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

Percentage Accurate: 97.4% → 98.8%

Time: 8.6s

Alternatives: 16

Speedup: 0.5×

• Unsound rule application detected in e-graph. Results may not be sound.

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.4% 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: 98.8% 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 96.8%

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

   1. associate-+l- 96.8%

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

   2. +-commutative 96.8%

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

   3. associate--l+ 96.8%

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

   4. associate-*l/ 96.8%

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

   5. *-commutative 96.8%

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

   6. fma-def 98.0%

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

   7. fma-neg 99.2%

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

   8. neg-sub0 99.2%

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

   9. associate-+l- 99.2%

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

   10. neg-sub0 99.2%

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

   11. +-commutative 99.2%

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

   12. unsub-neg 99.2%

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

   13. *-commutative 99.2%

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

   14. associate-*r/ 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 2: 98.7% accurate, 0.1× speedup

Math

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

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 y x (* (* 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(y, x, ((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(y, x, 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[(y * x + N[(N[(b * a), $MachinePrecision] * -0.25), $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 z around 0 37.5%

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

   3. Taylor expanded in c around 0 37.5%

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

      1. cancel-sign-sub-inv 37.5%

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

      2. metadata-eval 37.5%

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

      3. fma-def 75.0%

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

   5. Simplified 75.0%

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

4. Final simplification 99.2%

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

Alternative 3: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ t_3 := \left(b \cdot a\right) \cdot -0.25\\ t_4 := c + t_3\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+247}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-215}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+142}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y)))
        (t_2 (+ (* x y) (* 0.0625 (* t z))))
        (t_3 (* (* b a) -0.25))
        (t_4 (+ c t_3)))
   (if (<= (* b a) -1e+247)
     t_4
     (if (<= (* b a) -1e-215)
       t_2
       (if (<= (* b a) 2e-290)
         t_1
         (if (<= (* b a) 1e-250)
           t_2
           (if (<= (* b a) 1e-161)
             t_1
             (if (<= (* b a) 2e-120)
               (+ c (* t (* z 0.0625)))
               (if (<= (* b a) 1e+95)
                 t_2
                 (if (<= (* b a) 2e+142)
                   t_4
                   (if (<= (* b a) 3e+233) t_2 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (x * y) + (0.0625 * (t * z));
	double t_3 = (b * a) * -0.25;
	double t_4 = c + t_3;
	double tmp;
	if ((b * a) <= -1e+247) {
		tmp = t_4;
	} else if ((b * a) <= -1e-215) {
		tmp = t_2;
	} else if ((b * a) <= 2e-290) {
		tmp = t_1;
	} else if ((b * a) <= 1e-250) {
		tmp = t_2;
	} else if ((b * a) <= 1e-161) {
		tmp = t_1;
	} else if ((b * a) <= 2e-120) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 1e+95) {
		tmp = t_2;
	} else if ((b * a) <= 2e+142) {
		tmp = t_4;
	} else if ((b * a) <= 3e+233) {
		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) :: t_4
    real(8) :: tmp
    t_1 = c + (x * y)
    t_2 = (x * y) + (0.0625d0 * (t * z))
    t_3 = (b * a) * (-0.25d0)
    t_4 = c + t_3
    if ((b * a) <= (-1d+247)) then
        tmp = t_4
    else if ((b * a) <= (-1d-215)) then
        tmp = t_2
    else if ((b * a) <= 2d-290) then
        tmp = t_1
    else if ((b * a) <= 1d-250) then
        tmp = t_2
    else if ((b * a) <= 1d-161) then
        tmp = t_1
    else if ((b * a) <= 2d-120) then
        tmp = c + (t * (z * 0.0625d0))
    else if ((b * a) <= 1d+95) then
        tmp = t_2
    else if ((b * a) <= 2d+142) then
        tmp = t_4
    else if ((b * a) <= 3d+233) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (x * y);
	double t_2 = (x * y) + (0.0625 * (t * z));
	double t_3 = (b * a) * -0.25;
	double t_4 = c + t_3;
	double tmp;
	if ((b * a) <= -1e+247) {
		tmp = t_4;
	} else if ((b * a) <= -1e-215) {
		tmp = t_2;
	} else if ((b * a) <= 2e-290) {
		tmp = t_1;
	} else if ((b * a) <= 1e-250) {
		tmp = t_2;
	} else if ((b * a) <= 1e-161) {
		tmp = t_1;
	} else if ((b * a) <= 2e-120) {
		tmp = c + (t * (z * 0.0625));
	} else if ((b * a) <= 1e+95) {
		tmp = t_2;
	} else if ((b * a) <= 2e+142) {
		tmp = t_4;
	} else if ((b * a) <= 3e+233) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (x * y)
	t_2 = (x * y) + (0.0625 * (t * z))
	t_3 = (b * a) * -0.25
	t_4 = c + t_3
	tmp = 0
	if (b * a) <= -1e+247:
		tmp = t_4
	elif (b * a) <= -1e-215:
		tmp = t_2
	elif (b * a) <= 2e-290:
		tmp = t_1
	elif (b * a) <= 1e-250:
		tmp = t_2
	elif (b * a) <= 1e-161:
		tmp = t_1
	elif (b * a) <= 2e-120:
		tmp = c + (t * (z * 0.0625))
	elif (b * a) <= 1e+95:
		tmp = t_2
	elif (b * a) <= 2e+142:
		tmp = t_4
	elif (b * a) <= 3e+233:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z)))
	t_3 = Float64(Float64(b * a) * -0.25)
	t_4 = Float64(c + t_3)
	tmp = 0.0
	if (Float64(b * a) <= -1e+247)
		tmp = t_4;
	elseif (Float64(b * a) <= -1e-215)
		tmp = t_2;
	elseif (Float64(b * a) <= 2e-290)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e-250)
		tmp = t_2;
	elseif (Float64(b * a) <= 1e-161)
		tmp = t_1;
	elseif (Float64(b * a) <= 2e-120)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	elseif (Float64(b * a) <= 1e+95)
		tmp = t_2;
	elseif (Float64(b * a) <= 2e+142)
		tmp = t_4;
	elseif (Float64(b * a) <= 3e+233)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (x * y);
	t_2 = (x * y) + (0.0625 * (t * z));
	t_3 = (b * a) * -0.25;
	t_4 = c + t_3;
	tmp = 0.0;
	if ((b * a) <= -1e+247)
		tmp = t_4;
	elseif ((b * a) <= -1e-215)
		tmp = t_2;
	elseif ((b * a) <= 2e-290)
		tmp = t_1;
	elseif ((b * a) <= 1e-250)
		tmp = t_2;
	elseif ((b * a) <= 1e-161)
		tmp = t_1;
	elseif ((b * a) <= 2e-120)
		tmp = c + (t * (z * 0.0625));
	elseif ((b * a) <= 1e+95)
		tmp = t_2;
	elseif ((b * a) <= 2e+142)
		tmp = t_4;
	elseif ((b * a) <= 3e+233)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, Block[{t$95$4 = N[(c + t$95$3), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -1e+247], t$95$4, If[LessEqual[N[(b * a), $MachinePrecision], -1e-215], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 2e-290], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e-250], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 1e-161], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 2e-120], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 1e+95], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 2e+142], t$95$4, If[LessEqual[N[(b * a), $MachinePrecision], 3e+233], t$95$2, t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a b) < -9.99999999999999952e246 or 1.00000000000000002e95 < (*.f64 a b) < 2.0000000000000001e142

