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

Percentage Accurate: 97.8% → 98.5%

Time: 11.9s

Alternatives: 14

Speedup: 1.0×

• 33.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, \frac{z \cdot t}{16} + \left(c - b \cdot \left(a \cdot 0.25\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (fma y x (+ (/ (* z t) 16.0) (- c (* b (* a 0.25))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(y, x, (((z * t) / 16.0) + (c - (b * (a * 0.25)))));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(y, x, Float64(Float64(Float64(z * t) / 16.0) + Float64(c - Float64(b * Float64(a * 0.25)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(y * x + N[(N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision] + N[(c - N[(b * N[(a * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.7%

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

   1. associate-+l- N/A

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

   2. associate--l+ N/A

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

   3. *-commutative N/A

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

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{x}, \left(\frac{z \cdot t}{16} - \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\left(\frac{z \cdot t}{16}\right), \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(z \cdot t\right), 16\right), \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \left(\frac{a \cdot b}{4} - c\right)\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{\_.f64}\left(\left(\frac{a \cdot b}{4}\right), c\right)\right)\right) \]

   9. div-inv N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{\_.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{1}{4}\right), c\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{\_.f64}\left(\left(\left(b \cdot a\right) \cdot \frac{1}{4}\right), c\right)\right)\right) \]

   11. associate-*l* N/A

       \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{\_.f64}\left(\left(b \cdot \left(a \cdot \frac{1}{4}\right)\right), c\right)\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(a \cdot \frac{1}{4}\right)\right), c\right)\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \left(\frac{1}{4}\right)\right)\right), c\right)\right)\right) \]

   14. metadata-eval 98.5%

       \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 16\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(a, \frac{1}{4}\right)\right), c\right)\right)\right) \]

4. Applied egg-rr 98.5%

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

5. Final simplification 98.5%

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

Alternative 2: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ t_2 := 0.0625 \cdot \left(z \cdot t\right)\\ t_3 := t\_2 + t\_1\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{-108}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;c + \left(y \cdot x + t\_2\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+243}:\\ \;\;\;\;y \cdot x + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))) (t_2 (* 0.0625 (* z t))) (t_3 (+ t_2 t_1)))
   (if (<= b -4.7e-108)
     t_3
     (if (<= b 1.2e+132)
       (+ c (+ (* y x) t_2))
       (if (<= b 1.8e+243) (+ (* y x) t_1) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = 0.0625 * (z * t);
	double t_3 = t_2 + t_1;
	double tmp;
	if (b <= -4.7e-108) {
		tmp = t_3;
	} else if (b <= 1.2e+132) {
		tmp = c + ((y * x) + t_2);
	} else if (b <= 1.8e+243) {
		tmp = (y * x) + t_1;
	} 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 = a * (b * (-0.25d0))
    t_2 = 0.0625d0 * (z * t)
    t_3 = t_2 + t_1
    if (b <= (-4.7d-108)) then
        tmp = t_3
    else if (b <= 1.2d+132) then
        tmp = c + ((y * x) + t_2)
    else if (b <= 1.8d+243) then
        tmp = (y * x) + t_1
    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 = a * (b * -0.25);
	double t_2 = 0.0625 * (z * t);
	double t_3 = t_2 + t_1;
	double tmp;
	if (b <= -4.7e-108) {
		tmp = t_3;
	} else if (b <= 1.2e+132) {
		tmp = c + ((y * x) + t_2);
	} else if (b <= 1.8e+243) {
		tmp = (y * x) + t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	t_2 = 0.0625 * (z * t)
	t_3 = t_2 + t_1
	tmp = 0
	if b <= -4.7e-108:
		tmp = t_3
	elif b <= 1.2e+132:
		tmp = c + ((y * x) + t_2)
	elif b <= 1.8e+243:
		tmp = (y * x) + t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	t_2 = Float64(0.0625 * Float64(z * t))
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (b <= -4.7e-108)
		tmp = t_3;
	elseif (b <= 1.2e+132)
		tmp = Float64(c + Float64(Float64(y * x) + t_2));
	elseif (b <= 1.8e+243)
		tmp = Float64(Float64(y * x) + t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	t_2 = 0.0625 * (z * t);
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (b <= -4.7e-108)
		tmp = t_3;
	elseif (b <= 1.2e+132)
		tmp = c + ((y * x) + t_2);
	elseif (b <= 1.8e+243)
		tmp = (y * x) + t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[b, -4.7e-108], t$95$3, If[LessEqual[b, 1.2e+132], N[(c + N[(N[(y * x), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+243], N[(N[(y * x), $MachinePrecision] + t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.70000000000000013e-108 or 1.7999999999999998e243 < b

