Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B

Percentage Accurate: 99.9% → 99.9%

Time: 6.1s

Alternatives: 10

Speedup: 1.0×

• 26.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x + y) - z) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{\left(x + y\right) - z}{t \cdot 2} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 33.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x + y\right) - z}{t \cdot 2}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{x - z}{0}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+304}:\\ \;\;\;\;\frac{y}{t} \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (+ x y) z) (* t 2.0))))
   (if (<= t_1 -5e+43)
     (/ (- x z) 0.0)
     (if (<= t_1 4e+304) (* (/ y t) 0.5) (/ (+ y x) 0.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x + y) - z) / (t * 2.0);
	double tmp;
	if (t_1 <= -5e+43) {
		tmp = (x - z) / 0.0;
	} else if (t_1 <= 4e+304) {
		tmp = (y / t) * 0.5;
	} else {
		tmp = (y + x) / 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x + y) - z) / (t * 2.0d0)
    if (t_1 <= (-5d+43)) then
        tmp = (x - z) / 0.0d0
    else if (t_1 <= 4d+304) then
        tmp = (y / t) * 0.5d0
    else
        tmp = (y + x) / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x + y) - z) / (t * 2.0);
	double tmp;
	if (t_1 <= -5e+43) {
		tmp = (x - z) / 0.0;
	} else if (t_1 <= 4e+304) {
		tmp = (y / t) * 0.5;
	} else {
		tmp = (y + x) / 0.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x + y) - z) / (t * 2.0)
	tmp = 0
	if t_1 <= -5e+43:
		tmp = (x - z) / 0.0
	elif t_1 <= 4e+304:
		tmp = (y / t) * 0.5
	else:
		tmp = (y + x) / 0.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
	tmp = 0.0
	if (t_1 <= -5e+43)
		tmp = Float64(Float64(x - z) / 0.0);
	elseif (t_1 <= 4e+304)
		tmp = Float64(Float64(y / t) * 0.5);
	else
		tmp = Float64(Float64(y + x) / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x + y) - z) / (t * 2.0);
	tmp = 0.0;
	if (t_1 <= -5e+43)
		tmp = (x - z) / 0.0;
	elseif (t_1 <= 4e+304)
		tmp = (y / t) * 0.5;
	else
		tmp = (y + x) / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+43], N[(N[(x - z), $MachinePrecision] / 0.0), $MachinePrecision], If[LessEqual[t$95$1, 4e+304], N[(N[(y / t), $MachinePrecision] * 0.5), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / 0.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64))) < -5.0000000000000004e43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 87.7

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 87.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 87.7

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 87.7%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x + \color{blue}{-1 \cdot z}}{t + t} \]
   9. Step-by-step derivation

   10. Applied rewrites 68.8%

       \[\leadsto \frac{x - \color{blue}{z}}{t + t} \]
   11. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \frac{x - z}{\color{blue}{t + t}} \]

       2. flip-+ N/A

          \[\leadsto \frac{x - z}{\color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}} \]

   12. Applied rewrites 21.3%

       \[\leadsto \color{blue}{\frac{x - z}{0}} \]

   if -5.0000000000000004e43 < (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64))) < 3.9999999999999998e304

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      4. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      6. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot \frac{1}{2} \]

      7. lower-+.f64 71.2

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot 0.5 \]

   5. Applied rewrites 71.2%

      \[\leadsto \color{blue}{\frac{y + x}{t} \cdot 0.5} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{y}{t} \cdot \frac{1}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 36.4%

      \[\leadsto \frac{y}{t} \cdot 0.5 \]

   if 3.9999999999999998e304 < (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 93.5

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 93.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 93.5

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 93.5%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{x + y}}{t + t} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]

      2. lower-+.f64 75.5

         \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]

   10. Applied rewrites 75.5%

       \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]
   11. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \frac{y + x}{\color{blue}{t + t}} \]

       2. flip-+ N/A

          \[\leadsto \frac{y + x}{\color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}} \]