   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 a around inf 86.2%

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

      1. *-commutative 86.2%

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

   4. Simplified 86.2%

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

   if -9.99999999999999952e246 < (*.f64 a b) < -1.00000000000000004e-215 or 2.0000000000000001e-290 < (*.f64 a b) < 1.0000000000000001e-250 or 1.99999999999999996e-120 < (*.f64 a b) < 1.00000000000000002e95 or 2.0000000000000001e142 < (*.f64 a b) < 3.00000000000000014e233

   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. +-commutative 99.9%

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

      3. associate--l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l- 99.9%

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

      6. fma-neg 100.0%

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

      7. neg-sub0 100.0%

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

      8. associate--l- 100.0%

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

      9. associate-+l- 100.0%

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

      10. neg-sub0 100.0%

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

      11. *-commutative 100.0%

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

      12. associate-*r/ 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. fma-def 100.0%

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

      15. distribute-frac-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

   4. Taylor expanded in b around 0 88.9%

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

   5. Taylor expanded in c around 0 76.0%

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

   if -1.00000000000000004e-215 < (*.f64 a b) < 2.0000000000000001e-290 or 1.0000000000000001e-250 < (*.f64 a b) < 1.00000000000000003e-161

   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 x around inf 86.4%

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

   if 1.00000000000000003e-161 < (*.f64 a b) < 1.99999999999999996e-120

   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 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if 3.00000000000000014e233 < (*.f64 a b)

   1. Initial program 80.0%

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

   2. Taylor expanded in a around inf 84.9%

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

      1. *-commutative 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in a around inf 84.9%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+247}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-215}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-290}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{-250}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{-161}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+95}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+142}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 4: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + x \cdot y\\ t_3 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{-161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (+ c (* x y)))
        (t_3 (* (* b a) -0.25)))
   (if (<= (* b a) -5e+185)
     t_3
     (if (<= (* b a) -1e-215)
       t_1
       (if (<= (* b a) 1e-161)
         t_2
         (if (<= (* b a) 2e-120)
           t_1
           (if (<= (* b a) 1e+26)
             t_2
             (if (<= (* b a) 1e+159)
               t_1
               (if (<= (* b a) 3e+233) 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 + (x * y);
	double t_3 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = t_3;
	} else if ((b * a) <= -1e-215) {
		tmp = t_1;
	} else if ((b * a) <= 1e-161) {
		tmp = t_2;
	} else if ((b * a) <= 2e-120) {
		tmp = t_1;
	} else if ((b * a) <= 1e+26) {
		tmp = t_2;
	} else if ((b * a) <= 1e+159) {
		tmp = t_1;
	} else if ((b * a) <= 3e+233) {
		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 + (x * y)
    t_3 = (b * a) * (-0.25d0)
    if ((b * a) <= (-5d+185)) then
        tmp = t_3
    else if ((b * a) <= (-1d-215)) then
        tmp = t_1
    else if ((b * a) <= 1d-161) then
        tmp = t_2
    else if ((b * a) <= 2d-120) then
        tmp = t_1
    else if ((b * a) <= 1d+26) then
        tmp = t_2
    else if ((b * a) <= 1d+159) then
        tmp = t_1
    else if ((b * a) <= 3d+233) 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 + (x * y);
	double t_3 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = t_3;
	} else if ((b * a) <= -1e-215) {
		tmp = t_1;
	} else if ((b * a) <= 1e-161) {
		tmp = t_2;
	} else if ((b * a) <= 2e-120) {
		tmp = t_1;
	} else if ((b * a) <= 1e+26) {
		tmp = t_2;
	} else if ((b * a) <= 1e+159) {
		tmp = t_1;
	} else if ((b * a) <= 3e+233) {
		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 + (x * y)
	t_3 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -5e+185:
		tmp = t_3
	elif (b * a) <= -1e-215:
		tmp = t_1
	elif (b * a) <= 1e-161:
		tmp = t_2
	elif (b * a) <= 2e-120:
		tmp = t_1
	elif (b * a) <= 1e+26:
		tmp = t_2
	elif (b * a) <= 1e+159:
		tmp = t_1
	elif (b * a) <= 3e+233:
		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(x * y))
	t_3 = Float64(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -5e+185)
		tmp = t_3;
	elseif (Float64(b * a) <= -1e-215)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e-161)
		tmp = t_2;
	elseif (Float64(b * a) <= 2e-120)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e+26)
		tmp = t_2;
	elseif (Float64(b * a) <= 1e+159)
		tmp = t_1;
	elseif (Float64(b * a) <= 3e+233)
		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 + (x * y);
	t_3 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -5e+185)
		tmp = t_3;
	elseif ((b * a) <= -1e-215)
		tmp = t_1;
	elseif ((b * a) <= 1e-161)
		tmp = t_2;
	elseif ((b * a) <= 2e-120)
		tmp = t_1;
	elseif ((b * a) <= 1e+26)
		tmp = t_2;
	elseif ((b * a) <= 1e+159)
		tmp = t_1;
	elseif ((b * a) <= 3e+233)
		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[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+185], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], -1e-215], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e-161], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 2e-120], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e+26], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], 1e+159], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 3e+233], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e185 or 3.00000000000000014e233 < (*.f64 a b)