   1. Initial program 97.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

      2. *-lowering-*.f64 79.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   5. Simplified 79.2%

      \[\leadsto \left(\color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \frac{a \cdot b}{4}\right) + c \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{\frac{-1}{4}} \cdot \left(a \cdot b\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(\left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

      11. *-lowering-*.f64 67.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

   8. Simplified 67.3%

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

   if -4.70000000000000013e-108 < b < 1.2000000000000001e132

   1. Initial program 97.7%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}, c\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      4. *-lowering-*.f64 91.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, y\right)\right), c\right) \]

   5. Simplified 91.6%

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

   if 1.2000000000000001e132 < b < 1.7999999999999998e243

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 95.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   5. Simplified 95.5%

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

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot y + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\frac{-1}{4}} \cdot \left(a \cdot b\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

      10. *-lowering-*.f64 91.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

   8. Simplified 91.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-108}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{+132}:\\ \;\;\;\;c + \left(y \cdot x + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+243}:\\ \;\;\;\;y \cdot x + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+153}:\\ \;\;\;\;t\_1 + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+99}:\\ \;\;\;\;c + \left(y \cdot x + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(y \cdot x - \frac{b \cdot a}{4}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 0.0625 (* z t))))
   (if (<= (* b a) -5e+153)
     (+ t_1 (* a (* b -0.25)))
     (if (<= (* b a) 2e+99)
       (+ c (+ (* y x) t_1))
       (+ c (- (* y x) (/ (* b a) 4.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((b * a) <= -5e+153) {
		tmp = t_1 + (a * (b * -0.25));
	} else if ((b * a) <= 2e+99) {
		tmp = c + ((y * x) + t_1);
	} else {
		tmp = c + ((y * x) - ((b * a) / 4.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.0625d0 * (z * t)
    if ((b * a) <= (-5d+153)) then
        tmp = t_1 + (a * (b * (-0.25d0)))
    else if ((b * a) <= 2d+99) then
        tmp = c + ((y * x) + t_1)
    else
        tmp = c + ((y * x) - ((b * a) / 4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 0.0625 * (z * t);
	double tmp;
	if ((b * a) <= -5e+153) {
		tmp = t_1 + (a * (b * -0.25));
	} else if ((b * a) <= 2e+99) {
		tmp = c + ((y * x) + t_1);
	} else {
		tmp = c + ((y * x) - ((b * a) / 4.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = 0.0625 * (z * t)
	tmp = 0
	if (b * a) <= -5e+153:
		tmp = t_1 + (a * (b * -0.25))
	elif (b * a) <= 2e+99:
		tmp = c + ((y * x) + t_1)
	else:
		tmp = c + ((y * x) - ((b * a) / 4.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(0.0625 * Float64(z * t))
	tmp = 0.0
	if (Float64(b * a) <= -5e+153)
		tmp = Float64(t_1 + Float64(a * Float64(b * -0.25)));
	elseif (Float64(b * a) <= 2e+99)
		tmp = Float64(c + Float64(Float64(y * x) + t_1));
	else
		tmp = Float64(c + Float64(Float64(y * x) - Float64(Float64(b * a) / 4.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = 0.0625 * (z * t);
	tmp = 0.0;
	if ((b * a) <= -5e+153)
		tmp = t_1 + (a * (b * -0.25));
	elseif ((b * a) <= 2e+99)
		tmp = c + ((y * x) + t_1);
	else
		tmp = c + ((y * x) - ((b * a) / 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(b * a), $MachinePrecision], -5e+153], N[(t$95$1 + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b * a), $MachinePrecision], 2e+99], N[(c + N[(N[(y * x), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(c + N[(N[(y * x), $MachinePrecision] - N[(N[(b * a), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -5.00000000000000018e153

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

      2. *-lowering-*.f64 97.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   5. Simplified 97.2%

      \[\leadsto \left(\color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \frac{a \cdot b}{4}\right) + c \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{\frac{-1}{4}} \cdot \left(a \cdot b\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(\left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

      11. *-lowering-*.f64 97.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

   8. Simplified 97.2%

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

   if -5.00000000000000018e153 < (*.f64 a b) < 1.9999999999999999e99

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}, c\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      4. *-lowering-*.f64 93.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, y\right)\right), c\right) \]

   5. Simplified 93.3%

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

   if 1.9999999999999999e99 < (*.f64 a b)

