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

Percentage Accurate: 97.8% → 98.9%

Time: 8.3s

Alternatives: 16

Speedup: 0.5×

• 32.4% 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: 97.8% 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: 98.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

   1. associate-+l- 98.0%

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

   2. +-commutative 98.0%

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

   3. associate--l+ 98.0%

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

   4. associate-*l/ 98.0%

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

   5. *-commutative 98.0%

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

   6. fma-def 99.2%

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

   7. fma-neg 99.6%

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

   8. neg-sub0 99.6%

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

   9. associate-+l- 99.6%

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

   10. neg-sub0 99.6%

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

   11. +-commutative 99.6%

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

   12. unsub-neg 99.6%

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

   13. *-commutative 99.6%

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

   14. associate-*r/ 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 2: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{t \cdot z}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot 0.0625, t, c + \left(b \cdot a\right) \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (/ (* t z) 16.0) (* x y)) (/ (* b a) 4.0))))
   (if (<= t_1 INFINITY)
     (+ c t_1)
     (fma (* z 0.0625) t (+ c (* (* b a) -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = fma((z * 0.0625), t, (c + ((b * a) * -0.25)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(t * z) / 16.0) + Float64(x * y)) - Float64(Float64(b * a) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = fma(Float64(z * 0.0625), t, Float64(c + Float64(Float64(b * a) * -0.25)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(t * z), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(z * 0.0625), $MachinePrecision] * t + N[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $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 0 20.0%

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

      1. sub-neg 20.0%

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

      2. +-commutative 20.0%

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

      3. associate-+l+ 20.0%

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

      4. *-commutative 20.0%

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

      5. associate-*r* 20.0%

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

      6. fma-def 80.0%

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

      7. *-commutative 80.0%

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

      8. distribute-rgt-neg-in 80.0%

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

      9. metadata-eval 80.0%

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

   4. Applied egg-rr 80.0%

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

4. Final simplification 99.6%

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

Alternative 3: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{t \cdot z}{16} + x \cdot y\right) - \frac{b \cdot a}{4}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;c + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (+ (/ (* t z) 16.0) (* x y)) (/ (* b a) 4.0))))
   (if (<= t_1 INFINITY) (+ c t_1) (* (* b a) -0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = c + t_1;
	} else {
		tmp = (b * a) * -0.25;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = c + t_1;
	} else {
		tmp = (b * a) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0)
	tmp = 0
	if t_1 <= math.inf:
		tmp = c + t_1
	else:
		tmp = (b * a) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(t * z) / 16.0) + Float64(x * y)) - Float64(Float64(b * a) / 4.0))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(c + t_1);
	else
		tmp = Float64(Float64(b * a) * -0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((t * z) / 16.0) + (x * y)) - ((b * a) / 4.0);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = c + t_1;
	else
		tmp = (b * a) * -0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(t * z), $MachinePrecision] / 16.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(c + t$95$1), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * -0.25), $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 z around 0 60.0%