   1. Initial program 87.9%

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

   2. Taylor expanded in a around inf 80.4%

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

      1. *-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in a around inf 78.7%

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

   if -4.9999999999999999e185 < (*.f64 a b) < -1.00000000000000004e-215 or 1.00000000000000003e-161 < (*.f64 a b) < 1.99999999999999996e-120 or 1.00000000000000005e26 < (*.f64 a b) < 9.9999999999999993e158

   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 64.1%

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

      1. *-commutative 64.1%

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

      2. associate-*r* 64.1%

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

      3. *-commutative 64.1%

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

   4. Simplified 64.1%

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

   if -1.00000000000000004e-215 < (*.f64 a b) < 1.00000000000000003e-161 or 1.99999999999999996e-120 < (*.f64 a b) < 1.00000000000000005e26 or 9.9999999999999993e158 < (*.f64 a b) < 3.00000000000000014e233

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 77.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-215}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{-161}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+26}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 10^{+159}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 5: 98.3% accurate, 0.5× speedup

Math

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

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) (+ 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 = c + ((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 = c + ((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 = 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 = Float64(c + 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 = c + ((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[(c + N[(N[(b * a), $MachinePrecision] * -0.25), $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 a around inf 62.9%

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

      1. *-commutative 62.9%

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

   4. Simplified 62.9%

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

4. Final simplification 98.8%

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

Alternative 6: 64.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + t \cdot \left(z \cdot 0.0625\right)\\ t_2 := c + \left(b \cdot a\right) \cdot -0.25\\ t_3 := c + x \cdot y\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* t (* z 0.0625))))
        (t_2 (+ c (* (* b a) -0.25)))
        (t_3 (+ c (* x y))))
   (if (<= (* b a) -5e+185)
     t_2
     (if (<= (* b a) -1e-215)
       t_1
       (if (<= (* b a) 1e-161)
         t_3
         (if (<= (* b a) 2e-120) t_1 (if (<= (* b a) 1e+27) t_3 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 + ((b * a) * -0.25);
	double t_3 = c + (x * y);
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = t_2;
	} else if ((b * a) <= -1e-215) {
		tmp = t_1;
	} else if ((b * a) <= 1e-161) {
		tmp = t_3;
	} else if ((b * a) <= 2e-120) {
		tmp = t_1;
	} else if ((b * a) <= 1e+27) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = c + (t * (z * 0.0625d0))
    t_2 = c + ((b * a) * (-0.25d0))
    t_3 = c + (x * y)
    if ((b * a) <= (-5d+185)) then
        tmp = t_2
    else if ((b * a) <= (-1d-215)) then
        tmp = t_1
    else if ((b * a) <= 1d-161) then
        tmp = t_3
    else if ((b * a) <= 2d-120) then
        tmp = t_1
    else if ((b * a) <= 1d+27) then
        tmp = t_3
    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 + ((b * a) * -0.25);
	double t_3 = c + (x * y);
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = t_2;
	} else if ((b * a) <= -1e-215) {
		tmp = t_1;
	} else if ((b * a) <= 1e-161) {
		tmp = t_3;
	} else if ((b * a) <= 2e-120) {
		tmp = t_1;
	} else if ((b * a) <= 1e+27) {
		tmp = t_3;
	} 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 + ((b * a) * -0.25)
	t_3 = c + (x * y)
	tmp = 0
	if (b * a) <= -5e+185:
		tmp = t_2
	elif (b * a) <= -1e-215:
		tmp = t_1
	elif (b * a) <= 1e-161:
		tmp = t_3
	elif (b * a) <= 2e-120:
		tmp = t_1
	elif (b * a) <= 1e+27:
		tmp = t_3
	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(Float64(b * a) * -0.25))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (Float64(b * a) <= -5e+185)
		tmp = t_2;
	elseif (Float64(b * a) <= -1e-215)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e-161)
		tmp = t_3;
	elseif (Float64(b * a) <= 2e-120)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e+27)
		tmp = t_3;
	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 + ((b * a) * -0.25);
	t_3 = c + (x * y);
	tmp = 0.0;
	if ((b * a) <= -5e+185)
		tmp = t_2;
	elseif ((b * a) <= -1e-215)
		tmp = t_1;
	elseif ((b * a) <= 1e-161)
		tmp = t_3;
	elseif ((b * a) <= 2e-120)
		tmp = t_1;
	elseif ((b * a) <= 1e+27)
		tmp = t_3;
	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[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+185], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -1e-215], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e-161], t$95$3, If[LessEqual[N[(b * a), $MachinePrecision], 2e-120], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e+27], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e185 or 1e27 < (*.f64 a b)

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 69.2%

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

      1. *-commutative 69.2%

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

   4. Simplified 69.2%

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

   if -4.9999999999999999e185 < (*.f64 a b) < -1.00000000000000004e-215 or 1.00000000000000003e-161 < (*.f64 a b) < 1.99999999999999996e-120

   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 66.6%

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

      1. *-commutative 66.6%

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

      2. associate-*r* 66.6%

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

      3. *-commutative 66.6%

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

   4. Simplified 66.6%

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

   if -1.00000000000000004e-215 < (*.f64 a b) < 1.00000000000000003e-161 or 1.99999999999999996e-120 < (*.f64 a b) < 1e27

