;
	} else if ((x * y) <= 4.2e-186) {
		tmp = t_1;
	} else if ((x * y) <= 6.1e-62) {
		tmp = a * (b * -0.25);
	} else if ((x * y) <= 3.8e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (t * (z * 0.0625))
	t_2 = c + (x * y)
	tmp = 0
	if (x * y) <= -0.0053:
		tmp = t_2
	elif (x * y) <= 4.2e-186:
		tmp = t_1
	elif (x * y) <= 6.1e-62:
		tmp = a * (b * -0.25)
	elif (x * y) <= 3.8e+89:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(t * Float64(z * 0.0625)))
	t_2 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(x * y) <= -0.0053)
		tmp = t_2;
	elseif (Float64(x * y) <= 4.2e-186)
		tmp = t_1;
	elseif (Float64(x * y) <= 6.1e-62)
		tmp = Float64(a * Float64(b * -0.25));
	elseif (Float64(x * y) <= 3.8e+89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (t * (z * 0.0625));
	t_2 = c + (x * y);
	tmp = 0.0;
	if ((x * y) <= -0.0053)
		tmp = t_2;
	elseif ((x * y) <= 4.2e-186)
		tmp = t_1;
	elseif ((x * y) <= 6.1e-62)
		tmp = a * (b * -0.25);
	elseif ((x * y) <= 3.8e+89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -0.0053], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 4.2e-186], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 6.1e-62], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3.8e+89], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -0.00530000000000000002 or 3.80000000000000023e89 < (*.f64 x y)

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 75.5%

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

   if -0.00530000000000000002 < (*.f64 x y) < 4.2000000000000004e-186 or 6.1e-62 < (*.f64 x y) < 3.80000000000000023e89

   1. Initial program 97.6%

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

   2. Taylor expanded in z around inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-*r* 66.9%

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

   4. Simplified 66.9%

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

   if 4.2000000000000004e-186 < (*.f64 x y) < 6.1e-62

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.3%

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

   3. Taylor expanded in a around inf 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-*l* 73.2%

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

   5. Simplified 73.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.0053:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;x \cdot y \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;x \cdot y \leq 6.1 \cdot 10^{-62}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;x \cdot y \leq 3.8 \cdot 10^{+89}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 7: 43.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -0.00058:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-323}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* x y) -0.00058)
     (* x y)
     (if (<= (* x y) -4e-323)
       t_1
       (if (<= (* x y) 3.6e-196) c (if (<= (* x y) 2.1e+88) t_1 (* 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) <= -0.00058) {
		tmp = x * y;
	} else if ((x * y) <= -4e-323) {
		tmp = t_1;
	} else if ((x * y) <= 3.6e-196) {
		tmp = c;
	} else if ((x * y) <= 2.1e+88) {
		tmp = t_1;
	} 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) <= (-0.00058d0)) then
        tmp = x * y
    else if ((x * y) <= (-4d-323)) then
        tmp = t_1
    else if ((x * y) <= 3.6d-196) then
        tmp = c
    else if ((x * y) <= 2.1d+88) then
        tmp = t_1
    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) <= -0.00058) {
		tmp = x * y;
	} else if ((x * y) <= -4e-323) {
		tmp = t_1;
	} else if ((x * y) <= 3.6e-196) {
		tmp = c;
	} else if ((x * y) <= 2.1e+88) {
		tmp = t_1;
	} 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) <= -0.00058:
		tmp = x * y
	elif (x * y) <= -4e-323:
		tmp = t_1
	elif (x * y) <= 3.6e-196:
		tmp = c
	elif (x * y) <= 2.1e+88:
		tmp = t_1
	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) <= -0.00058)
		tmp = Float64(x * y);
	elseif (Float64(x * y) <= -4e-323)
		tmp = t_1;
	elseif (Float64(x * y) <= 3.6e-196)
		tmp = c;
	elseif (Float64(x * y) <= 2.1e+88)
		tmp = t_1;
	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) <= -0.00058)
		tmp = x * y;
	elseif ((x * y) <= -4e-323)
		tmp = t_1;
	elseif ((x * y) <= 3.6e-196)
		tmp = c;
	elseif ((x * y) <= 2.1e+88)
		tmp = t_1;
	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], -0.00058], N[(x * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e-323], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 3.6e-196], c, If[LessEqual[N[(x * y), $MachinePrecision], 2.1e+88], t$95$1, N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.8e-4 or 2.1e88 < (*.f64 x y)