   1. Initial program 94.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 88.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   5. Simplified 88.0%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \cdot a \leq -5 \cdot 10^{+153}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \cdot a \leq 2 \cdot 10^{+99}:\\ \;\;\;\;c + \left(y \cdot x + 0.0625 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c + \left(y \cdot x - \frac{b \cdot a}{4}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot x - t \cdot \left(z \cdot -0.0625\right)\\ \mathbf{if}\;y \cdot x \leq -5.4 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot x \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (* y x) (* t (* z -0.0625)))))
   (if (<= (* y x) -5.4e+118)
     t_1
     (if (<= (* y x) 3.6e+91) (+ (* 0.0625 (* z t)) (* a (* b -0.25))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (y * x) - (t * (z * -0.0625));
	double tmp;
	if ((y * x) <= -5.4e+118) {
		tmp = t_1;
	} else if ((y * x) <= 3.6e+91) {
		tmp = (0.0625 * (z * t)) + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * x) - (t * (z * (-0.0625d0)))
    if ((y * x) <= (-5.4d+118)) then
        tmp = t_1
    else if ((y * x) <= 3.6d+91) then
        tmp = (0.0625d0 * (z * t)) + (a * (b * (-0.25d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (y * x) - (t * (z * -0.0625));
	double tmp;
	if ((y * x) <= -5.4e+118) {
		tmp = t_1;
	} else if ((y * x) <= 3.6e+91) {
		tmp = (0.0625 * (z * t)) + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (y * x) - (t * (z * -0.0625))
	tmp = 0
	if (y * x) <= -5.4e+118:
		tmp = t_1
	elif (y * x) <= 3.6e+91:
		tmp = (0.0625 * (z * t)) + (a * (b * -0.25))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(y * x) - Float64(t * Float64(z * -0.0625)))
	tmp = 0.0
	if (Float64(y * x) <= -5.4e+118)
		tmp = t_1;
	elseif (Float64(y * x) <= 3.6e+91)
		tmp = Float64(Float64(0.0625 * Float64(z * t)) + Float64(a * Float64(b * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (y * x) - (t * (z * -0.0625));
	tmp = 0.0;
	if ((y * x) <= -5.4e+118)
		tmp = t_1;
	elseif ((y * x) <= 3.6e+91)
		tmp = (0.0625 * (z * t)) + (a * (b * -0.25));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * x), $MachinePrecision], -5.4e+118], t$95$1, If[LessEqual[N[(y * x), $MachinePrecision], 3.6e+91], N[(N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision] + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.4e118 or 3.6e91 < (*.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}, c\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      4. *-lowering-*.f64 88.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, y\right)\right), c\right) \]

   5. Simplified 88.2%

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

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\frac{1}{16} \cdot t\right) \cdot z + \color{blue}{x} \cdot y \]

      2. +-commutative N/A

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{1}{16} \cdot t\right) \cdot z} \]

      3. *-rgt-identity N/A

         \[\leadsto x \cdot y + \left(\left(\frac{1}{16} \cdot t\right) \cdot z\right) \cdot \color{blue}{1} \]

      4. cancel-sign-sub N/A

         \[\leadsto x \cdot y - \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right)\right) \cdot 1} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x \cdot y - \left(\mathsf{neg}\left(\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right) \cdot 1\right)\right) \]

      6. *-rgt-identity N/A

         \[\leadsto x \cdot y - \left(\mathsf{neg}\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot y - -1 \cdot \color{blue}{\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right)} \]

      8. associate-*r* N/A

         \[\leadsto x \cdot y - -1 \cdot \left(\frac{1}{16} \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot y - \left(-1 \cdot \frac{1}{16}\right) \cdot \color{blue}{\left(t \cdot z\right)} \]

      10. metadata-eval N/A

          \[\leadsto x \cdot y - \frac{-1}{16} \cdot \left(\color{blue}{t} \cdot z\right) \]

      11. associate-*r* N/A

          \[\leadsto x \cdot y - \left(\frac{-1}{16} \cdot t\right) \cdot \color{blue}{z} \]

      12. *-commutative N/A

          \[\leadsto x \cdot y - \left(t \cdot \frac{-1}{16}\right) \cdot z \]

      13. associate-*r* N/A

          \[\leadsto x \cdot y - t \cdot \color{blue}{\left(\frac{-1}{16} \cdot z\right)} \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot \left(\frac{-1}{16} \cdot z\right)\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot \left(\frac{-1}{16} \cdot z\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-1}{16} \cdot z\right)}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\frac{-1}{16}}\right)\right)\right) \]

      18. *-lowering-*.f64 81.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{16}}\right)\right)\right) \]

   8. Simplified 81.0%

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

   if -5.4e118 < (*.f64 x y) < 3.6e91

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

      2. *-lowering-*.f64 95.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   5. Simplified 95.6%

      \[\leadsto \left(\color{blue}{0.0625 \cdot \left(t \cdot z\right)} - \frac{a \cdot b}{4}\right) + c \]

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(\color{blue}{\frac{-1}{4}} \cdot \left(a \cdot b\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(\left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