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

   3. Taylor expanded in a around inf 80.0%

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

      1. *-commutative 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 99.6%

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

Alternative 4: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-174}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= (* b a) -2e+45)
     t_2
     (if (<= (* b a) -2e-86)
       t_1
       (if (<= (* b a) -5e-174)
         (+ c (* t (* z 0.0625)))
         (if (<= (* b a) 5e-43)
           t_1
           (if (<= (* b a) 2e+54) (+ (* 0.0625 (* t z)) (* x y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -2e+45) {
		tmp = t_2;
	} else if ((b * a) <= -2e-86) {
		tmp = t_1;
	} else if ((b * a) <= -5e-174) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 5e-43) {
		tmp = t_1;
	} else if ((b * a) <= 2e+54) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (b * (a * (-0.25d0)))
    if ((b * a) <= (-2d+45)) then
        tmp = t_2
    else if ((b * a) <= (-2d-86)) then
        tmp = t_1
    else if ((b * a) <= (-5d-174)) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((b * a) <= 5d-43) then
        tmp = t_1
    else if ((b * a) <= 2d+54) then
        tmp = (0.0625d0 * (t * z)) + (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -2e+45) {
		tmp = t_2;
	} else if ((b * a) <= -2e-86) {
		tmp = t_1;
	} else if ((b * a) <= -5e-174) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 5e-43) {
		tmp = t_1;
	} else if ((b * a) <= 2e+54) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if (b * a) <= -2e+45:
		tmp = t_2
	elif (b * a) <= -2e-86:
		tmp = t_1
	elif (b * a) <= -5e-174:
		tmp = c + (t * (z * 0.0625))
	elif (b * a) <= 5e-43:
		tmp = t_1
	elif (b * a) <= 2e+54:
		tmp = (0.0625 * (t * z)) + (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(b * a) <= -2e+45)
		tmp = t_2;
	elseif (Float64(b * a) <= -2e-86)
		tmp = t_1;
	elseif (Float64(b * a) <= -5e-174)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(b * a) <= 5e-43)
		tmp = t_1;
	elseif (Float64(b * a) <= 2e+54)
		tmp = Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((b * a) <= -2e+45)
		tmp = t_2;
	elseif ((b * a) <= -2e-86)
		tmp = t_1;
	elseif ((b * a) <= -5e-174)
		tmp = c + (t * (z * 0.0625));
	elseif ((b * a) <= 5e-43)
		tmp = t_1;
	elseif ((b * a) <= 2e+54)
		tmp = (0.0625 * (t * z)) + (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2e+45], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -2e-86], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -5e-174], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e-43], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 2e+54], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a b) < -1.9999999999999999e45 or 2.0000000000000002e54 < (*.f64 a b)

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 73.0%

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

   4. Simplified 73.0%

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

   if -1.9999999999999999e45 < (*.f64 a b) < -2.00000000000000017e-86 or -5.0000000000000002e-174 < (*.f64 a b) < 5.00000000000000019e-43

   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 inf 69.3%

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

   if -2.00000000000000017e-86 < (*.f64 a b) < -5.0000000000000002e-174

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 84.1%

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

      1. associate-*r* 84.1%

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

      2. *-commutative 84.1%

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

      3. associate-*r* 84.1%

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

   4. Simplified 84.1%

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

   if 5.00000000000000019e-43 < (*.f64 a b) < 2.0000000000000002e54

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 96.0%

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

   3. Taylor expanded in c around 0 83.9%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-86}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-174}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-43}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 5: 89.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := \left(b \cdot a\right) \cdot 0.25\\ t_3 := \left(c + t_1\right) - t_2\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_2\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;c + \left(t_1 + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z)))
        (t_2 (* (* b a) 0.25))
        (t_3 (- (+ c t_1) t_2)))
   (if (<= (* b a) -5e+162)
     t_3
     (if (<= (* b a) -2e+45)
       (- (+ c (* x y)) t_2)
       (if (<= (* b a) 2e+54) (+ c (+ t_1 (* x y))) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = (b * a) * 0.25;
	double t_3 = (c + t_1) - t_2;
	double tmp;
	if ((b * a) <= -5e+162) {
		tmp = t_3;
	} else if ((b * a) <= -2e+45) {
		tmp = (c + (x * y)) - t_2;
	} else if ((b * a) <= 2e+54) {
		tmp = c + (t_1 + (x * y));
	} 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 = 0.0625d0 * (t * z)
    t_2 = (b * a) * 0.25d0
    t_3 = (c + t_1) - t_2
    if ((b * a) <= (-5d+162)) then
        tmp = t_3
    else if ((b * a) <= (-2d+45)) then
        tmp = (c + (x * y)) - t_2
    else if ((b * a) <= 2d+54) then
        tmp = c + (t_1 + (x * y))
    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 = 0.0625 * (t * z);
	double t_2 = (b * a) * 0.25;
	double t_3 = (c + t_1) - t_2;
	double tmp;
	if ((b * a) <= -5e+162) {
		tmp = t_3;
	} else if ((b * a) <= -2e+45) {
		tmp = (c + (x * y)) - t_2;
	} else if ((b * a) <= 2e+54) {
		tmp = c + (t_1 + (x * y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	t_2 = (b * a) * 0.25
	t_3 = (c + t_1) - t_2
	tmp = 0
	if (b * a) <= -5e+162:
		tmp = t_3
	elif (b * a) <= -2e+45:
		tmp = (c + (x * y)) - t_2
	elif (b * a) <= 2e+54:
		tmp = c + (t_1 + (x * y))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	t_2 = Float64(Float64(b * a) * 0.25)
	t_3 = Float64(Float64(c + t_1) - t_2)
	tmp = 0.0
	if (Float64(b * a) <= -5e+162)
		tmp = t_3;
	elseif (Float64(b * a) <= -2e+45)
		tmp = Float64(Float64(c + Float64(x * y)) - t_2);
	elseif (Float64(b * a) <= 2e+54)
		tmp = Float64(c + Float64(t_1 + Float64(x * y)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	t_2 = (b * a) * 0.25;
	t_3 = (c + t_1) - t_2;
	tmp = 0.0;
	if ((b * a) <= -5e+162)
		tmp = t_3;
	elseif ((b * a) <= -2e+45)
		tmp = (c + (x * y)) - t_2;
	elseif ((b * a) <= 2e+54)
		tmp = c + (t_1 + (x * y));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$3 = N[(N[(c + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+162], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -2e+45], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+54], N[(c + N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999997e162 or 2.0000000000000002e54 < (*.f64 a b)