   12. Applied rewrites 51.6%

       \[\leadsto \color{blue}{\frac{y + x}{0}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 15.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x + y\right) - z}{t \cdot 2} \leq 2 \cdot 10^{-85}:\\ \;\;\;\;\frac{x - z}{0}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- (+ x y) z) (* t 2.0)) 2e-85) (/ (- x z) 0.0) (/ (+ y x) 0.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x + y) - z) / (t * 2.0)) <= 2e-85) {
		tmp = (x - z) / 0.0;
	} else {
		tmp = (y + x) / 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((((x + y) - z) / (t * 2.0d0)) <= 2d-85) then
        tmp = (x - z) / 0.0d0
    else
        tmp = (y + x) / 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((((x + y) - z) / (t * 2.0)) <= 2e-85) {
		tmp = (x - z) / 0.0;
	} else {
		tmp = (y + x) / 0.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (((x + y) - z) / (t * 2.0)) <= 2e-85:
		tmp = (x - z) / 0.0
	else:
		tmp = (y + x) / 0.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0)) <= 2e-85)
		tmp = Float64(Float64(x - z) / 0.0);
	else
		tmp = Float64(Float64(y + x) / 0.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((((x + y) - z) / (t * 2.0)) <= 2e-85)
		tmp = (x - z) / 0.0;
	else
		tmp = (y + x) / 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], 2e-85], N[(N[(x - z), $MachinePrecision] / 0.0), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / 0.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64))) < 2e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 88.6

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 88.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 88.6

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 88.6%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x + \color{blue}{-1 \cdot z}}{t + t} \]
   9. Step-by-step derivation

   10. Applied rewrites 69.1%

       \[\leadsto \frac{x - \color{blue}{z}}{t + t} \]
   11. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \frac{x - z}{\color{blue}{t + t}} \]

       2. flip-+ N/A

          \[\leadsto \frac{x - z}{\color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}} \]

   12. Applied rewrites 14.5%

       \[\leadsto \color{blue}{\frac{x - z}{0}} \]

   if 2e-85 < (/.f64 (-.f64 (+.f64 x y) z) (*.f64 t #s(literal 2 binary64)))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 90.5

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 90.5%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 90.5

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 90.5%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{x + y}}{t + t} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]

      2. lower-+.f64 70.9

         \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]

   10. Applied rewrites 70.9%

       \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]
   11. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \frac{y + x}{\color{blue}{t + t}} \]

       2. flip-+ N/A

          \[\leadsto \frac{y + x}{\color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}} \]

   12. Applied rewrites 16.3%

       \[\leadsto \color{blue}{\frac{y + x}{0}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{t} \cdot 0.5\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{-0.5 \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e+34)
   (* (/ x t) 0.5)
   (if (<= (+ x y) 5e+62) (/ (* -0.5 z) t) (* (/ y t) 0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e+34) {
		tmp = (x / t) * 0.5;
	} else if ((x + y) <= 5e+62) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1d+34)) then
        tmp = (x / t) * 0.5d0
    else if ((x + y) <= 5d+62) then
        tmp = ((-0.5d0) * z) / t
    else
        tmp = (y / t) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e+34) {
		tmp = (x / t) * 0.5;
	} else if ((x + y) <= 5e+62) {
		tmp = (-0.5 * z) / t;
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e+34:
		tmp = (x / t) * 0.5
	elif (x + y) <= 5e+62:
		tmp = (-0.5 * z) / t
	else:
		tmp = (y / t) * 0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e+34)
		tmp = Float64(Float64(x / t) * 0.5);
	elseif (Float64(x + y) <= 5e+62)
		tmp = Float64(Float64(-0.5 * z) / t);
	else
		tmp = Float64(Float64(y / t) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e+34)
		tmp = (x / t) * 0.5;
	elseif ((x + y) <= 5e+62)
		tmp = (-0.5 * z) / t;
	else
		tmp = (y / t) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+34], N[(N[(x / t), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 5e+62], N[(N[(-0.5 * z), $MachinePrecision] / t), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -9.99999999999999946e33

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      3. lower-/.f64 48.6

         \[\leadsto \color{blue}{\frac{x}{t}} \cdot 0.5 \]

   5. Applied rewrites 48.6%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot 0.5} \]

   if -9.99999999999999946e33 < (+.f64 x y) < 5.00000000000000029e62

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto \frac{-1}{2} \cdot \frac{\color{blue}{1 \cdot z}}{t} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\left(\frac{1}{t} \cdot z\right)} \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{2} \cdot \frac{1}{t}\right) \cdot z} \]