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 77.9%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -1 \cdot 10^{-215}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{-161}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+27}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 7: 43.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq 10^{+27}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))) (t_2 (* (* b a) -0.25)))
   (if (<= (* b a) -5e+185)
     t_2
     (if (<= (* b a) -5e-102)
       t_1
       (if (<= (* b a) 5e-157)
         (* x y)
         (if (<= (* b a) 2e-120) t_1 (if (<= (* b a) 1e+27) (* x y) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (t * z);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = t_2;
	} else if ((b * a) <= -5e-102) {
		tmp = t_1;
	} else if ((b * a) <= 5e-157) {
		tmp = x * y;
	} else if ((b * a) <= 2e-120) {
		tmp = t_1;
	} else if ((b * a) <= 1e+27) {
		tmp = 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 = 0.0625d0 * (t * z)
    t_2 = (b * a) * (-0.25d0)
    if ((b * a) <= (-5d+185)) then
        tmp = t_2
    else if ((b * a) <= (-5d-102)) then
        tmp = t_1
    else if ((b * a) <= 5d-157) then
        tmp = x * y
    else if ((b * a) <= 2d-120) then
        tmp = t_1
    else if ((b * a) <= 1d+27) then
        tmp = 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 = 0.0625 * (t * z);
	double t_2 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = t_2;
	} else if ((b * a) <= -5e-102) {
		tmp = t_1;
	} else if ((b * a) <= 5e-157) {
		tmp = x * y;
	} else if ((b * a) <= 2e-120) {
		tmp = t_1;
	} else if ((b * a) <= 1e+27) {
		tmp = x * y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (t * z)
	t_2 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -5e+185:
		tmp = t_2
	elif (b * a) <= -5e-102:
		tmp = t_1
	elif (b * a) <= 5e-157:
		tmp = x * y
	elif (b * a) <= 2e-120:
		tmp = t_1
	elif (b * a) <= 1e+27:
		tmp = x * y
	else:
		tmp = t_2
	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)
	tmp = 0.0
	if (Float64(b * a) <= -5e+185)
		tmp = t_2;
	elseif (Float64(b * a) <= -5e-102)
		tmp = t_1;
	elseif (Float64(b * a) <= 5e-157)
		tmp = Float64(x * y);
	elseif (Float64(b * a) <= 2e-120)
		tmp = t_1;
	elseif (Float64(b * a) <= 1e+27)
		tmp = 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 = 0.0625 * (t * z);
	t_2 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -5e+185)
		tmp = t_2;
	elseif ((b * a) <= -5e-102)
		tmp = t_1;
	elseif ((b * a) <= 5e-157)
		tmp = x * y;
	elseif ((b * a) <= 2e-120)
		tmp = t_1;
	elseif ((b * a) <= 1e+27)
		tmp = 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[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+185], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -5e-102], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 5e-157], N[(x * y), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e-120], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], 1e+27], N[(x * y), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e185 or 1e27 < (*.f64 a b)

   1. Initial program 92.0%

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

   2. Taylor expanded in a around inf 69.2%

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

      1. *-commutative 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in a around inf 63.6%

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

   if -4.9999999999999999e185 < (*.f64 a b) < -5.00000000000000026e-102 or 5.0000000000000002e-157 < (*.f64 a b) < 1.99999999999999996e-120

   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. +-commutative 99.9%

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

      3. associate--l+ 99.9%

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

      4. +-commutative 99.9%

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

      5. associate-+l- 99.9%

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

      6. fma-neg 99.9%

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

      7. neg-sub0 99.9%

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

      8. associate--l- 99.9%

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

      9. associate-+l- 99.9%

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

      10. neg-sub0 99.9%

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

      11. *-commutative 99.9%

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

      12. associate-*r/ 99.9%

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

      13. distribute-rgt-neg-in 99.9%

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

      14. fma-def 99.9%

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

      15. distribute-frac-neg 99.9%

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

      16. neg-mul-1 99.9%

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

      17. associate-/l* 99.9%

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

      18. associate-/r/ 99.9%

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

      19. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

   4. Taylor expanded in b around 0 88.5%

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

   5. Taylor expanded in t around inf 48.7%

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

   if -5.00000000000000026e-102 < (*.f64 a b) < 5.0000000000000002e-157 or 1.99999999999999996e-120 < (*.f64 a b) < 1e27

