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

Percentage Accurate: 86.2% → 99.2%

Time: 10.1s

Alternatives: 13

Speedup: 1.3×

• 22.6% 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: 86.2% 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: 99.2% 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 88.1%

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

3. Simplified 99.5%

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

Alternative 2: 92.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 (* z t)))))
   (if (<= (/ x y) -1e+130)
     t_1
     (if (<= (/ x y) -10000000.0)
       (+ (/ x y) (+ -2.0 (/ 2.0 t)))
       (if (<= (/ x y) 100000000000.0)
         (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / (z * t));
	double tmp;
	if ((x / y) <= -1e+130) {
		tmp = t_1;
	} else if ((x / y) <= -10000000.0) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else if ((x / y) <= 100000000000.0) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} 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 / (z * t))
    if ((x / y) <= (-1d+130)) then
        tmp = t_1
    else if ((x / y) <= (-10000000.0d0)) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else if ((x / y) <= 100000000000.0d0) then
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    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 / (z * t));
	double tmp;
	if ((x / y) <= -1e+130) {
		tmp = t_1;
	} else if ((x / y) <= -10000000.0) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else if ((x / y) <= 100000000000.0) {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / (z * t))
	tmp = 0
	if (x / y) <= -1e+130:
		tmp = t_1
	elif (x / y) <= -10000000.0:
		tmp = (x / y) + (-2.0 + (2.0 / t))
	elif (x / y) <= 100000000000.0:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)))
	tmp = 0.0
	if (Float64(x / y) <= -1e+130)
		tmp = t_1;
	elseif (Float64(x / y) <= -10000000.0)
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	elseif (Float64(x / y) <= 100000000000.0)
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / (z * t));
	tmp = 0.0;
	if ((x / y) <= -1e+130)
		tmp = t_1;
	elseif ((x / y) <= -10000000.0)
		tmp = (x / y) + (-2.0 + (2.0 / t));
	elseif ((x / y) <= 100000000000.0)
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	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[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+130], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -10000000.0], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 100000000000.0], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.0000000000000001e130 or 1e11 < (/.f64 x y)

   1. Initial program 88.0%

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

   3. Taylor expanded in z around 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 92.7%

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

   if -1.0000000000000001e130 < (/.f64 x y) < -1e7

   1. Initial program 77.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 94.8%

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

   5. Simplified 94.8%

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

   if -1e7 < (/.f64 x y) < 1e11

   1. Initial program 89.7%

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

   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 98.4%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq -10000000:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -6300000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1.04 \cdot 10^{-54}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -6300000.0)
     t_1
     (if (<= (/ x y) -1.04e-54)
       (/ 2.0 (* z t))
       (if (<= (/ x y) 2.9e-7) (+ -2.0 (/ 2.0 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) <= -6300000.0) {
		tmp = t_1;
	} else if ((x / y) <= -1.04e-54) {
		tmp = 2.0 / (z * t);
	} else if ((x / y) <= 2.9e-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 = (x / y) + (2.0d0 / t)
    if ((x / y) <= (-6300000.0d0)) then
        tmp = t_1
    else if ((x / y) <= (-1.04d-54)) then
        tmp = 2.0d0 / (z * t)
    else if ((x / y) <= 2.9d-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 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -6300000.0) {
		tmp = t_1;
	} else if ((x / y) <= -1.04e-54) {
		tmp = 2.0 / (z * t);
	} else if ((x / y) <= 2.9e-7) {
		tmp = -2.0 + (2.0 / 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) <= -6300000.0:
		tmp = t_1
	elif (x / y) <= -1.04e-54:
		tmp = 2.0 / (z * t)
	elif (x / y) <= 2.9e-7:
		tmp = -2.0 + (2.0 / 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) <= -6300000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= -1.04e-54)
		tmp = Float64(2.0 / Float64(z * t));
	elseif (Float64(x / y) <= 2.9e-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 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -6300000.0)
		tmp = t_1;
	elseif ((x / y) <= -1.04e-54)
		tmp = 2.0 / (z * t);
	elseif ((x / y) <= 2.9e-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[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -6300000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1.04e-54], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.9e-7], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.3e6 or 2.8999999999999998e-7 < (/.f64 x y)