      4. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)} \cdot \frac{1}{t}\right) \cdot z \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \frac{1}{t}\right) \cdot z} \]

      6. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} \cdot \frac{1}{t}\right) \cdot z \]

      7. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot 1}{t}} \cdot z \]

      8. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{-1}{2}}}{t} \cdot z \]

      9. lower-/.f64 69.0

         \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

   5. Applied rewrites 69.0%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 69.2%

      \[\leadsto \frac{-0.5 \cdot z}{\color{blue}{t}} \]

   if 5.00000000000000029e62 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      4. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      6. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot \frac{1}{2} \]

      7. lower-+.f64 86.1

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot 0.5 \]

   5. Applied rewrites 86.1%

      \[\leadsto \color{blue}{\frac{y + x}{t} \cdot 0.5} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{y}{t} \cdot \frac{1}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.4%

      \[\leadsto \frac{y}{t} \cdot 0.5 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 50.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{t} \cdot 0.5\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{-0.5}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -1e+34)
   (* (/ x t) 0.5)
   (if (<= (+ x y) 5e+62) (* (/ -0.5 t) z) (* (/ y t) 0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e+34) {
		tmp = (x / t) * 0.5;
	} else if ((x + y) <= 5e+62) {
		tmp = (-0.5 / t) * z;
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-1d+34)) then
        tmp = (x / t) * 0.5d0
    else if ((x + y) <= 5d+62) then
        tmp = ((-0.5d0) / t) * z
    else
        tmp = (y / t) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -1e+34) {
		tmp = (x / t) * 0.5;
	} else if ((x + y) <= 5e+62) {
		tmp = (-0.5 / t) * z;
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -1e+34:
		tmp = (x / t) * 0.5
	elif (x + y) <= 5e+62:
		tmp = (-0.5 / t) * z
	else:
		tmp = (y / t) * 0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -1e+34)
		tmp = Float64(Float64(x / t) * 0.5);
	elseif (Float64(x + y) <= 5e+62)
		tmp = Float64(Float64(-0.5 / t) * z);
	else
		tmp = Float64(Float64(y / t) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -1e+34)
		tmp = (x / t) * 0.5;
	elseif ((x + y) <= 5e+62)
		tmp = (-0.5 / t) * z;
	else
		tmp = (y / t) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e+34], N[(N[(x / t), $MachinePrecision] * 0.5), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 5e+62], N[(N[(-0.5 / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -9.99999999999999946e33

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{t}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{t} \cdot \frac{1}{2}} \]

      3. lower-/.f64 48.6

         \[\leadsto \color{blue}{\frac{x}{t}} \cdot 0.5 \]

   5. Applied rewrites 48.6%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot 0.5} \]

   if -9.99999999999999946e33 < (+.f64 x y) < 5.00000000000000029e62

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto \frac{-1}{2} \cdot \frac{\color{blue}{1 \cdot z}}{t} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\left(\frac{1}{t} \cdot z\right)} \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{2} \cdot \frac{1}{t}\right) \cdot z} \]

      4. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)} \cdot \frac{1}{t}\right) \cdot z \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \frac{1}{t}\right) \cdot z} \]

      6. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} \cdot \frac{1}{t}\right) \cdot z \]

      7. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot 1}{t}} \cdot z \]

      8. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{-1}{2}}}{t} \cdot z \]

      9. lower-/.f64 69.0

         \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

   5. Applied rewrites 69.0%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 5.00000000000000029e62 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      4. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      6. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot \frac{1}{2} \]

      7. lower-+.f64 86.1

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot 0.5 \]

