Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.7% → 99.1%

Time: 10.5s

Alternatives: 16

Speedup: 1.3×

• 23.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

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) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

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) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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 = ((2.0d0 + (2.0d0 / z)) / t) + ((-2.0d0) + (x / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.2%

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

3. Simplified 99.1%

   \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t} + \left(-2 + \frac{x}{y}\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-33}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-14}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -2e+30)
     t_1
     (if (<= (/ x y) -2e-33)
       (/ (+ 2.0 (/ 2.0 z)) t)
       (if (<= (/ x y) 1e-14) (+ -2.0 (/ (/ 2.0 z) t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -2e+30) {
		tmp = t_1;
	} else if ((x / y) <= -2e-33) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((x / y) <= 1e-14) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	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) + (2.0d0 / t)
    if ((x / y) <= (-2d+30)) then
        tmp = t_1
    else if ((x / y) <= (-2d-33)) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if ((x / y) <= 1d-14) then
        tmp = (-2.0d0) + ((2.0d0 / 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 t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -2e+30) {
		tmp = t_1;
	} else if ((x / y) <= -2e-33) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if ((x / y) <= 1e-14) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if (x / y) <= -2e+30:
		tmp = t_1
	elif (x / y) <= -2e-33:
		tmp = (2.0 + (2.0 / z)) / t
	elif (x / y) <= 1e-14:
		tmp = -2.0 + ((2.0 / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -2e+30)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e-33)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif (Float64(x / y) <= 1e-14)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -2e+30)
		tmp = t_1;
	elseif ((x / y) <= -2e-33)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif ((x / y) <= 1e-14)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+30], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e-33], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-14], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e30 or 9.99999999999999999e-15 < (/.f64 x y)

   1. Initial program 82.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 82.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 82.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 81.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{t}\right)\right) \]

   8. Simplified 81.0%

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

   if -2e30 < (/.f64 x y) < -2.0000000000000001e-33

   1. Initial program 91.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(2 + 2 \cdot \frac{1}{z}\right), \color{blue}{t}\right) \]

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

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(2 \cdot \frac{1}{z}\right)\right), t\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(\frac{2 \cdot 1}{z}\right)\right), t\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \left(\frac{2}{z}\right)\right), t\right) \]

      5. /-lowering-/.f64 85.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right) \]

   5. Simplified 85.3%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   if -2.0000000000000001e-33 < (/.f64 x y) < 9.99999999999999999e-15

   1. Initial program 84.8%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(\frac{2}{z}\right)}, t\right), -2\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 83.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right), -2\right) \]

   10. Simplified 83.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-33}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-14}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := t\_1 + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-12}:\\ \;\;\;\;t\_1 + -2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (+ t_1 (/ x y))))
   (if (<= (/ x y) -2e+30) t_2 (if (<= (/ x y) 5e-12) (+ t_1 -2.0) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = t_1 + (x / y);
	double tmp;
	if ((x / y) <= -2e+30) {
		tmp = t_2;
	} else if ((x / y) <= 5e-12) {
		tmp = t_1 + -2.0;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = t_1 + (x / y)
    if ((x / y) <= (-2d+30)) then
        tmp = t_2
    else if ((x / y) <= 5d-12) then
        tmp = t_1 + (-2.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = t_1 + (x / y);
	double tmp;
	if ((x / y) <= -2e+30) {
		tmp = t_2;
	} else if ((x / y) <= 5e-12) {
		tmp = t_1 + -2.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = t_1 + (x / y)
	tmp = 0
	if (x / y) <= -2e+30:
		tmp = t_2
	elif (x / y) <= 5e-12:
		tmp = t_1 + -2.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(t_1 + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -2e+30)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e-12)
		tmp = Float64(t_1 + -2.0);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = t_1 + (x / y);
	tmp = 0.0;
	if ((x / y) <= -2e+30)
		tmp = t_2;
	elseif ((x / y) <= 5e-12)
		tmp = t_1 + -2.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+30], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e-12], N[(t$95$1 + -2.0), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e30 or 4.9999999999999997e-12 < (/.f64 x y)

   1. Initial program 82.5%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{\left(\frac{x}{y}\right)}\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 97.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   7. Simplified 97.6%