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. +-commutative 99.1%

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

      3. associate--l+ 99.1%

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

      4. +-commutative 99.1%

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

      5. associate-+l- 99.1%

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

      6. fma-neg 99.1%

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

      7. neg-sub0 99.1%

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

      8. associate--l- 99.1%

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

      9. associate-+l- 99.1%

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

      10. neg-sub0 99.1%

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

      11. *-commutative 99.1%

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

      12. associate-*r/ 99.1%

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

      13. distribute-rgt-neg-in 99.1%

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

      14. fma-def 99.1%

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

      15. distribute-frac-neg 99.1%

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

      16. neg-mul-1 99.1%

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

      17. associate-/l* 99.1%

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

      18. associate-/r/ 99.1%

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

      19. metadata-eval 99.1%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

   4. Taylor expanded in b around 0 98.7%

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

   5. Taylor expanded in x around inf 48.3%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-102}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{-120}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 10^{+27}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 8: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ t_2 := x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ t_3 := c + x \cdot y\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-194}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-27}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* 0.0625 (* t z))))
        (t_2 (- (* x y) (* (* b a) 0.25)))
        (t_3 (+ c (* x y))))
   (if (<= a -1.15e+74)
     t_2
     (if (<= a -6.2e-15)
       t_1
       (if (<= a -2.1e-60)
         t_3
         (if (<= a -9.8e-210)
           t_1
           (if (<= a 1.6e-194)
             t_3
             (if (<= a 9.6e-27) (+ c (* t (* z 0.0625))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * y) + (0.0625 * (t * z));
	double t_2 = (x * y) - ((b * a) * 0.25);
	double t_3 = c + (x * y);
	double tmp;
	if (a <= -1.15e+74) {
		tmp = t_2;
	} else if (a <= -6.2e-15) {
		tmp = t_1;
	} else if (a <= -2.1e-60) {
		tmp = t_3;
	} else if (a <= -9.8e-210) {
		tmp = t_1;
	} else if (a <= 1.6e-194) {
		tmp = t_3;
	} else if (a <= 9.6e-27) {
		tmp = c + (t * (z * 0.0625));
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (x * y) + (0.0625d0 * (t * z))
    t_2 = (x * y) - ((b * a) * 0.25d0)
    t_3 = c + (x * y)
    if (a <= (-1.15d+74)) then
        tmp = t_2
    else if (a <= (-6.2d-15)) then
        tmp = t_1
    else if (a <= (-2.1d-60)) then
        tmp = t_3
    else if (a <= (-9.8d-210)) then
        tmp = t_1
    else if (a <= 1.6d-194) then
        tmp = t_3
    else if (a <= 9.6d-27) then
        tmp = c + (t * (z * 0.0625d0))
    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 = (x * y) + (0.0625 * (t * z));
	double t_2 = (x * y) - ((b * a) * 0.25);
	double t_3 = c + (x * y);
	double tmp;
	if (a <= -1.15e+74) {
		tmp = t_2;
	} else if (a <= -6.2e-15) {
		tmp = t_1;
	} else if (a <= -2.1e-60) {
		tmp = t_3;
	} else if (a <= -9.8e-210) {
		tmp = t_1;
	} else if (a <= 1.6e-194) {
		tmp = t_3;
	} else if (a <= 9.6e-27) {
		tmp = c + (t * (z * 0.0625));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (x * y) + (0.0625 * (t * z))
	t_2 = (x * y) - ((b * a) * 0.25)
	t_3 = c + (x * y)
	tmp = 0
	if a <= -1.15e+74:
		tmp = t_2
	elif a <= -6.2e-15:
		tmp = t_1
	elif a <= -2.1e-60:
		tmp = t_3
	elif a <= -9.8e-210:
		tmp = t_1
	elif a <= 1.6e-194:
		tmp = t_3
	elif a <= 9.6e-27:
		tmp = c + (t * (z * 0.0625))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(b * a) * 0.25))
	t_3 = Float64(c + Float64(x * y))
	tmp = 0.0
	if (a <= -1.15e+74)
		tmp = t_2;
	elseif (a <= -6.2e-15)
		tmp = t_1;
	elseif (a <= -2.1e-60)
		tmp = t_3;
	elseif (a <= -9.8e-210)
		tmp = t_1;
	elseif (a <= 1.6e-194)
		tmp = t_3;
	elseif (a <= 9.6e-27)
		tmp = Float64(c + Float64(t * Float64(z * 0.0625)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * y) + (0.0625 * (t * z));
	t_2 = (x * y) - ((b * a) * 0.25);
	t_3 = c + (x * y);
	tmp = 0.0;
	if (a <= -1.15e+74)
		tmp = t_2;
	elseif (a <= -6.2e-15)
		tmp = t_1;
	elseif (a <= -2.1e-60)
		tmp = t_3;
	elseif (a <= -9.8e-210)
		tmp = t_1;
	elseif (a <= 1.6e-194)
		tmp = t_3;
	elseif (a <= 9.6e-27)
		tmp = c + (t * (z * 0.0625));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+74], t$95$2, If[LessEqual[a, -6.2e-15], t$95$1, If[LessEqual[a, -2.1e-60], t$95$3, If[LessEqual[a, -9.8e-210], t$95$1, If[LessEqual[a, 1.6e-194], t$95$3, If[LessEqual[a, 9.6e-27], N[(c + N[(t * N[(z * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.1499999999999999e74 or 9.60000000000000008e-27 < a

   1. Initial program 92.5%

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

   2. Taylor expanded in z around 0 72.9%

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

   3. Taylor expanded in c around 0 67.4%

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

   if -1.1499999999999999e74 < a < -6.1999999999999998e-15 or -2.09999999999999991e-60 < a < -9.7999999999999996e-210

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. fma-neg 100.0%

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

      7. neg-sub0 100.0%

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

      8. associate--l- 100.0%

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

      9. associate-+l- 100.0%

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

      10. neg-sub0 100.0%

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

      11. *-commutative 100.0%

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

      12. associate-*r/ 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. fma-def 100.0%

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

      15. distribute-frac-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

   4. Taylor expanded in b around 0 95.9%

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

   5. Taylor expanded in c around 0 70.2%

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

   if -6.1999999999999998e-15 < a < -2.09999999999999991e-60 or -9.7999999999999996e-210 < a < 1.6000000000000001e-194

   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 74.0%

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

   if 1.6000000000000001e-194 < a < 9.60000000000000008e-27

   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 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-*r* 59.2%

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

      3. *-commutative 59.2%

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

   4. Simplified 59.2%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+74}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-60}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-210}:\\ \;\;\;\;x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-194}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-27}:\\ \;\;\;\;c + t \cdot \left(z \cdot 0.0625\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 9: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + x \cdot y\\ t_2 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \cdot a \leq -2000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-23}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* x y))) (t_2 (* (* b a) -0.25)))
   (if (<= (* b a) -5e+258)
     t_2
     (if (<= (* b a) -2000000000000.0)
       t_1
       (if (<= (* b a) -5e-23)
         (* 0.0625 (* t z))
         (if (<= (* b a) 3e+233) 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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5e+258) {
		tmp = t_2;
	} else if ((b * a) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((b * a) <= -5e-23) {
		tmp = 0.0625 * (t * z);
	} else if ((b * a) <= 3e+233) {
		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 = (b * a) * (-0.25d0)
    if ((b * a) <= (-5d+258)) then
        tmp = t_2
    else if ((b * a) <= (-2000000000000.0d0)) then
        tmp = t_1
    else if ((b * a) <= (-5d-23)) then
        tmp = 0.0625d0 * (t * z)
    else if ((b * a) <= 3d+233) 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 = (b * a) * -0.25;
	double tmp;
	if ((b * a) <= -5e+258) {
		tmp = t_2;
	} else if ((b * a) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((b * a) <= -5e-23) {
		tmp = 0.0625 * (t * z);
	} else if ((b * a) <= 3e+233) {
		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 = (b * a) * -0.25
	tmp = 0
	if (b * a) <= -5e+258:
		tmp = t_2
	elif (b * a) <= -2000000000000.0:
		tmp = t_1
	elif (b * a) <= -5e-23:
		tmp = 0.0625 * (t * z)
	elif (b * a) <= 3e+233:
		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(Float64(b * a) * -0.25)
	tmp = 0.0
	if (Float64(b * a) <= -5e+258)
		tmp = t_2;
	elseif (Float64(b * a) <= -2000000000000.0)
		tmp = t_1;
	elseif (Float64(b * a) <= -5e-23)
		tmp = Float64(0.0625 * Float64(t * z));
	elseif (Float64(b * a) <= 3e+233)
		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 = (b * a) * -0.25;
	tmp = 0.0;
	if ((b * a) <= -5e+258)
		tmp = t_2;
	elseif ((b * a) <= -2000000000000.0)
		tmp = t_1;
	elseif ((b * a) <= -5e-23)
		tmp = 0.0625 * (t * z);
	elseif ((b * a) <= 3e+233)
		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[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+258], t$95$2, If[LessEqual[N[(b * a), $MachinePrecision], -2000000000000.0], t$95$1, If[LessEqual[N[(b * a), $MachinePrecision], -5e-23], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 3e+233], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5e258 or 3.00000000000000014e233 < (*.f64 a b)