   5. Applied rewrites 86.1%

      \[\leadsto \color{blue}{\frac{y + x}{t} \cdot 0.5} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{y}{t} \cdot \frac{1}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.4%

      \[\leadsto \frac{y}{t} \cdot 0.5 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 44.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{+109}:\\ \;\;\;\;\frac{x - z}{0}\\ \mathbf{elif}\;x + y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{-0.5}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -4e+109)
   (/ (- x z) 0.0)
   (if (<= (+ x y) 5e+62) (* (/ -0.5 t) z) (* (/ y t) 0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e+109) {
		tmp = (x - z) / 0.0;
	} else if ((x + y) <= 5e+62) {
		tmp = (-0.5 / t) * z;
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-4d+109)) then
        tmp = (x - z) / 0.0d0
    else if ((x + y) <= 5d+62) then
        tmp = ((-0.5d0) / t) * z
    else
        tmp = (y / t) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e+109) {
		tmp = (x - z) / 0.0;
	} else if ((x + y) <= 5e+62) {
		tmp = (-0.5 / t) * z;
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -4e+109:
		tmp = (x - z) / 0.0
	elif (x + y) <= 5e+62:
		tmp = (-0.5 / t) * z
	else:
		tmp = (y / t) * 0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -4e+109)
		tmp = Float64(Float64(x - z) / 0.0);
	elseif (Float64(x + y) <= 5e+62)
		tmp = Float64(Float64(-0.5 / t) * z);
	else
		tmp = Float64(Float64(y / t) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -4e+109)
		tmp = (x - z) / 0.0;
	elseif ((x + y) <= 5e+62)
		tmp = (-0.5 / t) * z;
	else
		tmp = (y / t) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e+109], N[(N[(x - z), $MachinePrecision] / 0.0), $MachinePrecision], If[LessEqual[N[(x + y), $MachinePrecision], 5e+62], N[(N[(-0.5 / t), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x y) < -3.99999999999999993e109

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 95.8

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 95.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 95.8

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 95.8%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x + \color{blue}{-1 \cdot z}}{t + t} \]
   9. Step-by-step derivation

   10. Applied rewrites 61.6%

       \[\leadsto \frac{x - \color{blue}{z}}{t + t} \]
   11. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \frac{x - z}{\color{blue}{t + t}} \]

       2. flip-+ N/A

          \[\leadsto \frac{x - z}{\color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}} \]

   12. Applied rewrites 16.8%

       \[\leadsto \color{blue}{\frac{x - z}{0}} \]

   if -3.99999999999999993e109 < (+.f64 x y) < 5.00000000000000029e62

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-lft-identity N/A

         \[\leadsto \frac{-1}{2} \cdot \frac{\color{blue}{1 \cdot z}}{t} \]

      2. associate-*l/ N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\left(\frac{1}{t} \cdot z\right)} \]

      3. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{2} \cdot \frac{1}{t}\right) \cdot z} \]

      4. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\left(\mathsf{neg}\left(\frac{1}{2}\right)\right)} \cdot \frac{1}{t}\right) \cdot z \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \frac{1}{t}\right) \cdot z} \]

      6. metadata-eval N/A

         \[\leadsto \left(\color{blue}{\frac{-1}{2}} \cdot \frac{1}{t}\right) \cdot z \]

      7. associate-*r/ N/A

         \[\leadsto \color{blue}{\frac{\frac{-1}{2} \cdot 1}{t}} \cdot z \]

      8. metadata-eval N/A

         \[\leadsto \frac{\color{blue}{\frac{-1}{2}}}{t} \cdot z \]

      9. lower-/.f64 64.2

         \[\leadsto \color{blue}{\frac{-0.5}{t}} \cdot z \]

   5. Applied rewrites 64.2%

      \[\leadsto \color{blue}{\frac{-0.5}{t} \cdot z} \]

   if 5.00000000000000029e62 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      4. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      6. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot \frac{1}{2} \]

      7. lower-+.f64 86.1

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot 0.5 \]

   5. Applied rewrites 86.1%

      \[\leadsto \color{blue}{\frac{y + x}{t} \cdot 0.5} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{y}{t} \cdot \frac{1}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.4%

      \[\leadsto \frac{y}{t} \cdot 0.5 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -4 \cdot 10^{-275}:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) -4e-275) (/ (- x z) (+ t t)) (/ (- y z) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e-275) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y - z) / (t + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= (-4d-275)) then
        tmp = (x - z) / (t + t)
    else
        tmp = (y - z) / (t + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= -4e-275) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y - z) / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= -4e-275:
		tmp = (x - z) / (t + t)
	else:
		tmp = (y - z) / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= -4e-275)
		tmp = Float64(Float64(x - z) / Float64(t + t));
	else
		tmp = Float64(Float64(y - z) / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= -4e-275)
		tmp = (x - z) / (t + t);
	else
		tmp = (y - z) / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], -4e-275], N[(N[(x - z), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -3.99999999999999974e-275