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0 88.7%

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

   if -4.9999999999999997e162 < (*.f64 a b) < -1.9999999999999999e45

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 94.4%

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

   if -1.9999999999999999e45 < (*.f64 a b) < 2.0000000000000002e54

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 95.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+162}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 6: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-164}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (+ c (* b (* a -0.25)))))
   (if (<= (* b a) -2e+45)
     t_2
     (if (<= (* b a) -2e-86)
       t_1
       (if (<= (* b a) -2e-164)
         (+ c (* t (* z 0.0625)))
         (if (<= (* b a) 2e+54) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -2e+45) {
		tmp = t_2;
	} else if ((b * a) <= -2e-86) {
		tmp = t_1;
	} else if ((b * a) <= -2e-164) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 2e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = c + (b * (a * (-0.25d0)))
    if ((b * a) <= (-2d+45)) then
        tmp = t_2
    else if ((b * a) <= (-2d-86)) then
        tmp = t_1
    else if ((b * a) <= (-2d-164)) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((b * a) <= 2d+54) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = c + (b * (a * -0.25));
	double tmp;
	if ((b * a) <= -2e+45) {
		tmp = t_2;
	} else if ((b * a) <= -2e-86) {
		tmp = t_1;
	} else if ((b * a) <= -2e-164) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 2e+54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = c + (b * (a * -0.25))
	tmp = 0
	if (b * a) <= -2e+45:
		tmp = t_2
	elif (b * a) <= -2e-86:
		tmp = t_1
	elif (b * a) <= -2e-164:
		tmp = c + (t * (z * 0.0625))
	elif (b * a) <= 2e+54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(c + Float64(b * Float64(a * -0.25)))
	tmp = 0.0
	if (Float64(b * a) <= -2e+45)
		tmp = t_2;
	elseif (Float64(b * a) <= -2e-86)
		tmp = t_1;
	elseif (Float64(b * a) <= -2e-164)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(b * a) <= 2e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = c + (b * (a * -0.25));
	tmp = 0.0;
	if ((b * a) <= -2e+45)
		tmp = t_2;
	elseif ((b * a) <= -2e-86)
		tmp = t_1;
	elseif ((b * a) <= -2e-164)
		tmp = c + (t * (z * 0.0625));
	elseif ((b * a) <= 2e+54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -2e+45], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -2e-86], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -2e-164], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+54], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.9999999999999999e45 or 2.0000000000000002e54 < (*.f64 a b)

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 73.0%

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

   4. Simplified 73.0%

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

   if -1.9999999999999999e45 < (*.f64 a b) < -2.00000000000000017e-86 or -1.99999999999999992e-164 < (*.f64 a b) < 2.0000000000000002e54