   1. Initial program 86.0%

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

   2. Taylor expanded in a around inf 86.6%

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

      1. *-commutative 86.6%

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

   4. Simplified 86.6%

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

   5. Taylor expanded in a around inf 86.6%

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

   if -5e258 < (*.f64 a b) < -2e12 or -5.0000000000000002e-23 < (*.f64 a b) < 3.00000000000000014e233

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 63.3%

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

   if -2e12 < (*.f64 a b) < -5.0000000000000002e-23

   1. Initial program 100.0%

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

      1. associate-+l- 100.0%

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

      2. +-commutative 100.0%

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

      3. associate--l+ 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+l- 100.0%

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

      6. fma-neg 100.0%

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

      7. neg-sub0 100.0%

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

      8. associate--l- 100.0%

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

      9. associate-+l- 100.0%

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

      10. neg-sub0 100.0%

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

      11. *-commutative 100.0%

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

      12. associate-*r/ 100.0%

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

      13. distribute-rgt-neg-in 100.0%

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

      14. fma-def 100.0%

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

      15. distribute-frac-neg 100.0%

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

      16. neg-mul-1 100.0%

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

      17. associate-/l* 100.0%

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

      18. associate-/r/ 100.0%

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

      19. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

   4. Taylor expanded in b around 0 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+258}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq -2000000000000:\\ \;\;\;\;c + x \cdot y\\ \mathbf{elif}\;b \cdot a \leq -5 \cdot 10^{-23}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 10: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot 0.25\\ t_2 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;\left(c + x \cdot y\right) - t_1\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+54}:\\ \;\;\;\;c + \left(x \cdot y + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + t_2\right) - t_1\\ \end{array} \end{array} \]

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+185)
     (- (+ c (* x y)) t_1)
     (if (<= (* b a) 5e+54) (+ c (+ (* x y) t_2)) (- (+ c t_2) 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 t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = (c + (x * y)) - t_1;
	} else if ((b * a) <= 5e+54) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * a) * 0.25d0
    t_2 = 0.0625d0 * (t * z)
    if ((b * a) <= (-5d+185)) then
        tmp = (c + (x * y)) - t_1
    else if ((b * a) <= 5d+54) then
        tmp = c + ((x * y) + t_2)
    else
        tmp = (c + t_2) - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b * a) * 0.25;
	double t_2 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -5e+185) {
		tmp = (c + (x * y)) - t_1;
	} else if ((b * a) <= 5e+54) {
		tmp = c + ((x * y) + t_2);
	} else {
		tmp = (c + t_2) - t_1;
	}
	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+185:
		tmp = (c + (x * y)) - t_1
	elif (b * a) <= 5e+54:
		tmp = c + ((x * y) + t_2)
	else:
		tmp = (c + t_2) - t_1
	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+185)
		tmp = Float64(Float64(c + Float64(x * y)) - t_1);
	elseif (Float64(b * a) <= 5e+54)
		tmp = Float64(c + Float64(Float64(x * y) + t_2));
	else
		tmp = Float64(Float64(c + t_2) - t_1);
	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+185)
		tmp = (c + (x * y)) - t_1;
	elseif ((b * a) <= 5e+54)
		tmp = c + ((x * y) + t_2);
	else
		tmp = (c + t_2) - 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]}, Block[{t$95$2 = N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+185], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 5e+54], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(c + t$95$2), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e185

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 88.3%

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

   if -4.9999999999999999e185 < (*.f64 a b) < 5.00000000000000005e54

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 94.4%

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

   if 5.00000000000000005e54 < (*.f64 a b)

   1. Initial program 89.4%

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

   2. Taylor expanded in x around 0 79.5%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 5 \cdot 10^{+54}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c + 0.0625 \cdot \left(t \cdot z\right)\right) - \left(b \cdot a\right) \cdot 0.25\\ \end{array} \]

Alternative 11: 84.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot a\right) \cdot -0.25\\ \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+247}:\\ \;\;\;\;c + t_1\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* b a) -0.25)))
   (if (<= (* b a) -1e+247)
     (+ c t_1)
     (if (<= (* b a) 3e+233) (+ c (+ (* x y) (* 0.0625 (* t z)))) 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) <= -1e+247) {
		tmp = c + t_1;
	} else if ((b * a) <= 3e+233) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} 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) <= (-1d+247)) then
        tmp = c + t_1
    else if ((b * a) <= 3d+233) then
        tmp = c + ((x * y) + (0.0625d0 * (t * z)))
    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) <= -1e+247) {
		tmp = c + t_1;
	} else if ((b * a) <= 3e+233) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} 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) <= -1e+247:
		tmp = c + t_1
	elif (b * a) <= 3e+233:
		tmp = c + ((x * y) + (0.0625 * (t * z)))
	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) <= -1e+247)
		tmp = Float64(c + t_1);
	elseif (Float64(b * a) <= 3e+233)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z))));
	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) <= -1e+247)
		tmp = c + t_1;
	elseif ((b * a) <= 3e+233)
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	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], -1e+247], N[(c + t$95$1), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 3e+233], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -9.99999999999999952e246