      11. *-lowering-*.f64 71.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

   8. Simplified 71.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -5.4 \cdot 10^{+118}:\\ \;\;\;\;y \cdot x - t \cdot \left(z \cdot -0.0625\right)\\ \mathbf{elif}\;y \cdot x \leq 3.6 \cdot 10^{+91}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right) + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x - t \cdot \left(z \cdot -0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ t_2 := y \cdot x - t \cdot \left(z \cdot -0.0625\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-240}:\\ \;\;\;\;y \cdot x + t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-21}:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))) (t_2 (- (* y x) (* t (* z -0.0625)))))
   (if (<= z -9e+66)
     t_2
     (if (<= z -4.5e-240) (+ (* y x) t_1) (if (<= z 1.6e-21) (+ c t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = (y * x) - (t * (z * -0.0625));
	double tmp;
	if (z <= -9e+66) {
		tmp = t_2;
	} else if (z <= -4.5e-240) {
		tmp = (y * x) + t_1;
	} else if (z <= 1.6e-21) {
		tmp = c + 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 = a * (b * (-0.25d0))
    t_2 = (y * x) - (t * (z * (-0.0625d0)))
    if (z <= (-9d+66)) then
        tmp = t_2
    else if (z <= (-4.5d-240)) then
        tmp = (y * x) + t_1
    else if (z <= 1.6d-21) then
        tmp = c + 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 = a * (b * -0.25);
	double t_2 = (y * x) - (t * (z * -0.0625));
	double tmp;
	if (z <= -9e+66) {
		tmp = t_2;
	} else if (z <= -4.5e-240) {
		tmp = (y * x) + t_1;
	} else if (z <= 1.6e-21) {
		tmp = c + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	t_2 = (y * x) - (t * (z * -0.0625))
	tmp = 0
	if z <= -9e+66:
		tmp = t_2
	elif z <= -4.5e-240:
		tmp = (y * x) + t_1
	elif z <= 1.6e-21:
		tmp = c + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	t_2 = Float64(Float64(y * x) - Float64(t * Float64(z * -0.0625)))
	tmp = 0.0
	if (z <= -9e+66)
		tmp = t_2;
	elseif (z <= -4.5e-240)
		tmp = Float64(Float64(y * x) + t_1);
	elseif (z <= 1.6e-21)
		tmp = Float64(c + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	t_2 = (y * x) - (t * (z * -0.0625));
	tmp = 0.0;
	if (z <= -9e+66)
		tmp = t_2;
	elseif (z <= -4.5e-240)
		tmp = (y * x) + t_1;
	elseif (z <= 1.6e-21)
		tmp = c + 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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * x), $MachinePrecision] - N[(t * N[(z * -0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+66], t$95$2, If[LessEqual[z, -4.5e-240], N[(N[(y * x), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 1.6e-21], N[(c + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999997e66 or 1.6000000000000001e-21 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in a around 0

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right)}, c\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \left(x \cdot y\right)\right), c\right) \]

      4. *-lowering-*.f64 79.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), \mathsf{*.f64}\left(x, y\right)\right), c\right) \]

   5. Simplified 79.7%

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

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y} \]
   7. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\frac{1}{16} \cdot t\right) \cdot z + \color{blue}{x} \cdot y \]

      2. +-commutative N/A

         \[\leadsto x \cdot y + \color{blue}{\left(\frac{1}{16} \cdot t\right) \cdot z} \]

      3. *-rgt-identity N/A

         \[\leadsto x \cdot y + \left(\left(\frac{1}{16} \cdot t\right) \cdot z\right) \cdot \color{blue}{1} \]

      4. cancel-sign-sub N/A

         \[\leadsto x \cdot y - \color{blue}{\left(\mathsf{neg}\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right)\right) \cdot 1} \]

      5. distribute-lft-neg-out N/A

         \[\leadsto x \cdot y - \left(\mathsf{neg}\left(\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right) \cdot 1\right)\right) \]

      6. *-rgt-identity N/A

         \[\leadsto x \cdot y - \left(\mathsf{neg}\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto x \cdot y - -1 \cdot \color{blue}{\left(\left(\frac{1}{16} \cdot t\right) \cdot z\right)} \]

      8. associate-*r* N/A

         \[\leadsto x \cdot y - -1 \cdot \left(\frac{1}{16} \cdot \color{blue}{\left(t \cdot z\right)}\right) \]

      9. associate-*r* N/A

         \[\leadsto x \cdot y - \left(-1 \cdot \frac{1}{16}\right) \cdot \color{blue}{\left(t \cdot z\right)} \]

      10. metadata-eval N/A

          \[\leadsto x \cdot y - \frac{-1}{16} \cdot \left(\color{blue}{t} \cdot z\right) \]