   1. Initial program 87.2%

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

   3. Taylor expanded in 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 83.2%

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

   5. Simplified 83.2%

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

   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 82.0%

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

   8. Simplified 82.0%

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

   if -6.3e6 < (/.f64 x y) < -1.04e-54

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l/ N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

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

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. /-lowering-/.f64 80.5%

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

   5. Simplified 80.5%

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

      1. associate-/l/ N/A

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

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

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

      3. *-lowering-*.f64 80.7%

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

   7. Applied egg-rr 80.7%

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

   if -1.04e-54 < (/.f64 x y) < 2.8999999999999998e-7

   1. Initial program 87.6%

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

   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 99.5%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 66.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6300000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.04 \cdot 10^{-54}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;t \leq -0.042:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-139}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= t -0.042)
     t_1
     (if (<= t 1.6e-139)
       (/ (+ 2.0 (/ 2.0 z)) t)
       (if (<= t 7.3e-16) (+ (/ x y) (/ 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 (t <= -0.042) {
		tmp = t_1;
	} else if (t <= 1.6e-139) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (t <= 7.3e-16) {
		tmp = (x / y) + (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 (t <= (-0.042d0)) then
        tmp = t_1
    else if (t <= 1.6d-139) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if (t <= 7.3d-16) then
        tmp = (x / y) + (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 (t <= -0.042) {
		tmp = t_1;
	} else if (t <= 1.6e-139) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (t <= 7.3e-16) {
		tmp = (x / y) + (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 t <= -0.042:
		tmp = t_1
	elif t <= 1.6e-139:
		tmp = (2.0 + (2.0 / z)) / t
	elif t <= 7.3e-16:
		tmp = (x / y) + (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 (t <= -0.042)
		tmp = t_1;
	elseif (t <= 1.6e-139)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif (t <= 7.3e-16)
		tmp = Float64(Float64(x / y) + 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 (t <= -0.042)
		tmp = t_1;
	elseif (t <= 1.6e-139)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif (t <= 7.3e-16)
		tmp = (x / y) + (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[t, -0.042], t$95$1, If[LessEqual[t, 1.6e-139], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 7.3e-16], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.0420000000000000026 or 7.3000000000000003e-16 < t

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 85.6%

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

   if -0.0420000000000000026 < t < 1.6e-139

   1. Initial program 98.7%

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

   3. Taylor expanded in 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 84.3%

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

   5. Simplified 84.3%

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

   if 1.6e-139 < t < 7.3000000000000003e-16

   1. Initial program 99.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 79.6%

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

   5. Simplified 79.6%

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

   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 79.6%

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

   8. Simplified 79.6%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.042:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-139}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 7.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -5900000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -5900000.0)
     t_1
     (if (<= (/ x y) 2.9e-7) (+ -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) <= -5900000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2.9e-7) {
		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) <= (-5900000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 2.9d-7) 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) <= -5900000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2.9e-7) {
		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) <= -5900000.0:
		tmp = t_1
	elif (x / y) <= 2.9e-7:
		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) <= -5900000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2.9e-7)
		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) <= -5900000.0)
		tmp = t_1;
	elseif ((x / y) <= 2.9e-7)
		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], -5900000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2.9e-7], 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) < -5.9e6 or 2.8999999999999998e-7 < (/.f64 x y)