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. associate--l+ 95.3%

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

      3. fma-def 96.3%

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

      4. associate-*l/ 96.3%

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

      5. fma-neg 96.3%

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

      6. sub-neg 96.3%

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

      7. distribute-neg-in 96.3%

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

      8. remove-double-neg 96.3%

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

      9. associate-/l* 96.3%

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

      10. distribute-frac-neg 96.3%

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

      11. associate-/r/ 96.3%

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

      12. fma-def 96.3%

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

      13. neg-mul-1 96.3%

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

      14. *-commutative 96.3%

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

      15. associate-/l* 96.3%

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

      16. metadata-eval 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in a around 0 87.0%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 87.0%

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

      2. *-commutative 87.0%

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

      3. associate-*r* 87.0%

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

   6. Simplified 87.0%

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

   7. Taylor expanded in x around inf 63.0%

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

   if -5.8e-4 < (*.f64 x y) < -3.95253e-323 or 3.6000000000000001e-196 < (*.f64 x y) < 2.1e88

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. associate--l+ 98.1%

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

      3. fma-def 98.1%

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

      4. associate-*l/ 98.1%

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

      5. fma-neg 99.0%

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

      6. sub-neg 99.0%

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

      7. distribute-neg-in 99.0%

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

      8. remove-double-neg 99.0%

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

      9. associate-/l* 98.9%

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

      10. distribute-frac-neg 98.9%

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

      11. associate-/r/ 99.0%

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

      12. fma-def 99.0%

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

      13. neg-mul-1 99.0%

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

      14. *-commutative 99.0%

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

      15. associate-/l* 99.0%

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

      16. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in a around 0 65.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 65.1%

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

      2. *-commutative 65.1%

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

      3. associate-*r* 65.1%

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

   6. Simplified 65.1%

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

   7. Taylor expanded in t around inf 39.1%

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

   if -3.95253e-323 < (*.f64 x y) < 3.6000000000000001e-196

   1. Initial program 97.7%

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

   2. Taylor expanded in c around inf 41.2%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -0.00058:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{-323}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;x \cdot y \leq 3.6 \cdot 10^{-196}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \cdot y \leq 2.1 \cdot 10^{+88}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;x \cdot y \leq -1.36 \cdot 10^{-5} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+61}\right):\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t_1\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (or (<= (* x y) -1.36e-5) (not (<= (* x y) 2.4e+61)))
     (+ c (+ (* x y) t_1))
     (- (+ c t_1) (* (* a b) 0.25)))))

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) <= -1.36e-5) || !((x * y) <= 2.4e+61)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if (((x * y) <= (-1.36d-5)) .or. (.not. ((x * y) <= 2.4d+61))) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (c + t_1) - ((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 t_1 = 0.0625 * (z * t);
	double tmp;
	if (((x * y) <= -1.36e-5) || !((x * y) <= 2.4e+61)) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (c + t_1) - ((a * b) * 0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if ((x * y) <= -1.36e-5) or not ((x * y) <= 2.4e+61):
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (c + t_1) - ((a * b) * 0.25)
	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) <= -1.36e-5) || !(Float64(x * y) <= 2.4e+61))
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(Float64(c + t_1) - Float64(Float64(a * b) * 0.25));
	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) <= -1.36e-5) || ~(((x * y) <= 2.4e+61)))
		tmp = c + ((x * y) + t_1);
	else
		tmp = (c + t_1) - ((a * b) * 0.25);
	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[Or[LessEqual[N[(x * y), $MachinePrecision], -1.36e-5], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2.4e+61]], $MachinePrecision]], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$1), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.36000000000000002e-5 or 2.3999999999999999e61 < (*.f64 x y)