   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 a around inf 86.3%

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

      1. *-commutative 86.3%

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

   4. Simplified 86.3%

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

   if -9.99999999999999952e246 < (*.f64 a b) < 3.00000000000000014e233

   1. Initial program 99.5%

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

   2. Taylor expanded in a around 0 91.3%

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

   if 3.00000000000000014e233 < (*.f64 a b)

   1. Initial program 80.0%

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

   2. Taylor expanded in a around inf 84.9%

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

      1. *-commutative 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in a around inf 84.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -1 \cdot 10^{+247}:\\ \;\;\;\;c + \left(b \cdot a\right) \cdot -0.25\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 12: 84.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+258}:\\ \;\;\;\;t_1 - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + \left(x \cdot y + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* t z))))
   (if (<= (* b a) -5e+258)
     (- t_1 (* (* b a) 0.25))
     (if (<= (* b a) 3e+233) (+ c (+ (* x y) 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 = 0.0625 * (t * z);
	double tmp;
	if ((b * a) <= -5e+258) {
		tmp = t_1 - ((b * a) * 0.25);
	} else if ((b * a) <= 3e+233) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (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) <= (-5d+258)) then
        tmp = t_1 - ((b * a) * 0.25d0)
    else if ((b * a) <= 3d+233) then
        tmp = c + ((x * y) + t_1)
    else
        tmp = (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) <= -5e+258) {
		tmp = t_1 - ((b * a) * 0.25);
	} else if ((b * a) <= 3e+233) {
		tmp = c + ((x * y) + t_1);
	} else {
		tmp = (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) <= -5e+258:
		tmp = t_1 - ((b * a) * 0.25)
	elif (b * a) <= 3e+233:
		tmp = c + ((x * y) + t_1)
	else:
		tmp = (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) <= -5e+258)
		tmp = Float64(t_1 - Float64(Float64(b * a) * 0.25));
	elseif (Float64(b * a) <= 3e+233)
		tmp = Float64(c + Float64(Float64(x * y) + 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 = 0.0625 * (t * z);
	tmp = 0.0;
	if ((b * a) <= -5e+258)
		tmp = t_1 - ((b * a) * 0.25);
	elseif ((b * a) <= 3e+233)
		tmp = c + ((x * y) + 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[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+258], N[(t$95$1 - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 3e+233], N[(c + N[(N[(x * y), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5e258

   1. Initial program 92.0%

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

   2. Taylor expanded in x around 0 92.0%

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

   3. Taylor expanded in c around 0 92.0%

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

   if -5e258 < (*.f64 a b) < 3.00000000000000014e233

   1. Initial program 99.5%

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

   2. Taylor expanded in a around 0 90.9%

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

   if 3.00000000000000014e233 < (*.f64 a b)

   1. Initial program 80.0%

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

   2. Taylor expanded in a around inf 84.9%

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

      1. *-commutative 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in a around inf 84.9%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+258}:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 13: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* b a) -5e+185)
   (- (+ c (* x y)) (* (* b a) 0.25))
   (if (<= (* b a) 3e+233)
     (+ c (+ (* x y) (* 0.0625 (* t z))))
     (* (* 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) <= -5e+185) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else if ((b * a) <= 3e+233) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} else {
		tmp = (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) <= (-5d+185)) then
        tmp = (c + (x * y)) - ((b * a) * 0.25d0)
    else if ((b * a) <= 3d+233) then
        tmp = c + ((x * y) + (0.0625d0 * (t * z)))
    else
        tmp = (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) <= -5e+185) {
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	} else if ((b * a) <= 3e+233) {
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	} else {
		tmp = (b * a) * -0.25;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b * a) <= -5e+185:
		tmp = (c + (x * y)) - ((b * a) * 0.25)
	elif (b * a) <= 3e+233:
		tmp = c + ((x * y) + (0.0625 * (t * z)))
	else:
		tmp = (b * a) * -0.25
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b * a) <= -5e+185)
		tmp = Float64(Float64(c + Float64(x * y)) - Float64(Float64(b * a) * 0.25));
	elseif (Float64(b * a) <= 3e+233)
		tmp = Float64(c + Float64(Float64(x * y) + Float64(0.0625 * Float64(t * z))));
	else
		tmp = Float64(Float64(b * 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) <= -5e+185)
		tmp = (c + (x * y)) - ((b * a) * 0.25);
	elseif ((b * a) <= 3e+233)
		tmp = c + ((x * y) + (0.0625 * (t * z)));
	else
		tmp = (b * a) * -0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b * a), $MachinePrecision], -5e+185], N[(N[(c + N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 3e+233], N[(c + N[(N[(x * y), $MachinePrecision] + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -4.9999999999999999e185

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 88.3%

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

   if -4.9999999999999999e185 < (*.f64 a b) < 3.00000000000000014e233

   1. Initial program 99.4%

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

   2. Taylor expanded in a around 0 91.6%

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

   if 3.00000000000000014e233 < (*.f64 a b)

   1. Initial program 80.0%

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

   2. Taylor expanded in a around inf 84.9%

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

      1. *-commutative 84.9%

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

   4. Simplified 84.9%

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

   5. Taylor expanded in a around inf 84.9%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+185}:\\ \;\;\;\;\left(c + x \cdot y\right) - \left(b \cdot a\right) \cdot 0.25\\ \mathbf{elif}\;b \cdot a \leq 3 \cdot 10^{+233}:\\ \;\;\;\;c + \left(x \cdot y + 0.0625 \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \end{array} \]