   1. Initial program 87.2%

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

   3. Taylor expanded in 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 83.2%

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

   5. Simplified 83.2%

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

   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 82.0%

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

   8. Simplified 82.0%

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

   if -5.9e6 < (/.f64 x y) < 2.8999999999999998e-7

   1. Initial program 89.1%

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

   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%

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

   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 80.2%

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

   10. Simplified 80.2%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5900000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -1.08e-16)
     t_1
     (if (<= z 1.35e-20) (+ (/ 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 <= -1.08e-16) {
		tmp = t_1;
	} else if (z <= 1.35e-20) {
		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 <= (-1.08d-16)) then
        tmp = t_1
    else if (z <= 1.35d-20) 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 <= -1.08e-16) {
		tmp = t_1;
	} else if (z <= 1.35e-20) {
		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 <= -1.08e-16:
		tmp = t_1
	elif z <= 1.35e-20:
		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 <= -1.08e-16)
		tmp = t_1;
	elseif (z <= 1.35e-20)
		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 <= -1.08e-16)
		tmp = t_1;
	elseif (z <= 1.35e-20)
		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, -1.08e-16], t$95$1, If[LessEqual[z, 1.35e-20], 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 < -1.08e-16 or 1.35e-20 < z

   1. Initial program 78.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 98.5%

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

   5. Simplified 98.5%

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

   if -1.08e-16 < z < 1.35e-20

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 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 84.3%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-21}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -3.1e-65) t_1 (if (<= z 2.1e-21) (+ -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 <= -3.1e-65) {
		tmp = t_1;
	} else if (z <= 2.1e-21) {
		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 <= (-3.1d-65)) then
        tmp = t_1
    else if (z <= 2.1d-21) 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 <= -3.1e-65) {
		tmp = t_1;
	} else if (z <= 2.1e-21) {
		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 <= -3.1e-65:
		tmp = t_1
	elif z <= 2.1e-21:
		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 <= -3.1e-65)
		tmp = t_1;
	elseif (z <= 2.1e-21)
		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 <= -3.1e-65)
		tmp = t_1;
	elseif (z <= 2.1e-21)
		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, -3.1e-65], t$95$1, If[LessEqual[z, 2.1e-21], 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 < -3.10000000000000016e-65 or 2.10000000000000013e-21 < z

   1. Initial program 81.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 93.5%

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

   5. Simplified 93.5%

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

   if -3.10000000000000016e-65 < z < 2.10000000000000013e-21

   1. Initial program 98.9%

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

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t} + \left(-2 + \frac{x}{y}\right)} \]
   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 76.1%

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

   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 76.1%

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

   10. Simplified 76.1%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-21}:\\ \;\;\;\;-2 + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -460:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 36000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= (/ x y) -460.0)
     t_1
     (if (<= (/ x y) 36000000000.0) (+ -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) <= -460.0) {
		tmp = t_1;
	} else if ((x / y) <= 36000000000.0) {
		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) <= (-460.0d0)) then
        tmp = t_1
    else if ((x / y) <= 36000000000.0d0) 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) <= -460.0) {
		tmp = t_1;
	} else if ((x / y) <= 36000000000.0) {
		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) <= -460.0:
		tmp = t_1
	elif (x / y) <= 36000000000.0:
		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) <= -460.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 36000000000.0)
		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) <= -460.0)
		tmp = t_1;
	elseif ((x / y) <= 36000000000.0)
		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], -460.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 36000000000.0], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -460 or 3.6e10 < (/.f64 x y)

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 73.0%

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

   if -460 < (/.f64 x y) < 3.6e10

   1. Initial program 89.5%

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

   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 98.4%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 60.2%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -460:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 36000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6800000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 36000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6800000000000.0)
   (/ x y)
   (if (<= (/ x y) 36000000000.0) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6800000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 36000000000.0) {
		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) <= (-6800000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 36000000000.0d0) 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) <= -6800000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 36000000000.0) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6800000000000.0:
		tmp = x / y
	elif (x / y) <= 36000000000.0:
		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) <= -6800000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 36000000000.0)
		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) <= -6800000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 36000000000.0)
		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], -6800000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 36000000000.0], 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) < -6.8e12 or 3.6e10 < (/.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 x around inf