   1. Initial program 95.5%

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

   2. Taylor expanded in a around 0 87.5%

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

   if -1.36000000000000002e-5 < (*.f64 x y) < 2.3999999999999999e61

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 93.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1.36 \cdot 10^{-5} \lor \neg \left(x \cdot y \leq 2.4 \cdot 10^{+61}\right):\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(z \cdot t\right)\right) - \left(a \cdot b\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+167}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+269}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* a b) -2e+167)
   (+ c (* (* a b) -0.25))
   (if (<= (* a b) 5e+269)
     (+ c (+ (* x y) (* 0.0625 (* z t))))
     (* 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+167) {
		tmp = c + ((a * b) * -0.25);
	} else if ((a * b) <= 5e+269) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} 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 ((a * b) <= (-2d+167)) then
        tmp = c + ((a * b) * (-0.25d0))
    else if ((a * b) <= 5d+269) then
        tmp = c + ((x * y) + (0.0625d0 * (z * t)))
    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 ((a * b) <= -2e+167) {
		tmp = c + ((a * b) * -0.25);
	} else if ((a * b) <= 5e+269) {
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	} else {
		tmp = a * (b * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (a * b) <= -2e+167:
		tmp = c + ((a * b) * -0.25)
	elif (a * b) <= 5e+269:
		tmp = c + ((x * y) + (0.0625 * (z * t)))
	else:
		tmp = a * (b * -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -2e+167)
		tmp = Float64(c + Float64(Float64(a * b) * -0.25));
	elseif (Float64(a * b) <= 5e+269)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(z * t))));
	else
		tmp = 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+167)
		tmp = c + ((a * b) * -0.25);
	elseif ((a * b) <= 5e+269)
		tmp = c + ((x * y) + (0.0625 * (z * t)));
	else
		tmp = 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+167], N[(c + N[(N[(a * b), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+269], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -2.0000000000000001e167

   1. Initial program 97.2%

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

   2. Taylor expanded in a around inf 81.5%

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

      1. *-commutative 81.5%

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

   4. Simplified 81.5%

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

   if -2.0000000000000001e167 < (*.f64 a b) < 5.0000000000000002e269

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 88.0%

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

   if 5.0000000000000002e269 < (*.f64 a b)

   1. Initial program 78.9%

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

   2. Taylor expanded in x around 0 78.9%

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

   3. Taylor expanded in a around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l* 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+167}:\\ \;\;\;\;c + \left(a \cdot b\right) \cdot -0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+269}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 10: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+89}:\\ \;\;\;\;t_1 - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+269}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* a b) -2e+89)
     (- t_1 (* (* a b) 0.25))
     (if (<= (* a b) 5e+269) (+ c (+ (* x y) t_1)) (* a (* b -0.25))))))

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 ((a * b) <= -2e+89) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+269) {
		tmp = c + ((x * y) + t_1);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((a * b) <= (-2d+89)) then
        tmp = t_1 - ((a * b) * 0.25d0)
    else if ((a * b) <= 5d+269) then
        tmp = c + ((x * y) + t_1)
    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 t_1 = 0.0625 * (z * t);
	double tmp;
	if ((a * b) <= -2e+89) {
		tmp = t_1 - ((a * b) * 0.25);
	} else if ((a * b) <= 5e+269) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = a * (b * -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (a * b) <= -2e+89:
		tmp = t_1 - ((a * b) * 0.25)
	elif (a * b) <= 5e+269:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = a * (b * -0.25)
	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(a * b) <= -2e+89)
		tmp = Float64(t_1 - Float64(Float64(a * b) * 0.25));
	elseif (Float64(a * b) <= 5e+269)
		tmp = Float64(c + Float64(Float64(x * y) + t_1));
	else
		tmp = Float64(a * Float64(b * -0.25));
	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 ((a * b) <= -2e+89)
		tmp = t_1 - ((a * b) * 0.25);
	elseif ((a * b) <= 5e+269)
		tmp = c + ((x * y) + t_1);
	else
		tmp = a * (b * -0.25);
	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[(a * b), $MachinePrecision], -2e+89], N[(t$95$1 - N[(N[(a * b), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 5e+269], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.99999999999999999e89

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 87.2%

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

   3. Taylor expanded in c around 0 78.2%

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

   if -1.99999999999999999e89 < (*.f64 a b) < 5.0000000000000002e269

   1. Initial program 98.4%

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

   2. Taylor expanded in a around 0 89.6%

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

   if 5.0000000000000002e269 < (*.f64 a b)

   1. Initial program 78.9%

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

   2. Taylor expanded in x around 0 78.9%

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

   3. Taylor expanded in a around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. associate-*l* 89.5%

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

   5. Simplified 89.5%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot b \leq -2 \cdot 10^{+89}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) - \left(a \cdot b\right) \cdot 0.25\\ \mathbf{elif}\;a \cdot b \leq 5 \cdot 10^{+269}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]