Alternative 14: 43.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \cdot a \leq -7.2 \cdot 10^{+243} \lor \neg \left(b \cdot a \leq 1.65 \cdot 10^{+28}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* b a) -7.2e+243) (not (<= (* b a) 1.65e+28)))
   (* (* b a) -0.25)
   (* x y)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -7.2e+243) || !((b * a) <= 1.65e+28)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (((b * a) <= (-7.2d+243)) .or. (.not. ((b * a) <= 1.65d+28))) then
        tmp = (b * a) * (-0.25d0)
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (((b * a) <= -7.2e+243) || !((b * a) <= 1.65e+28)) {
		tmp = (b * a) * -0.25;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((b * a) <= -7.2e+243) or not ((b * a) <= 1.65e+28):
		tmp = (b * a) * -0.25
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(b * a) <= -7.2e+243) || !(Float64(b * a) <= 1.65e+28))
		tmp = Float64(Float64(b * a) * -0.25);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((b * a) <= -7.2e+243) || ~(((b * a) <= 1.65e+28)))
		tmp = (b * a) * -0.25;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(b * a), $MachinePrecision], -7.2e+243], N[Not[LessEqual[N[(b * a), $MachinePrecision], 1.65e+28]], $MachinePrecision]], N[(N[(b * a), $MachinePrecision] * -0.25), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -7.1999999999999993e243 or 1.65e28 < (*.f64 a b)

   1. Initial program 91.5%

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

   2. Taylor expanded in a around inf 71.9%

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

      1. *-commutative 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in a around inf 66.0%

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

   if -7.1999999999999993e243 < (*.f64 a b) < 1.65e28

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. +-commutative 99.4%

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

      3. associate--l+ 99.4%

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

      4. +-commutative 99.4%

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

      5. associate-+l- 99.4%

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

      6. fma-neg 99.4%

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

      7. neg-sub0 99.4%

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

      8. associate--l- 99.4%

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

      9. associate-+l- 99.4%

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

      10. neg-sub0 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-*r/ 99.4%

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

      13. distribute-rgt-neg-in 99.4%

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

      14. fma-def 99.4%

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

      15. distribute-frac-neg 99.4%

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

      16. neg-mul-1 99.4%

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

      17. associate-/l* 99.4%

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

      18. associate-/r/ 99.4%

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

      19. metadata-eval 99.4%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

   4. Taylor expanded in b around 0 94.8%

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

   5. Taylor expanded in x around inf 40.6%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -7.2 \cdot 10^{+243} \lor \neg \left(b \cdot a \leq 1.65 \cdot 10^{+28}\right):\\ \;\;\;\;\left(b \cdot a\right) \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 15: 37.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-39}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 10^{-10}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= x -5e+79)
   (* x y)
   (if (<= x -1.9e-39)
     c
     (if (<= x -1.65e-77) (* x y) (if (<= x 1e-10) c (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (x <= -5e+79) {
		tmp = x * y;
	} else if (x <= -1.9e-39) {
		tmp = c;
	} else if (x <= -1.65e-77) {
		tmp = x * y;
	} else if (x <= 1e-10) {
		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 <= (-5d+79)) then
        tmp = x * y
    else if (x <= (-1.9d-39)) then
        tmp = c
    else if (x <= (-1.65d-77)) then
        tmp = x * y
    else if (x <= 1d-10) 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 <= -5e+79) {
		tmp = x * y;
	} else if (x <= -1.9e-39) {
		tmp = c;
	} else if (x <= -1.65e-77) {
		tmp = x * y;
	} else if (x <= 1e-10) {
		tmp = c;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if x <= -5e+79:
		tmp = x * y
	elif x <= -1.9e-39:
		tmp = c
	elif x <= -1.65e-77:
		tmp = x * y
	elif x <= 1e-10:
		tmp = c
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (x <= -5e+79)
		tmp = Float64(x * y);
	elseif (x <= -1.9e-39)
		tmp = c;
	elseif (x <= -1.65e-77)
		tmp = Float64(x * y);
	elseif (x <= 1e-10)
		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 <= -5e+79)
		tmp = x * y;
	elseif (x <= -1.9e-39)
		tmp = c;
	elseif (x <= -1.65e-77)
		tmp = x * y;
	elseif (x <= 1e-10)
		tmp = c;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[x, -5e+79], N[(x * y), $MachinePrecision], If[LessEqual[x, -1.9e-39], c, If[LessEqual[x, -1.65e-77], N[(x * y), $MachinePrecision], If[LessEqual[x, 1e-10], c, N[(x * y), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x < -5e79 or -1.9000000000000001e-39 < x < -1.64999999999999996e-77 or 1.00000000000000004e-10 < x

   1. Initial program 95.5%

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

      1. associate-+l- 95.5%

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

      2. +-commutative 95.5%

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

      3. associate--l+ 95.5%

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

      4. +-commutative 95.5%

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

      5. associate-+l- 95.5%

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

      6. fma-neg 97.7%

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

      7. neg-sub0 97.7%

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

      8. associate--l- 97.7%

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

      9. associate-+l- 97.7%

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

      10. neg-sub0 97.7%

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

      11. *-commutative 97.7%

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

      12. associate-*r/ 97.7%

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

      13. distribute-rgt-neg-in 97.7%

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

      14. fma-def 97.7%

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

      15. distribute-frac-neg 97.7%

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

      16. neg-mul-1 97.7%

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

      17. associate-/l* 97.7%

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

      18. associate-/r/ 97.7%

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

      19. metadata-eval 97.7%

          \[\leadsto \mathsf{fma}\left(x, y, \mathsf{fma}\left(b, \color{blue}{-0.25} \cdot a, c + \frac{z \cdot t}{16}\right)\right) \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \mathsf{fma}\left(b, -0.25 \cdot a, \mathsf{fma}\left(z, \frac{t}{16}, c\right)\right)\right)} \]

   4. Taylor expanded in b around 0 85.8%

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

   5. Taylor expanded in x around inf 54.9%

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

   if -5e79 < x < -1.9000000000000001e-39 or -1.64999999999999996e-77 < x < 1.00000000000000004e-10

   1. Initial program 98.3%

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

   2. Taylor expanded in c around inf 29.5%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+79}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-39}:\\ \;\;\;\;c\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 10^{-10}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 16: 22.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

2. Taylor expanded in c around inf 20.2%

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

3. Final simplification 20.2%

   \[\leadsto c \]

Reproduce

herbie shell --seed 2023176 
(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))