      11. associate-*r* N/A

          \[\leadsto x \cdot y - \left(\frac{-1}{16} \cdot t\right) \cdot \color{blue}{z} \]

      12. *-commutative N/A

          \[\leadsto x \cdot y - \left(t \cdot \frac{-1}{16}\right) \cdot z \]

      13. associate-*r* N/A

          \[\leadsto x \cdot y - t \cdot \color{blue}{\left(\frac{-1}{16} \cdot z\right)} \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\left(x \cdot y\right), \color{blue}{\left(t \cdot \left(\frac{-1}{16} \cdot z\right)\right)}\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{t} \cdot \left(\frac{-1}{16} \cdot z\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \color{blue}{\left(\frac{-1}{16} \cdot z\right)}\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \left(z \cdot \color{blue}{\frac{-1}{16}}\right)\right)\right) \]

      18. *-lowering-*.f64 66.0%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(t, \mathsf{*.f64}\left(z, \color{blue}{\frac{-1}{16}}\right)\right)\right) \]

   8. Simplified 66.0%

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

   if -8.9999999999999997e66 < z < -4.5000000000000001e-240

   1. Initial program 98.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 87.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   5. Simplified 87.8%

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

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot y + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\frac{-1}{4}} \cdot \left(a \cdot b\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

      10. *-lowering-*.f64 69.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

   8. Simplified 69.5%

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

   if -4.5000000000000001e-240 < z < 1.6000000000000001e-21

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{-1}{4}\right), c\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(b \cdot \frac{-1}{4}\right)\right), c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(\frac{-1}{4} \cdot b\right)\right), c\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{-1}{4} \cdot b\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot \frac{-1}{4}\right)\right), c\right) \]

      6. *-lowering-*.f64 66.3%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{-1}{4}\right)\right), c\right) \]

   5. Simplified 66.3%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+66}:\\ \;\;\;\;y \cdot x - t \cdot \left(z \cdot -0.0625\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-240}:\\ \;\;\;\;y \cdot x + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-21}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x - t \cdot \left(z \cdot -0.0625\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ t_2 := c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+90}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-239}:\\ \;\;\;\;y \cdot x + t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;c + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))) (t_2 (+ c (* 0.0625 (* z t)))))
   (if (<= z -1.2e+90)
     t_2
     (if (<= z -1.5e-239) (+ (* y x) t_1) (if (<= z 4.5e-17) (+ c t_1) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double t_2 = c + (0.0625 * (z * t));
	double tmp;
	if (z <= -1.2e+90) {
		tmp = t_2;
	} else if (z <= -1.5e-239) {
		tmp = (y * x) + t_1;
	} else if (z <= 4.5e-17) {
		tmp = c + 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 = a * (b * (-0.25d0))
    t_2 = c + (0.0625d0 * (z * t))
    if (z <= (-1.2d+90)) then
        tmp = t_2
    else if (z <= (-1.5d-239)) then
        tmp = (y * x) + t_1
    else if (z <= 4.5d-17) then
        tmp = c + 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 = a * (b * -0.25);
	double t_2 = c + (0.0625 * (z * t));
	double tmp;
	if (z <= -1.2e+90) {
		tmp = t_2;
	} else if (z <= -1.5e-239) {
		tmp = (y * x) + t_1;
	} else if (z <= 4.5e-17) {
		tmp = c + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	t_2 = c + (0.0625 * (z * t))
	tmp = 0
	if z <= -1.2e+90:
		tmp = t_2
	elif z <= -1.5e-239:
		tmp = (y * x) + t_1
	elif z <= 4.5e-17:
		tmp = c + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	t_2 = Float64(c + Float64(0.0625 * Float64(z * t)))
	tmp = 0.0
	if (z <= -1.2e+90)
		tmp = t_2;
	elseif (z <= -1.5e-239)
		tmp = Float64(Float64(y * x) + t_1);
	elseif (z <= 4.5e-17)
		tmp = Float64(c + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	t_2 = c + (0.0625 * (z * t));
	tmp = 0.0;
	if (z <= -1.2e+90)
		tmp = t_2;
	elseif (z <= -1.5e-239)
		tmp = (y * x) + t_1;
	elseif (z <= 4.5e-17)
		tmp = c + 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[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+90], t$95$2, If[LessEqual[z, -1.5e-239], N[(N[(y * x), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[z, 4.5e-17], N[(c + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000005e90 or 4.49999999999999978e-17 < z

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), c\right) \]

      2. *-lowering-*.f64 62.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), c\right) \]

   5. Simplified 62.8%

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

   if -1.20000000000000005e90 < z < -1.4999999999999999e-239

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 88.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   5. Simplified 88.6%