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

   if -2e30 < (/.f64 x y) < 4.9999999999999997e-12

   1. Initial program 85.5%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 99.1%

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

Alternative 4: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.46:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -9 \cdot 10^{-38}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -0.46)
   (/ x y)
   (if (<= (/ x y) -9e-38) (/ 2.0 t) (if (<= (/ x y) 2.0) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.46) {
		tmp = x / y;
	} else if ((x / y) <= -9e-38) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	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) <= (-0.46d0)) then
        tmp = x / y
    else if ((x / y) <= (-9d-38)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.46) {
		tmp = x / y;
	} else if ((x / y) <= -9e-38) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -0.46:
		tmp = x / y
	elif (x / y) <= -9e-38:
		tmp = 2.0 / t
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -0.46)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -9e-38)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -0.46)
		tmp = x / y;
	elseif ((x / y) <= -9e-38)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -0.46], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -9e-38], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.46000000000000002 or 2 < (/.f64 x y)

   1. Initial program 82.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 68.6%

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

   5. Simplified 68.6%

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

   if -0.46000000000000002 < (/.f64 x y) < -9.00000000000000018e-38

   1. Initial program 99.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 68.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2}{t}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 56.9%

         \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{t}\right) \]

   8. Simplified 56.9%

      \[\leadsto \color{blue}{\frac{2}{t}} \]

   if -9.00000000000000018e-38 < (/.f64 x y) < 2

   1. Initial program 85.0%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 99.8%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-2} \]
   9. Step-by-step derivation

   10. Simplified 39.5%

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

Alternative 5: 90.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-8}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+30)
   (+ (/ x y) (/ 2.0 t))
   (if (<= (/ x y) 1e-8)
     (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)
     (+ (/ x y) (/ 2.0 (* z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+30) {
		tmp = (x / y) + (2.0 / t);
	} else if ((x / y) <= 1e-8) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = (x / y) + (2.0 / (z * 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+30)) then
        tmp = (x / y) + (2.0d0 / t)
    else if ((x / y) <= 1d-8) then
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    else
        tmp = (x / y) + (2.0d0 / (z * 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+30) {
		tmp = (x / y) + (2.0 / t);
	} else if ((x / y) <= 1e-8) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+30:
		tmp = (x / y) + (2.0 / t)
	elif (x / y) <= 1e-8:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+30)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (Float64(x / y) <= 1e-8)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+30)
		tmp = (x / y) + (2.0 / t);
	elseif ((x / y) <= 1e-8)
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+30], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-8], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e30

   1. Initial program 76.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 85.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 85.9%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 85.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{t}\right)\right) \]

   8. Simplified 85.9%

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

   if -2e30 < (/.f64 x y) < 1e-8

   1. Initial program 85.7%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 99.1%

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

   if 1e-8 < (/.f64 x y)

   1. Initial program 87.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\color{blue}{2}, \mathsf{*.f64}\left(t, z\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.0%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-8}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= z -7.8e-70)
     t_1
     (if (<= z 5e-79)
       (/ (/ 2.0 z) t)
       (if (<= z 1.5e+161) t_1 (+ (/ x y) (/ 2.0 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -7.8e-70) {
		tmp = t_1;
	} else if (z <= 5e-79) {
		tmp = (2.0 / z) / t;
	} else if (z <= 1.5e+161) {
		tmp = t_1;
	} else {
		tmp = (x / y) + (2.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (z <= (-7.8d-70)) then
        tmp = t_1
    else if (z <= 5d-79) then
        tmp = (2.0d0 / z) / t
    else if (z <= 1.5d+161) then
        tmp = t_1
    else
        tmp = (x / y) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -7.8e-70) {
		tmp = t_1;
	} else if (z <= 5e-79) {
		tmp = (2.0 / z) / t;
	} else if (z <= 1.5e+161) {
		tmp = t_1;
	} else {
		tmp = (x / y) + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if z <= -7.8e-70:
		tmp = t_1
	elif z <= 5e-79:
		tmp = (2.0 / z) / t
	elif z <= 1.5e+161:
		tmp = t_1
	else:
		tmp = (x / y) + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (z <= -7.8e-70)
		tmp = t_1;
	elseif (z <= 5e-79)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (z <= 1.5e+161)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (z <= -7.8e-70)
		tmp = t_1;
	elseif (z <= 5e-79)
		tmp = (2.0 / z) / t;
	elseif (z <= 1.5e+161)
		tmp = t_1;
	else
		tmp = (x / y) + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-70], t$95$1, If[LessEqual[z, 5e-79], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1.5e+161], t$95$1, N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.80000000000000038e-70 or 4.99999999999999999e-79 < z < 1.50000000000000006e161

   1. Initial program 80.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 69.9%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -7.80000000000000038e-70 < z < 4.99999999999999999e-79