Alternative 11: 53.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+158} \lor \neg \left(z \leq 1.2 \cdot 10^{-31}\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -9.5e+158) (not (<= z 1.2e-31)))
   (* 0.0625 (* z t))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -9.5e+158) || !(z <= 1.2e-31)) {
		tmp = 0.0625 * (z * t);
	} 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 ((z <= (-9.5d+158)) .or. (.not. (z <= 1.2d-31))) then
        tmp = 0.0625d0 * (z * t)
    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 ((z <= -9.5e+158) || !(z <= 1.2e-31)) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -9.5e+158) or not (z <= 1.2e-31):
		tmp = 0.0625 * (z * t)
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -9.5e+158) || !(z <= 1.2e-31))
		tmp = Float64(0.0625 * Float64(z * t));
	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 ((z <= -9.5e+158) || ~((z <= 1.2e-31)))
		tmp = 0.0625 * (z * t);
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -9.5e+158], N[Not[LessEqual[z, 1.2e-31]], $MachinePrecision]], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.49999999999999913e158 or 1.2e-31 < z

   1. Initial program 95.6%

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

      1. associate-+l- 95.6%

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

      2. associate--l+ 95.6%

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

      3. fma-def 95.6%

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

      4. associate-*l/ 95.6%

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

      5. fma-neg 97.8%

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

      6. sub-neg 97.8%

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

      7. distribute-neg-in 97.8%

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

      8. remove-double-neg 97.8%

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

      9. associate-/l* 97.8%

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

      10. distribute-frac-neg 97.8%

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

      11. associate-/r/ 97.8%

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

      12. fma-def 97.8%

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

      13. neg-mul-1 97.8%

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

      14. *-commutative 97.8%

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

      15. associate-/l* 97.8%

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

      16. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in a around 0 77.2%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*r* 77.2%

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

   6. Simplified 77.2%

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

   7. Taylor expanded in t around inf 53.1%

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

   if -9.49999999999999913e158 < z < 1.2e-31

   1. Initial program 97.6%

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

   2. Taylor expanded in x around inf 62.7%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+158} \lor \neg \left(z \leq 1.2 \cdot 10^{-31}\right):\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 12: 37.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+122}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1.9e+122) c (if (<= c 7.6e+82) (* x y) c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.9e+122) {
		tmp = c;
	} else if (c <= 7.6e+82) {
		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 (c <= (-1.9d+122)) then
        tmp = c
    else if (c <= 7.6d+82) 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 (c <= -1.9e+122) {
		tmp = c;
	} else if (c <= 7.6e+82) {
		tmp = x * y;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1.9e+122:
		tmp = c
	elif c <= 7.6e+82:
		tmp = x * y
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1.9e+122)
		tmp = c;
	elseif (c <= 7.6e+82)
		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 (c <= -1.9e+122)
		tmp = c;
	elseif (c <= 7.6e+82)
		tmp = x * y;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1.9e+122], c, If[LessEqual[c, 7.6e+82], N[(x * y), $MachinePrecision], c]]

Derivation

1. Split input into 2 regimes

2. if c < -1.8999999999999999e122 or 7.60000000000000067e82 < c

   1. Initial program 96.0%

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

   2. Taylor expanded in c around inf 55.3%

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

   if -1.8999999999999999e122 < c < 7.60000000000000067e82

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. associate--l+ 97.2%

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

      3. fma-def 97.2%

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

      4. associate-*l/ 97.2%

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

      5. fma-neg 97.2%

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

      6. sub-neg 97.2%

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

      7. distribute-neg-in 97.2%

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

      8. remove-double-neg 97.2%

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

      9. associate-/l* 97.1%

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

      10. distribute-frac-neg 97.1%

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

      11. associate-/r/ 97.2%

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

      12. fma-def 97.2%

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

      13. neg-mul-1 97.2%

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

      14. *-commutative 97.2%

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

      15. associate-/l* 97.2%

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

      16. metadata-eval 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in a around 0 71.9%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{c + 0.0625 \cdot \left(t \cdot z\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 71.9%

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

      2. *-commutative 71.9%

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

      3. associate-*r* 71.9%

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

   6. Simplified 71.9%

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

   7. Taylor expanded in x around inf 39.5%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{+122}:\\ \;\;\;\;c\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+82}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]

Alternative 13: 21.8% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return c;
}

Python

def code(x, y, z, t, a, b, c):
	return c

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 96.9%

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

2. Taylor expanded in c around inf 21.1%

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

3. Final simplification 21.1%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023271 
(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))