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 90.8

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 90.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 90.8

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 90.8%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x + \color{blue}{-1 \cdot z}}{t + t} \]
   9. Step-by-step derivation

   10. Applied rewrites 69.7%

       \[\leadsto \frac{x - \color{blue}{z}}{t + t} \]

   if -3.99999999999999974e-275 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. lower--.f64 71.1

         \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]

   5. Applied rewrites 71.1%

      \[\leadsto \frac{\color{blue}{y - z}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{y - z}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{y - z}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{y - z}{\color{blue}{t + t}} \]

      4. lower-+.f64 71.1

         \[\leadsto \frac{y - z}{\color{blue}{t + t}} \]

   7. Applied rewrites 71.1%

      \[\leadsto \frac{y - z}{\color{blue}{t + t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+94}:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y + x}{t + t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e+94) (/ (- x z) (+ t t)) (/ (+ y x) (+ t t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+94) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y + x) / (t + t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= 2d+94) then
        tmp = (x - z) / (t + t)
    else
        tmp = (y + x) / (t + t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+94) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y + x) / (t + t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2e+94:
		tmp = (x - z) / (t + t)
	else:
		tmp = (y + x) / (t + t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2e+94)
		tmp = Float64(Float64(x - z) / Float64(t + t));
	else
		tmp = Float64(Float64(y + x) / Float64(t + t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 2e+94)
		tmp = (x - z) / (t + t);
	else
		tmp = (y + x) / (t + t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e+94], N[(N[(x - z), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(N[(y + x), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 2e94

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 87.6

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 87.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 87.6

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 87.6%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x + \color{blue}{-1 \cdot z}}{t + t} \]
   9. Step-by-step derivation

   10. Applied rewrites 75.0%

       \[\leadsto \frac{x - \color{blue}{z}}{t + t} \]

   if 2e94 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 94.3

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 94.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 94.3

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 94.3%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in z around 0

      \[\leadsto \frac{\color{blue}{x + y}}{t + t} \]
   9. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]

      2. lower-+.f64 90.9

         \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]

   10. Applied rewrites 90.9%

       \[\leadsto \frac{\color{blue}{y + x}}{t + t} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 64.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq 2 \cdot 10^{+94}:\\ \;\;\;\;\frac{x - z}{t + t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x y) 2e+94) (/ (- x z) (+ t t)) (* (/ y t) 0.5)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+94) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x + y) <= 2d+94) then
        tmp = (x - z) / (t + t)
    else
        tmp = (y / t) * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + y) <= 2e+94) {
		tmp = (x - z) / (t + t);
	} else {
		tmp = (y / t) * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + y) <= 2e+94:
		tmp = (x - z) / (t + t)
	else:
		tmp = (y / t) * 0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + y) <= 2e+94)
		tmp = Float64(Float64(x - z) / Float64(t + t));
	else
		tmp = Float64(Float64(y / t) * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + y) <= 2e+94)
		tmp = (x - z) / (t + t);
	else
		tmp = (y / t) * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + y), $MachinePrecision], 2e+94], N[(N[(x - z), $MachinePrecision] / N[(t + t), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < 2e94

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

      2. associate--l+ N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

      3. +-commutative N/A

         \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

      4. distribute-rgt-in N/A

         \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

      5. associate-*l/ N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

      6. associate-/l* N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

      7. *-inverses N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

      8. *-rgt-identity N/A

         \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

      9. lower-fma.f64 N/A

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

      10. lower--.f64 N/A

          \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

      11. lower-/.f64 87.6

          \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   5. Applied rewrites 87.6%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

      2. *-commutative N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

      3. count-2-rev N/A

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

      4. lower-+.f64 87.6

         \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   7. Applied rewrites 87.6%

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   8. Taylor expanded in y around 0

      \[\leadsto \frac{x + \color{blue}{-1 \cdot z}}{t + t} \]
   9. Step-by-step derivation