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

   6. Taylor expanded in c around 0

      \[\leadsto \color{blue}{x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv N/A

         \[\leadsto x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)} \]

      2. metadata-eval N/A

         \[\leadsto x \cdot y + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\frac{-1}{4}} \cdot \left(a \cdot b\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right)\right) \]

      9. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

      10. *-lowering-*.f64 71.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right)\right) \]

   8. Simplified 71.5%

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

   if -1.4999999999999999e-239 < z < 4.49999999999999978e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{-1}{4}\right), c\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(b \cdot \frac{-1}{4}\right)\right), c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(\frac{-1}{4} \cdot b\right)\right), c\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{-1}{4} \cdot b\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot \frac{-1}{4}\right)\right), c\right) \]

      6. *-lowering-*.f64 65.4%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{-1}{4}\right)\right), c\right) \]

   5. Simplified 65.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+90}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-239}:\\ \;\;\;\;y \cdot x + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-17}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot x\\ \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot x \leq 3.7 \cdot 10^{+49}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* y x))))
   (if (<= (* y x) -2e+119)
     t_1
     (if (<= (* y x) 3.7e+49) (+ c (* a (* b -0.25))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (y * x);
	double tmp;
	if ((y * x) <= -2e+119) {
		tmp = t_1;
	} else if ((y * x) <= 3.7e+49) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (y * x)
    if ((y * x) <= (-2d+119)) then
        tmp = t_1
    else if ((y * x) <= 3.7d+49) then
        tmp = c + (a * (b * (-0.25d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (y * x);
	double tmp;
	if ((y * x) <= -2e+119) {
		tmp = t_1;
	} else if ((y * x) <= 3.7e+49) {
		tmp = c + (a * (b * -0.25));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (y * x)
	tmp = 0
	if (y * x) <= -2e+119:
		tmp = t_1
	elif (y * x) <= 3.7e+49:
		tmp = c + (a * (b * -0.25))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(y * x))
	tmp = 0.0
	if (Float64(y * x) <= -2e+119)
		tmp = t_1;
	elseif (Float64(y * x) <= 3.7e+49)
		tmp = Float64(c + Float64(a * Float64(b * -0.25)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (y * x);
	tmp = 0.0;
	if ((y * x) <= -2e+119)
		tmp = t_1;
	elseif ((y * x) <= 3.7e+49)
		tmp = c + (a * (b * -0.25));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * x), $MachinePrecision], -2e+119], t$95$1, If[LessEqual[N[(y * x), $MachinePrecision], 3.7e+49], N[(c + N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.99999999999999989e119 or 3.70000000000000018e49 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right) \]

   5. Simplified 74.0%

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

   if -1.99999999999999989e119 < (*.f64 x y) < 3.70000000000000018e49

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{-1}{4} \cdot \left(a \cdot b\right)\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(a \cdot b\right) \cdot \frac{-1}{4}\right), c\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(b \cdot \frac{-1}{4}\right)\right), c\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(a \cdot \left(\frac{-1}{4} \cdot b\right)\right), c\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(\frac{-1}{4} \cdot b\right)\right), c\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \left(b \cdot \frac{-1}{4}\right)\right), c\right) \]

      6. *-lowering-*.f64 66.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \frac{-1}{4}\right)\right), c\right) \]

   5. Simplified 66.2%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -2 \cdot 10^{+119}:\\ \;\;\;\;c + y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 3.7 \cdot 10^{+49}:\\ \;\;\;\;c + a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c + y \cdot x\\ \mathbf{if}\;y \cdot x \leq -4.8 \cdot 10^{+140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot x \leq 1.66 \cdot 10^{+59}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ c (* y x))))
   (if (<= (* y x) -4.8e+140)
     t_1
     (if (<= (* y x) 1.66e+59) (+ c (* 0.0625 (* z t))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (y * x);
	double tmp;
	if ((y * x) <= -4.8e+140) {
		tmp = t_1;
	} else if ((y * x) <= 1.66e+59) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c + (y * x)
    if ((y * x) <= (-4.8d+140)) then
        tmp = t_1
    else if ((y * x) <= 1.66d+59) then
        tmp = c + (0.0625d0 * (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = c + (y * x);
	double tmp;
	if ((y * x) <= -4.8e+140) {
		tmp = t_1;
	} else if ((y * x) <= 1.66e+59) {
		tmp = c + (0.0625 * (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = c + (y * x)
	tmp = 0
	if (y * x) <= -4.8e+140:
		tmp = t_1
	elif (y * x) <= 1.66e+59:
		tmp = c + (0.0625 * (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(c + Float64(y * x))
	tmp = 0.0
	if (Float64(y * x) <= -4.8e+140)
		tmp = t_1;
	elseif (Float64(y * x) <= 1.66e+59)
		tmp = Float64(c + Float64(0.0625 * Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = c + (y * x);
	tmp = 0.0;
	if ((y * x) <= -4.8e+140)
		tmp = t_1;
	elseif ((y * x) <= 1.66e+59)
		tmp = c + (0.0625 * (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(c + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * x), $MachinePrecision], -4.8e+140], t$95$1, If[LessEqual[N[(y * x), $MachinePrecision], 1.66e+59], N[(c + N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -4.7999999999999999e140 or 1.6599999999999999e59 < (*.f64 x y)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 76.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right) \]