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

      1. /-lowering-/.f64 73.5%

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

   5. Simplified 73.5%

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

   if -6.8e12 < (/.f64 x y) < 3.6e10

   1. Initial program 89.1%

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

   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 97.1%

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

   8. Taylor expanded in z around inf

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

   10. Simplified 59.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6800000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 36000000000:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0056:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4.4e-5) (/ x y) (if (<= (/ x y) 0.0056) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.4e-5) {
		tmp = x / y;
	} else if ((x / y) <= 0.0056) {
		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) <= (-4.4d-5)) then
        tmp = x / y
    else if ((x / y) <= 0.0056d0) 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) <= -4.4e-5) {
		tmp = x / y;
	} else if ((x / y) <= 0.0056) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4.4e-5:
		tmp = x / y
	elif (x / y) <= 0.0056:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4.4e-5)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 0.0056)
		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) <= -4.4e-5)
		tmp = x / y;
	elseif ((x / y) <= 0.0056)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4.4e-5], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0056], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.3999999999999999e-5 or 0.00559999999999999994 < (/.f64 x y)

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 68.3%

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

   5. Simplified 68.3%

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

   if -4.3999999999999999e-5 < (/.f64 x y) < 0.00559999999999999994

   1. Initial program 88.9%

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

   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%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 43.6%

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

Alternative 11: 62.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-139}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= t -4.6e-95) t_1 (if (<= t 1.6e-139) (/ 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 (t <= -4.6e-95) {
		tmp = t_1;
	} else if (t <= 1.6e-139) {
		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 (t <= (-4.6d-95)) then
        tmp = t_1
    else if (t <= 1.6d-139) 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 (t <= -4.6e-95) {
		tmp = t_1;
	} else if (t <= 1.6e-139) {
		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 t <= -4.6e-95:
		tmp = t_1
	elif t <= 1.6e-139:
		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 (t <= -4.6e-95)
		tmp = t_1;
	elseif (t <= 1.6e-139)
		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 (t <= -4.6e-95)
		tmp = t_1;
	elseif (t <= 1.6e-139)
		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[t, -4.6e-95], t$95$1, If[LessEqual[t, 1.6e-139], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.59999999999999998e-95 or 1.6e-139 < t

   1. Initial program 83.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 77.5%

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

   if -4.59999999999999998e-95 < t < 1.6e-139

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l/ N/A

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

      2. metadata-eval N/A

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

      3. associate-*r/ N/A

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

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

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. /-lowering-/.f64 53.5%

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

   5. Simplified 53.5%

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

      1. associate-/l/ N/A

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

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

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

      3. *-lowering-*.f64 53.5%

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

   7. Applied egg-rr 53.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-95}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-139}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -500:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-15}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -500.0) -2.0 (if (<= t 1.62e-15) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -500.0) {
		tmp = -2.0;
	} else if (t <= 1.62e-15) {
		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 <= (-500.0d0)) then
        tmp = -2.0d0
    else if (t <= 1.62d-15) 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 <= -500.0) {
		tmp = -2.0;
	} else if (t <= 1.62e-15) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -500.0:
		tmp = -2.0
	elif t <= 1.62e-15:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -500.0)
		tmp = -2.0;
	elseif (t <= 1.62e-15)
		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 <= -500.0)
		tmp = -2.0;
	elseif (t <= 1.62e-15)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -500.0], -2.0, If[LessEqual[t, 1.62e-15], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -500 or 1.62000000000000009e-15 < t

   1. Initial program 79.1%

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

   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 51.9%

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

   8. Taylor expanded in t around inf

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

   10. Simplified 37.8%

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

   if -500 < t < 1.62000000000000009e-15

   1. Initial program 98.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 33.4%

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

   8. Simplified 33.4%

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

Alternative 13: 20.7% 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 88.1%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t} + \left(-2 + \frac{x}{y}\right)} \]
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 63.7%

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

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: 99.2% 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 2024138 
(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))))