   10. Applied rewrites 75.0%

       \[\leadsto \frac{x - \color{blue}{z}}{t + t} \]

   if 2e94 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. div-add-rev N/A

         \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right)} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right) \cdot \frac{1}{2}} \]

      4. div-add-rev N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      5. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y}{t}} \cdot \frac{1}{2} \]

      6. +-commutative N/A

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot \frac{1}{2} \]

      7. lower-+.f64 90.9

         \[\leadsto \frac{\color{blue}{y + x}}{t} \cdot 0.5 \]

   5. Applied rewrites 90.9%

      \[\leadsto \color{blue}{\frac{y + x}{t} \cdot 0.5} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{y}{t} \cdot \frac{1}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 50.5%

      \[\leadsto \frac{y}{t} \cdot 0.5 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 15.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \frac{x - z}{0} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- x z) 0.0))

C

double code(double x, double y, double z, double t) {
	return (x - z) / 0.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - z) / 0.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - z) / 0.0;
}

Python

def code(x, y, z, t):
	return (x - z) / 0.0

Julia

function code(x, y, z, t)
	return Float64(Float64(x - z) / 0.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - z) / 0.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - z), $MachinePrecision] / 0.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf

   \[\leadsto \frac{\color{blue}{y \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)}}{t \cdot 2} \]
4. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \frac{y \cdot \left(\color{blue}{\left(\frac{x}{y} + 1\right)} - \frac{z}{y}\right)}{t \cdot 2} \]

   2. associate--l+ N/A

      \[\leadsto \frac{y \cdot \color{blue}{\left(\frac{x}{y} + \left(1 - \frac{z}{y}\right)\right)}}{t \cdot 2} \]

   3. +-commutative N/A

      \[\leadsto \frac{y \cdot \color{blue}{\left(\left(1 - \frac{z}{y}\right) + \frac{x}{y}\right)}}{t \cdot 2} \]

   4. distribute-rgt-in N/A

      \[\leadsto \frac{\color{blue}{\left(1 - \frac{z}{y}\right) \cdot y + \frac{x}{y} \cdot y}}{t \cdot 2} \]

   5. associate-*l/ N/A

      \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{\frac{x \cdot y}{y}}}{t \cdot 2} \]

   6. associate-/l* N/A

      \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x \cdot \frac{y}{y}}}{t \cdot 2} \]

   7. *-inverses N/A

      \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + x \cdot \color{blue}{1}}{t \cdot 2} \]

   8. *-rgt-identity N/A

      \[\leadsto \frac{\left(1 - \frac{z}{y}\right) \cdot y + \color{blue}{x}}{t \cdot 2} \]

   9. lower-fma.f64 N/A

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]

   10. lower--.f64 N/A

       \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{1 - \frac{z}{y}}, y, x\right)}{t \cdot 2} \]

   11. lower-/.f64 89.4

       \[\leadsto \frac{\mathsf{fma}\left(1 - \color{blue}{\frac{z}{y}}, y, x\right)}{t \cdot 2} \]

5. Applied rewrites 89.4%

   \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}}{t \cdot 2} \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t \cdot 2}} \]

   2. *-commutative N/A

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{2 \cdot t}} \]

   3. count-2-rev N/A

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

   4. lower-+.f64 89.4

      \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

7. Applied rewrites 89.4%

   \[\leadsto \frac{\mathsf{fma}\left(1 - \frac{z}{y}, y, x\right)}{\color{blue}{t + t}} \]

8. Taylor expanded in y around 0

   \[\leadsto \frac{x + \color{blue}{-1 \cdot z}}{t + t} \]
9. Step-by-step derivation

10. Applied rewrites 69.5%

    \[\leadsto \frac{x - \color{blue}{z}}{t + t} \]
11. Step-by-step derivation

    1. lift-+.f64 N/A

       \[\leadsto \frac{x - z}{\color{blue}{t + t}} \]

    2. flip-+ N/A

       \[\leadsto \frac{x - z}{\color{blue}{\frac{t \cdot t - t \cdot t}{t - t}}} \]

12. Applied rewrites 14.5%

    \[\leadsto \color{blue}{\frac{x - z}{0}} \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2024329 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))