   5. Simplified 76.0%

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

   if -4.7999999999999999e140 < (*.f64 x y) < 1.6599999999999999e59

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right)\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \left(t \cdot z\right)\right), c\right) \]

      2. *-lowering-*.f64 58.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, z\right)\right), c\right) \]

   5. Simplified 58.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -4.8 \cdot 10^{+140}:\\ \;\;\;\;c + y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 1.66 \cdot 10^{+59}:\\ \;\;\;\;c + 0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 44.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -3.6 \cdot 10^{+119}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 9.1 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* y x) -3.6e+119)
   (* y x)
   (if (<= (* y x) 9.1e+49) (* a (* b -0.25)) (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * x) <= -3.6e+119) {
		tmp = y * x;
	} else if ((y * x) <= 9.1e+49) {
		tmp = a * (b * -0.25);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y * x) <= (-3.6d+119)) then
        tmp = y * x
    else if ((y * x) <= 9.1d+49) then
        tmp = a * (b * (-0.25d0))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * x) <= -3.6e+119) {
		tmp = y * x;
	} else if ((y * x) <= 9.1e+49) {
		tmp = a * (b * -0.25);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y * x) <= -3.6e+119:
		tmp = y * x
	elif (y * x) <= 9.1e+49:
		tmp = a * (b * -0.25)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(y * x) <= -3.6e+119)
		tmp = Float64(y * x);
	elseif (Float64(y * x) <= 9.1e+49)
		tmp = Float64(a * Float64(b * -0.25));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y * x) <= -3.6e+119)
		tmp = y * x;
	elseif ((y * x) <= 9.1e+49)
		tmp = a * (b * -0.25);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(y * x), $MachinePrecision], -3.6e+119], N[(y * x), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 9.1e+49], N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.60000000000000001e119 or 9.09999999999999986e49 < (*.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 65.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 65.4%

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

   if -3.60000000000000001e119 < (*.f64 x y) < 9.09999999999999986e49

   1. Initial program 99.3%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}} \]

      2. associate-*l* N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      6. *-lowering-*.f64 42.4%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right) \]

   5. Simplified 42.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -3.6 \cdot 10^{+119}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 9.1 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -1.8 \cdot 10^{+141}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 1.7 \cdot 10^{+63}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* y x) -1.8e+141)
   (* y x)
   (if (<= (* y x) 1.7e+63) (* 0.0625 (* z t)) (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * x) <= -1.8e+141) {
		tmp = y * x;
	} else if ((y * x) <= 1.7e+63) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y * x) <= (-1.8d+141)) then
        tmp = y * x
    else if ((y * x) <= 1.7d+63) then
        tmp = 0.0625d0 * (z * t)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * x) <= -1.8e+141) {
		tmp = y * x;
	} else if ((y * x) <= 1.7e+63) {
		tmp = 0.0625 * (z * t);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y * x) <= -1.8e+141:
		tmp = y * x
	elif (y * x) <= 1.7e+63:
		tmp = 0.0625 * (z * t)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(y * x) <= -1.8e+141)
		tmp = Float64(y * x);
	elseif (Float64(y * x) <= 1.7e+63)
		tmp = Float64(0.0625 * Float64(z * t));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y * x) <= -1.8e+141)
		tmp = y * x;
	elseif ((y * x) <= 1.7e+63)
		tmp = 0.0625 * (z * t);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(y * x), $MachinePrecision], -1.8e+141], N[(y * x), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 1.7e+63], N[(0.0625 * N[(z * t), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.8000000000000001e141 or 1.6999999999999999e63 < (*.f64 x y)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 67.8%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 67.8%

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

   if -1.8000000000000001e141 < (*.f64 x y) < 1.6999999999999999e63

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{16}, \color{blue}{\left(t \cdot z\right)}\right) \]

      2. *-lowering-*.f64 34.5%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{16}, \mathsf{*.f64}\left(t, \color{blue}{z}\right)\right) \]