   1. Initial program 97.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{z}\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot 1}{t}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t}\right), z\right) \]

      7. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, t\right), z\right) \]

   5. Simplified 76.2%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right) \]

   7. Applied egg-rr 76.2%

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

   if 1.50000000000000006e161 < z

   1. Initial program 60.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 100.0%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 86.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{t}\right)\right) \]

   8. Simplified 86.0%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+161}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 3 \cdot 10^{-12}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -7.2e-10)
     t_1
     (if (<= (/ x y) 3e-12) (+ -2.0 (/ (/ 2.0 z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -7.2e-10) {
		tmp = t_1;
	} else if ((x / y) <= 3e-12) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	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) + (2.0d0 / t)
    if ((x / y) <= (-7.2d-10)) then
        tmp = t_1
    else if ((x / y) <= 3d-12) then
        tmp = (-2.0d0) + ((2.0d0 / 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 t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -7.2e-10) {
		tmp = t_1;
	} else if ((x / y) <= 3e-12) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if (x / y) <= -7.2e-10:
		tmp = t_1
	elif (x / y) <= 3e-12:
		tmp = -2.0 + ((2.0 / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -7.2e-10)
		tmp = t_1;
	elseif (Float64(x / y) <= 3e-12)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -7.2e-10)
		tmp = t_1;
	elseif ((x / y) <= 3e-12)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -7.2e-10], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 3e-12], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -7.2e-10 or 3.0000000000000001e-12 < (/.f64 x y)

   1. Initial program 83.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 81.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 81.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(\frac{2}{t}\right)}\right) \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 78.6%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(2, \color{blue}{t}\right)\right) \]

   8. Simplified 78.6%

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

   if -7.2e-10 < (/.f64 x y) < 3.0000000000000001e-12

   1. Initial program 85.4%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(\frac{2}{z}\right)}, t\right), -2\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 82.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right), -2\right) \]

   10. Simplified 82.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3 \cdot 10^{-12}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -900:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -900.0) t_1 (if (<= z 2.2e-32) (+ (/ x y) (/ 2.0 (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -900.0) {
		tmp = t_1;
	} else if (z <= 2.2e-32) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	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) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-900.0d0)) then
        tmp = t_1
    else if (z <= 2.2d-32) then
        tmp = (x / y) + (2.0d0 / (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 t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -900.0) {
		tmp = t_1;
	} else if (z <= 2.2e-32) {
		tmp = (x / y) + (2.0 / (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -900.0:
		tmp = t_1
	elif z <= 2.2e-32:
		tmp = (x / y) + (2.0 / (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -900.0)
		tmp = t_1;
	elseif (z <= 2.2e-32)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -900.0)
		tmp = t_1;
	elseif (z <= 2.2e-32)
		tmp = (x / y) + (2.0 / (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -900.0], t$95$1, If[LessEqual[z, 2.2e-32], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -900 or 2.2e-32 < z

   1. Initial program 71.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 97.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 97.7%

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

   if -900 < z < 2.2e-32

   1. Initial program 98.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(\color{blue}{2}, \mathsf{*.f64}\left(t, z\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 86.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -900:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -2.6e-69) t_1 (if (<= z 2.9e-5) (+ -2.0 (/ (/ 2.0 z) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -2.6e-69) {
		tmp = t_1;
	} else if (z <= 2.9e-5) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	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) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-2.6d-69)) then
        tmp = t_1
    else if (z <= 2.9d-5) then
        tmp = (-2.0d0) + ((2.0d0 / 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 t_1 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -2.6e-69) {
		tmp = t_1;
	} else if (z <= 2.9e-5) {
		tmp = -2.0 + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -2.6e-69:
		tmp = t_1
	elif z <= 2.9e-5:
		tmp = -2.0 + ((2.0 / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -2.6e-69)
		tmp = t_1;
	elseif (z <= 2.9e-5)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -2.6e-69)
		tmp = t_1;
	elseif (z <= 2.9e-5)
		tmp = -2.0 + ((2.0 / z) / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-69], t$95$1, If[LessEqual[z, 2.9e-5], N[(-2.0 + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000002e-69 or 2.9e-5 < z

   1. Initial program 74.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 95.9%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 95.9%

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

   if -2.6000000000000002e-69 < z < 2.9e-5

   1. Initial program 97.9%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 86.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{\left(\frac{2}{z}\right)}, t\right), -2\right) \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 85.0%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right), -2\right) \]