   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 inf 67.5%

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

   if -2.00000000000000017e-86 < (*.f64 a b) < -1.99999999999999992e-164

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 82.9%

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

      1. associate-*r* 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-*r* 82.9%

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

   4. Simplified 82.9%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-86}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{-164}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 7: 88.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+162}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{+45} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;c + \left(t_2 + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) 0.25)) (t_2 (* 0.0625 (* t z))))
   (if (<= (* b a) -5e+162)
     (- t_2 t_1)
     (if (or (<= (* b a) -2e+45) (not (<= (* b a) 2e+28)))
       (- (+ c (* x y)) t_1)
       (+ c (+ t_2 (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -5e+162) {
		tmp = t_2 - t_1;
	} else if (((b * a) <= -2e+45) || !((b * a) <= 2e+28)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = c + (t_2 + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = 0.0625d0 * (t * z)
    if ((b * a) <= (-5d+162)) then
        tmp = t_2 - t_1
    else if (((b * a) <= (-2d+45)) .or. (.not. ((b * a) <= 2d+28))) then
        tmp = (c + (x * y)) - t_1
    else
        tmp = c + (t_2 + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -5e+162) {
		tmp = t_2 - t_1;
	} else if (((b * a) <= -2e+45) || !((b * a) <= 2e+28)) {
		tmp = (c + (x * y)) - t_1;
	} else {
		tmp = c + (t_2 + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * 0.25
	t_2 = 0.0625 * (t * z)
	tmp = 0
	if (b * a) <= -5e+162:
		tmp = t_2 - t_1
	elif ((b * a) <= -2e+45) or not ((b * a) <= 2e+28):
		tmp = (c + (x * y)) - t_1
	else:
		tmp = c + (t_2 + (x * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * 0.25)
	t_2 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (Float64(b * a) <= -5e+162)
		tmp = Float64(t_2 - t_1);
	elseif ((Float64(b * a) <= -2e+45) || !(Float64(b * a) <= 2e+28))
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	else
		tmp = Float64(c + Float64(t_2 + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * 0.25;
	t_2 = 0.0625 * (t * z);
	tmp = 0.0;
	if ((b * a) <= -5e+162)
		tmp = t_2 - t_1;
	elseif (((b * a) <= -2e+45) || ~(((b * a) <= 2e+28)))
		tmp = (c + (x * y)) - t_1;
	else
		tmp = c + (t_2 + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+162], N[(t$95$2 - t$95$1), $MachinePrecision], If[Or[LessEqual[N[(b * a), $MachinePrecision], -2e+45], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+28]], $MachinePrecision]], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(c + N[(t$95$2 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999997e162

   1. Initial program 92.9%

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

   2. Taylor expanded in x around 0 88.2%

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

   3. Taylor expanded in c around 0 85.7%

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

   if -4.9999999999999997e162 < (*.f64 a b) < -1.9999999999999999e45 or 1.99999999999999992e28 < (*.f64 a b)

   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 z around 0 89.9%

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

   if -1.9999999999999999e45 < (*.f64 a b) < 1.99999999999999992e28

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 95.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+162}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq -2 \cdot 10^{+45} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+28}\right):\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \end{array} \]

Alternative 8: 44.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -7.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-185}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -9.8e+42)
     t_1
     (if (<= (* b a) -7.5e-87)
       (* x y)
       (if (<= (* b a) -4.4e-185) c (if (<= (* b a) 4.6e+55) (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -9.8e+42) {
		tmp = t_1;
	} else if ((b * a) <= -7.5e-87) {
		tmp = x * y;
	} else if ((b * a) <= -4.4e-185) {
		tmp = c;
	} else if ((b * a) <= 4.6e+55) {
		tmp = x * y;
	} 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 = (b * a) * (-0.25d0)
    if ((b * a) <= (-9.8d+42)) then
        tmp = t_1
    else if ((b * a) <= (-7.5d-87)) then
        tmp = x * y
    else if ((b * a) <= (-4.4d-185)) then
        tmp = c
    else if ((b * a) <= 4.6d+55) then
        tmp = x * y
    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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -9.8e+42) {
		tmp = t_1;
	} else if ((b * a) <= -7.5e-87) {
		tmp = x * y;
	} else if ((b * a) <= -4.4e-185) {
		tmp = c;
	} else if ((b * a) <= 4.6e+55) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -9.8e+42:
		tmp = t_1
	elif (b * a) <= -7.5e-87:
		tmp = x * y
	elif (b * a) <= -4.4e-185:
		tmp = c
	elif (b * a) <= 4.6e+55:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -9.8e+42)
		tmp = t_1;
	elseif (Float64(b * a) <= -7.5e-87)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= -4.4e-185)
		tmp = c;
	elseif (Float64(b * a) <= 4.6e+55)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -9.8e+42)
		tmp = t_1;
	elseif ((b * a) <= -7.5e-87)
		tmp = x * y;
	elseif ((b * a) <= -4.4e-185)
		tmp = c;
	elseif ((b * a) <= 4.6e+55)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -9.8e+42], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -7.5e-87], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], -4.4e-185], c, If[LessEqual[N[(b * a), $MachinePrecision], 4.6e+55], N[(x * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.8000000000000004e42 or 4.59999999999999975e55 < (*.f64 a b)