   5. Simplified 34.5%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -1.8 \cdot 10^{+141}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 1.7 \cdot 10^{+63}:\\ \;\;\;\;0.0625 \cdot \left(z \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot x \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 7.3 \cdot 10^{+50}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (* y x) -3.1e+84) (* y x) (if (<= (* y x) 7.3e+50) c (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * x) <= -3.1e+84) {
		tmp = y * x;
	} else if ((y * x) <= 7.3e+50) {
		tmp = c;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((y * x) <= (-3.1d+84)) then
        tmp = y * x
    else if ((y * x) <= 7.3d+50) then
        tmp = c
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((y * x) <= -3.1e+84) {
		tmp = y * x;
	} else if ((y * x) <= 7.3e+50) {
		tmp = c;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (y * x) <= -3.1e+84:
		tmp = y * x
	elif (y * x) <= 7.3e+50:
		tmp = c
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(y * x) <= -3.1e+84)
		tmp = Float64(y * x);
	elseif (Float64(y * x) <= 7.3e+50)
		tmp = c;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((y * x) <= -3.1e+84)
		tmp = y * x;
	elseif ((y * x) <= 7.3e+50)
		tmp = c;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(y * x), $MachinePrecision], -3.1e+84], N[(y * x), $MachinePrecision], If[LessEqual[N[(y * x), $MachinePrecision], 7.3e+50], c, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -3.10000000000000003e84 or 7.3000000000000003e50 < (*.f64 x y)

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 64.1%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 64.1%

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

   if -3.10000000000000003e84 < (*.f64 x y) < 7.3000000000000003e50

   1. Initial program 99.3%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c} \]
   4. Step-by-step derivation

   5. Simplified 26.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot x \leq -3.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \cdot x \leq 7.3 \cdot 10^{+50}:\\ \;\;\;\;c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (((y * x) + (z * (t / 16.0d0))) - ((b * a) / 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \frac{t}{16}\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\frac{t}{16} \cdot z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(\frac{t}{16}\right), z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

   4. /-lowering-/.f64 98.0%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, 16\right), z\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, b\right), 4\right)\right), c\right) \]

4. Applied egg-rr 98.0%

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

5. Final simplification 98.0%

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

Alternative 13: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot -0.25\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+109}:\\ \;\;\;\;c + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (* b -0.25))))
   (if (<= b -4.7e-108) t_1 (if (<= b 8.5e+109) (+ c (* y x)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b * -0.25);
	double tmp;
	if (b <= -4.7e-108) {
		tmp = t_1;
	} else if (b <= 8.5e+109) {
		tmp = c + (y * x);
	} 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 = a * (b * (-0.25d0))
    if (b <= (-4.7d-108)) then
        tmp = t_1
    else if (b <= 8.5d+109) then
        tmp = c + (y * x)
    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 = a * (b * -0.25);
	double tmp;
	if (b <= -4.7e-108) {
		tmp = t_1;
	} else if (b <= 8.5e+109) {
		tmp = c + (y * x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b * -0.25)
	tmp = 0
	if b <= -4.7e-108:
		tmp = t_1
	elif b <= 8.5e+109:
		tmp = c + (y * x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b * -0.25))
	tmp = 0.0
	if (b <= -4.7e-108)
		tmp = t_1;
	elseif (b <= 8.5e+109)
		tmp = Float64(c + Float64(y * x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b * -0.25);
	tmp = 0.0;
	if (b <= -4.7e-108)
		tmp = t_1;
	elseif (b <= 8.5e+109)
		tmp = c + (y * x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b * -0.25), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e-108], t$95$1, If[LessEqual[b, 8.5e+109], N[(c + N[(y * x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -4.70000000000000013e-108 or 8.5000000000000004e109 < b

   1. Initial program 97.8%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(a \cdot b\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(a \cdot b\right) \cdot \color{blue}{\frac{-1}{4}} \]

      2. associate-*l* N/A

         \[\leadsto a \cdot \color{blue}{\left(b \cdot \frac{-1}{4}\right)} \]

      3. *-commutative N/A

         \[\leadsto a \cdot \left(\frac{-1}{4} \cdot \color{blue}{b}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{-1}{4} \cdot b\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(b \cdot \color{blue}{\frac{-1}{4}}\right)\right) \]

      6. *-lowering-*.f64 52.7%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\frac{-1}{4}}\right)\right) \]

   5. Simplified 52.7%

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

   if -4.70000000000000013e-108 < b < 8.5000000000000004e109

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, c\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 61.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), c\right) \]

   5. Simplified 61.7%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-108}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+109}:\\ \;\;\;\;c + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot -0.25\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.6% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Taylor expanded in c around inf

   \[\leadsto \color{blue}{c} \]
4. Step-by-step derivation

5. Simplified 18.9%

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

Reproduce

herbie shell --seed 2024185 
(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))