   10. Simplified 85.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -0.028:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= (/ x y) -0.028)
     t_1
     (if (<= (/ x y) 5.8e-7) (+ -2.0 (/ 2.0 t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if ((x / y) <= -0.028) {
		tmp = t_1;
	} else if ((x / y) <= 5.8e-7) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	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 = (-2.0d0) + (x / y)
    if ((x / y) <= (-0.028d0)) then
        tmp = t_1
    else if ((x / y) <= 5.8d-7) then
        tmp = (-2.0d0) + (2.0d0 / 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 t_1 = -2.0 + (x / y);
	double tmp;
	if ((x / y) <= -0.028) {
		tmp = t_1;
	} else if ((x / y) <= 5.8e-7) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if (x / y) <= -0.028:
		tmp = t_1
	elif (x / y) <= 5.8e-7:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -0.028)
		tmp = t_1;
	elseif (Float64(x / y) <= 5.8e-7)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if ((x / y) <= -0.028)
		tmp = t_1;
	elseif ((x / y) <= 5.8e-7)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.028], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5.8e-7], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.0280000000000000006 or 5.7999999999999995e-7 < (/.f64 x y)

   1. Initial program 82.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 69.9%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -0.0280000000000000006 < (/.f64 x y) < 5.7999999999999995e-7

   1. Initial program 86.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 58.1%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 58.1%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + -2 \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 57.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   8. Simplified 57.8%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.028:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5.8 \cdot 10^{-7}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -36000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 39:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -36000000000.0)
   (/ x y)
   (if (<= (/ x y) 39.0) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -36000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 39.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	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) <= (-36000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 39.0d0) then
        tmp = (-2.0d0) + (2.0d0 / t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -36000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 39.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -36000000000.0:
		tmp = x / y
	elif (x / y) <= 39.0:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -36000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 39.0)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -36000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 39.0)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -36000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 39.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.6e10 or 39 < (/.f64 x y)

   1. Initial program 82.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 70.2%

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

   5. Simplified 70.2%

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

   if -3.6e10 < (/.f64 x y) < 39

   1. Initial program 85.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 57.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 57.6%

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

   6. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t} + -2 \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right) \]

      4. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right) \]

      6. /-lowering-/.f64 56.8%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right) \]

   8. Simplified 56.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -36000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 39:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= z -8.5e-70) t_1 (if (<= z 3.95e-78) (/ (/ 2.0 z) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -8.5e-70) {
		tmp = t_1;
	} else if (z <= 3.95e-78) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_1;
	}
	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 = (-2.0d0) + (x / y)
    if (z <= (-8.5d-70)) then
        tmp = t_1
    else if (z <= 3.95d-78) then
        tmp = (2.0d0 / 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 t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -8.5e-70) {
		tmp = t_1;
	} else if (z <= 3.95e-78) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if z <= -8.5e-70:
		tmp = t_1
	elif z <= 3.95e-78:
		tmp = (2.0 / z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (z <= -8.5e-70)
		tmp = t_1;
	elseif (z <= 3.95e-78)
		tmp = Float64(Float64(2.0 / z) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (z <= -8.5e-70)
		tmp = t_1;
	elseif (z <= 3.95e-78)
		tmp = (2.0 / z) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e-70], t$95$1, If[LessEqual[z, 3.95e-78], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000002e-70 or 3.94999999999999985e-78 < z

   1. Initial program 76.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 68.2%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -8.5000000000000002e-70 < z < 3.94999999999999985e-78

   1. Initial program 97.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{z}\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot 1}{t}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t}\right), z\right) \]

      7. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, t\right), z\right) \]

   5. Simplified 76.2%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{z}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, z\right), t\right) \]

   7. Applied egg-rr 76.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-70}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= z -2.05e-69) t_1 (if (<= z 7.5e-78) (/ (/ 2.0 t) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -2.05e-69) {
		tmp = t_1;
	} else if (z <= 7.5e-78) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	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 = (-2.0d0) + (x / y)
    if (z <= (-2.05d-69)) then
        tmp = t_1
    else if (z <= 7.5d-78) then
        tmp = (2.0d0 / t) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -2.05e-69) {
		tmp = t_1;
	} else if (z <= 7.5e-78) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if z <= -2.05e-69:
		tmp = t_1
	elif z <= 7.5e-78:
		tmp = (2.0 / t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (z <= -2.05e-69)
		tmp = t_1;
	elseif (z <= 7.5e-78)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (z <= -2.05e-69)
		tmp = t_1;
	elseif (z <= 7.5e-78)
		tmp = (2.0 / t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e-69], t$95$1, If[LessEqual[z, 7.5e-78], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.04999999999999995e-69 or 7.50000000000000041e-78 < z