   1. Initial program 95.1%

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

   2. Taylor expanded in z around 0 83.7%

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

   3. Taylor expanded in a around inf 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   if -9.8000000000000004e42 < (*.f64 a b) < -7.5000000000000002e-87 or -4.4000000000000001e-185 < (*.f64 a b) < 4.59999999999999975e55

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 70.3%

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

   3. Taylor expanded in y around inf 40.8%

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

   if -7.5000000000000002e-87 < (*.f64 a b) < -4.4000000000000001e-185

   1. Initial program 99.9%

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

   2. Taylor expanded in c around inf 42.1%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -9.8 \cdot 10^{+42}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -7.5 \cdot 10^{-87}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -4.4 \cdot 10^{-185}:\\ \;\;\;\;c\\ \mathbf{elif}\;b \cdot a \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 9: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* b a) -2e+45)
   (- (* x y) (* (* b a) 0.25))
   (if (<= (* b a) 2e+54)
     (+ c (+ (* 0.0625 (* t z)) (* x y)))
     (+ c (* b (* a -0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b * a) <= -2e+45) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if ((b * a) <= 2e+54) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = c + (b * (a * -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 ((b * a) <= (-2d+45)) then
        tmp = (x * y) - ((b * a) * 0.25d0)
    else if ((b * a) <= 2d+54) then
        tmp = c + ((0.0625d0 * (t * z)) + (x * y))
    else
        tmp = c + (b * (a * (-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 ((b * a) <= -2e+45) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if ((b * a) <= 2e+54) {
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b * a) <= -2e+45:
		tmp = (x * y) - ((b * a) * 0.25)
	elif (b * a) <= 2e+54:
		tmp = c + ((0.0625 * (t * z)) + (x * y))
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b * a) <= -2e+45)
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	elseif (Float64(b * a) <= 2e+54)
		tmp = Float64(c + Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y)));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b * a) <= -2e+45)
		tmp = (x * y) - ((b * a) * 0.25);
	elseif ((b * a) <= 2e+54)
		tmp = c + ((0.0625 * (t * z)) + (x * y));
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b * a), $MachinePrecision], -2e+45], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+54], N[(c + N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -1.9999999999999999e45

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0 81.0%

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

   3. Taylor expanded in c around 0 72.5%

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

   if -1.9999999999999999e45 < (*.f64 a b) < 2.0000000000000002e54

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 95.8%

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

   if 2.0000000000000002e54 < (*.f64 a b)

   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 inf 78.6%

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

      1. *-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 10: 85.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+168}:\\ \;\;\;\;t_1 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;c + \left(t_1 + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= (* b a) -1e+168)
     (- t_1 (* (* b a) 0.25))
     (if (<= (* b a) 2e+54) (+ c (+ t_1 (* x y))) (+ c (* b (* a -0.25)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -1e+168) {
		tmp = t_1 - ((b * a) * 0.25);
	} else if ((b * a) <= 2e+54) {
		tmp = c + (t_1 + (x * y));
	} else {
		tmp = c + (b * (a * -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 * (t * z)
    if ((b * a) <= (-1d+168)) then
        tmp = t_1 - ((b * a) * 0.25d0)
    else if ((b * a) <= 2d+54) then
        tmp = c + (t_1 + (x * y))
    else
        tmp = c + (b * (a * (-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 * (t * z);
	double tmp;
	if ((b * a) <= -1e+168) {
		tmp = t_1 - ((b * a) * 0.25);
	} else if ((b * a) <= 2e+54) {
		tmp = c + (t_1 + (x * y));
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if (b * a) <= -1e+168:
		tmp = t_1 - ((b * a) * 0.25)
	elif (b * a) <= 2e+54:
		tmp = c + (t_1 + (x * y))
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (Float64(b * a) <= -1e+168)
		tmp = Float64(t_1 - Float64(Float64(b * a) * 0.25));
	elseif (Float64(b * a) <= 2e+54)
		tmp = Float64(c + Float64(t_1 + Float64(x * y)));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	tmp = 0.0;
	if ((b * a) <= -1e+168)
		tmp = t_1 - ((b * a) * 0.25);
	elseif ((b * a) <= 2e+54)
		tmp = c + (t_1 + (x * y));
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+168], N[(t$95$1 - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+54], N[(c + N[(t$95$1 + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.9999999999999993e167

   1. Initial program 92.7%

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

   2. Taylor expanded in x around 0 88.0%

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

   3. Taylor expanded in c around 0 85.4%

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

   if -9.9999999999999993e167 < (*.f64 a b) < 2.0000000000000002e54

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 92.7%

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

   if 2.0000000000000002e54 < (*.f64 a b)

   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 inf 78.6%

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

      1. *-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. associate-*r* 78.6%

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

   4. Simplified 78.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+168}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+54}:\\ \;\;\;\;c + \left(0.0625 \cdot \left(t \cdot z\right) + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 11: 60.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-18}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-138}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-68}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= a -1e+75)
   (- (* x y) (* (* b a) 0.25))
   (if (<= a -1e-18)
     (+ c (* t (* z 0.0625)))
     (if (<= a -7.5e-138)
       (+ (* 0.0625 (* t z)) (* x y))
       (if (<= a 1.9e-68) (+ c (* x y)) (+ c (* b (* a -0.25))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (a <= -1e+75) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if (a <= -1e-18) {
		tmp = c + (t * (z * 0.0625));
	} else if (a <= -7.5e-138) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else if (a <= 1.9e-68) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -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 <= (-1d+75)) then
        tmp = (x * y) - ((b * a) * 0.25d0)
    else if (a <= (-1d-18)) then
        tmp = c + (t * (z * 0.0625d0))
    else if (a <= (-7.5d-138)) then
        tmp = (0.0625d0 * (t * z)) + (x * y)
    else if (a <= 1.9d-68) then
        tmp = c + (x * y)
    else
        tmp = c + (b * (a * (-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 <= -1e+75) {
		tmp = (x * y) - ((b * a) * 0.25);
	} else if (a <= -1e-18) {
		tmp = c + (t * (z * 0.0625));
	} else if (a <= -7.5e-138) {
		tmp = (0.0625 * (t * z)) + (x * y);
	} else if (a <= 1.9e-68) {
		tmp = c + (x * y);
	} else {
		tmp = c + (b * (a * -0.25));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if a <= -1e+75:
		tmp = (x * y) - ((b * a) * 0.25)
	elif a <= -1e-18:
		tmp = c + (t * (z * 0.0625))
	elif a <= -7.5e-138:
		tmp = (0.0625 * (t * z)) + (x * y)
	elif a <= 1.9e-68:
		tmp = c + (x * y)
	else:
		tmp = c + (b * (a * -0.25))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (a <= -1e+75)
		tmp = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25));
	elseif (a <= -1e-18)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (a <= -7.5e-138)
		tmp = Float64(Float64(0.0625 * Float64(t * z)) + Float64(x * y));
	elseif (a <= 1.9e-68)
		tmp = Float64(c + Float64(x * y));
	else
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (a <= -1e+75)
		tmp = (x * y) - ((b * a) * 0.25);
	elseif (a <= -1e-18)
		tmp = c + (t * (z * 0.0625));
	elseif (a <= -7.5e-138)
		tmp = (0.0625 * (t * z)) + (x * y);
	elseif (a <= 1.9e-68)
		tmp = c + (x * y);
	else
		tmp = c + (b * (a * -0.25));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[a, -1e+75], N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-18], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e-138], N[(N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.9e-68], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -9.99999999999999927e74