   1. Initial program 76.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 68.2%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -2.04999999999999995e-69 < z < 7.50000000000000041e-78

   1. Initial program 97.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{z}\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot 1}{t}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t}\right), z\right) \]

      7. /-lowering-/.f64 76.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, t\right), z\right) \]

   5. Simplified 76.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-69}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 64.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= z -1.3e-69) t_1 (if (<= z 3.6e-72) (/ 2.0 (* z t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -1.3e-69) {
		tmp = t_1;
	} else if (z <= 3.6e-72) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	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 = (-2.0d0) + (x / y)
    if (z <= (-1.3d-69)) then
        tmp = t_1
    else if (z <= 3.6d-72) then
        tmp = 2.0d0 / (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 t_1 = -2.0 + (x / y);
	double tmp;
	if (z <= -1.3e-69) {
		tmp = t_1;
	} else if (z <= 3.6e-72) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if z <= -1.3e-69:
		tmp = t_1
	elif z <= 3.6e-72:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (z <= -1.3e-69)
		tmp = t_1;
	elseif (z <= 3.6e-72)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (z <= -1.3e-69)
		tmp = t_1;
	elseif (z <= 3.6e-72)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e-69], t$95$1, If[LessEqual[z, 3.6e-72], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3000000000000001e-69 or 3.6e-72 < z

   1. Initial program 75.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{-2}\right) \]
   4. Step-by-step derivation

   5. Simplified 68.4%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -1.3000000000000001e-69 < z < 3.6e-72

   1. Initial program 97.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{z}\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2 \cdot 1}{t}\right), z\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{2}{t}\right), z\right) \]

      7. /-lowering-/.f64 75.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(2, t\right), z\right) \]

   5. Simplified 75.7%

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

      1. associate-/l/ N/A

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

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

         \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{\left(z \cdot t\right)}\right) \]

      3. *-lowering-*.f64 75.7%

         \[\leadsto \mathsf{/.f64}\left(2, \mathsf{*.f64}\left(z, \color{blue}{t}\right)\right) \]

   7. Applied egg-rr 75.7%

      \[\leadsto \color{blue}{\frac{2}{z \cdot t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-69}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-72}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 36.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 1.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	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 (t <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 1.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 1.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1 < t

   1. Initial program 71.8%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
   6. Step-by-step derivation

   7. Simplified 61.8%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{-2} \]
   9. Step-by-step derivation

   10. Simplified 38.6%

       \[\leadsto \color{blue}{-2} \]

   if -1 < t < 1

   1. Initial program 98.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \frac{1 - t}{t}\right)}\right) \]
   4. Step-by-step derivation

      1. div-sub N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} - \color{blue}{\frac{t}{t}}\right)\right)\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \color{blue}{\left(\mathsf{neg}\left(\frac{t}{t}\right)\right)}\right)\right)\right) \]

      3. *-inverses N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + \left(\mathsf{neg}\left(1\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \left(\frac{1}{t} + -1\right)\right)\right) \]

      5. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot -1}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(2 \cdot \frac{1}{t}\right), \color{blue}{-2}\right)\right) \]

      8. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2 \cdot 1}{t}\right), -2\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\left(\frac{2}{t}\right), -2\right)\right) \]

      10. /-lowering-/.f64 59.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(2, t\right), -2\right)\right) \]

   5. Simplified 59.4%

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

   6. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2}{t}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 33.9%

         \[\leadsto \mathsf{/.f64}\left(2, \color{blue}{t}\right) \]

   8. Simplified 33.9%

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

Alternative 16: 19.5% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return -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 = -2.0d0
end function

Java

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

Python

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

Julia

function code(x, y, z, t)
	return -2.0
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 84.2%

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

3. Simplified 99.1%

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

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(2, \mathsf{/.f64}\left(2, z\right)\right), t\right), \color{blue}{-2}\right) \]
6. Step-by-step derivation

7. Simplified 69.2%

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

8. Taylor expanded in t around inf

   \[\leadsto \color{blue}{-2} \]
9. Step-by-step derivation

10. Simplified 21.6%

    \[\leadsto \color{blue}{-2} \]
11. Add Preprocessing

Developer Target 1: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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 = (((2.0d0 / z) + 2.0d0) / t) - (2.0d0 - (x / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024161 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))