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 74.4%

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

   3. Taylor expanded in c around 0 69.6%

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

   if -9.99999999999999927e74 < a < -1.0000000000000001e-18

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 70.3%

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

      1. associate-*r* 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*r* 70.3%

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

   4. Simplified 70.3%

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

   if -1.0000000000000001e-18 < a < -7.4999999999999995e-138

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 94.2%

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

   3. Taylor expanded in c around 0 77.1%

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

   if -7.4999999999999995e-138 < a < 1.90000000000000019e-68

   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 inf 65.6%

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

   if 1.90000000000000019e-68 < 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. Taylor expanded in a around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*r* 66.8%

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

   4. Simplified 66.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot -0.25\right)} + c \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+75}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-18}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-138}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) + x \cdot y\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-68}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \end{array} \]

Alternative 12: 64.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+54}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -2e+45) (not (<= (* b a) 2e+54)))
   (+ c (* b (* a -0.25)))
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -2e+45) || !((b * a) <= 2e+54)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-2d+45)) .or. (.not. ((b * a) <= 2d+54))) then
        tmp = c + (b * (a * (-0.25d0)))
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -2e+45) || !((b * a) <= 2e+54)) {
		tmp = c + (b * (a * -0.25));
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -2e+45) or not ((b * a) <= 2e+54):
		tmp = c + (b * (a * -0.25))
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -2e+45) || !(Float64(b * a) <= 2e+54))
		tmp = Float64(c + Float64(b * Float64(a * -0.25)));
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -2e+45) || ~(((b * a) <= 2e+54)))
		tmp = c + (b * (a * -0.25));
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -2e+45], N[Not[LessEqual[N[(b * a), $MachinePrecision], 2e+54]], $MachinePrecision]], N[(c + N[(b * N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.9999999999999999e45 or 2.0000000000000002e54 < (*.f64 a b)

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf 73.0%

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

      1. *-commutative 73.0%

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

      2. *-commutative 73.0%

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

      3. associate-*r* 73.0%

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

   4. Simplified 73.0%

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

   if -1.9999999999999999e45 < (*.f64 a b) < 2.0000000000000002e54

   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 inf 65.1%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -2 \cdot 10^{+45} \lor \neg \left(b \cdot a \leq 2 \cdot 10^{+54}\right):\\ \;\;\;\;c + b \cdot \left(a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 13: 37.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;c\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= z -1.6e+119)
     t_1
     (if (<= z -1.2e-99)
       (* x y)
       (if (<= z -4.4e-304) c (if (<= z 2e-85) (* x y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double tmp;
	if (z <= -1.6e+119) {
		tmp = t_1;
	} else if (z <= -1.2e-99) {
		tmp = x * y;
	} else if (z <= -4.4e-304) {
		tmp = c;
	} else if (z <= 2e-85) {
		tmp = x * y;
	} 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 = 0.0625d0 * (t * z)
    if (z <= (-1.6d+119)) then
        tmp = t_1
    else if (z <= (-1.2d-99)) then
        tmp = x * y
    else if (z <= (-4.4d-304)) then
        tmp = c
    else if (z <= 2d-85) then
        tmp = x * y
    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 = 0.0625 * (t * z);
	double tmp;
	if (z <= -1.6e+119) {
		tmp = t_1;
	} else if (z <= -1.2e-99) {
		tmp = x * y;
	} else if (z <= -4.4e-304) {
		tmp = c;
	} else if (z <= 2e-85) {
		tmp = x * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	tmp = 0
	if z <= -1.6e+119:
		tmp = t_1
	elif z <= -1.2e-99:
		tmp = x * y
	elif z <= -4.4e-304:
		tmp = c
	elif z <= 2e-85:
		tmp = x * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(t * z))
	tmp = 0.0
	if (z <= -1.6e+119)
		tmp = t_1;
	elseif (z <= -1.2e-99)
		tmp = Float64(x * y);
	elseif (z <= -4.4e-304)
		tmp = c;
	elseif (z <= 2e-85)
		tmp = Float64(x * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (t * z);
	tmp = 0.0;
	if (z <= -1.6e+119)
		tmp = t_1;
	elseif (z <= -1.2e-99)
		tmp = x * y;
	elseif (z <= -4.4e-304)
		tmp = c;
	elseif (z <= 2e-85)
		tmp = x * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+119], t$95$1, If[LessEqual[z, -1.2e-99], N[(x * y), $MachinePrecision], If[LessEqual[z, -4.4e-304], c, If[LessEqual[z, 2e-85], N[(x * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999995e119 or 2e-85 < z

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 62.3%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*r* 62.3%

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

   4. Simplified 62.3%

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

   5. Taylor expanded in t around inf 44.4%

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

   if -1.59999999999999995e119 < z < -1.2e-99 or -4.4e-304 < z < 2e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.7%

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

   3. Taylor expanded in y around inf 41.9%

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

   if -1.2e-99 < z < -4.4e-304

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 34.3%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+119}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-99}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-304}:\\ \;\;\;\;c\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-85}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \end{array} \]

Alternative 14: 63.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+162} \lor \neg \left(b \cdot a \leq 1.2 \cdot 10^{+109}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -1e+162) (not (<= (* b a) 1.2e+109)))
   (* (* b a) -0.25)
   (+ c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1e+162) || !((b * a) <= 1.2e+109)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-1d+162)) .or. (.not. ((b * a) <= 1.2d+109))) then
        tmp = (b * a) * (-0.25d0)
    else
        tmp = c + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -1e+162) || !((b * a) <= 1.2e+109)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = c + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -1e+162) or not ((b * a) <= 1.2e+109):
		tmp = (b * a) * -0.25
	else:
		tmp = c + (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -1e+162) || !(Float64(b * a) <= 1.2e+109))
		tmp = Float64(Float64(b * a) * -0.25);
	else
		tmp = Float64(c + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -1e+162) || ~(((b * a) <= 1.2e+109)))
		tmp = (b * a) * -0.25;
	else
		tmp = c + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -1e+162], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.2e+109]], $MachinePrecision]], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision], N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -9.9999999999999994e161 or 1.19999999999999994e109 < (*.f64 a b)

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 80.9%

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

   3. Taylor expanded in a around inf 69.2%

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

      1. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -9.9999999999999994e161 < (*.f64 a b) < 1.19999999999999994e109

   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 inf 64.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+162} \lor \neg \left(b \cdot a \leq 1.2 \cdot 10^{+109}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;c + x \cdot y\\ \end{array} \]

Alternative 15: 36.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.01 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -1.01e+62) (* x y) (if (<= x 3.4e-124) c (* x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.01e+62) {
		tmp = x * y;
	} else if (x <= 3.4e-124) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (x <= (-1.01d+62)) then
        tmp = x * y
    else if (x <= 3.4d-124) then
        tmp = c
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -1.01e+62) {
		tmp = x * y;
	} else if (x <= 3.4e-124) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -1.01e+62:
		tmp = x * y
	elif x <= 3.4e-124:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -1.01e+62)
		tmp = Float64(x * y);
	elseif (x <= 3.4e-124)
		tmp = c;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (x <= -1.01e+62)
		tmp = x * y;
	elseif (x <= 3.4e-124)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -1.01e+62], N[(x * y), $MachinePrecision], If[LessEqual[x, 3.4e-124], c, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01e62 or 3.4000000000000001e-124 < x

   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 z around 0 82.8%

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

   3. Taylor expanded in y around inf 44.9%

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

   if -1.01e62 < x < 3.4000000000000001e-124

   1. Initial program 97.4%

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

   2. Taylor expanded in c around inf 28.4%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.01 \cdot 10^{+62}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-124}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 16: 21.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in c around inf 22.7%

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

3. Final simplification 22.7%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023257 
(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))