Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 88.6% → 89.6%

Time: 12.0s

Alternatives: 16

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 5e+239) t_1 (+ 1.0 (/ (- -1.0 (/ -1.0 x)) x)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+239) {
		tmp = t_1;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= 5d+239) then
        tmp = t_1
    else
        tmp = 1.0d0 + (((-1.0d0) - ((-1.0d0) / x)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+239) {
		tmp = t_1;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 5e+239:
		tmp = t_1
	else:
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 5e+239)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 5e+239)
		tmp = t_1;
	else
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+239], t$95$1, N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000007e239

   1. Initial program 97.5%

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

   if 5.00000000000000007e239 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 67.4

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1 - \frac{1}{x}}{x}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{1 - \frac{1}{x}}{x}} \]

      5. sub-neg N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)}}{x} \]

      6. distribute-neg-frac N/A

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{x} \]

      7. metadata-eval N/A

         \[\leadsto 1 - \frac{1 + \frac{\color{blue}{-1}}{x}}{x} \]

      8. lower-+.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \frac{-1}{x}}}{x} \]

      9. lower-/.f64 76.2

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{-1}{x}}}{x} \]

   8. Simplified 76.2%

      \[\leadsto \color{blue}{1 - \frac{1 + \frac{-1}{x}}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+239}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{y \cdot z}{t\_1 \cdot \left(x + 1\right)}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0.02:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{x}{x + 1} + \frac{x}{t\_1 \cdot \left(-1 - x\right)}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (* y z) (* t_1 (+ x 1.0))))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -5e+19)
     t_2
     (if (<= t_3 0.02)
       (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
       (if (<= t_3 2.0)
         (+ (/ x (+ x 1.0)) (/ x (* t_1 (- -1.0 x))))
         (if (<= t_3 5e+239) t_2 (+ 1.0 (/ (- -1.0 (/ -1.0 x)) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 0.02) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = (x / (x + 1.0)) + (x / (t_1 * (-1.0 - x)));
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (y * z) / (t_1 * (x + 1.0d0))
    t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_3 <= (-5d+19)) then
        tmp = t_2
    else if (t_3 <= 0.02d0) then
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    else if (t_3 <= 2.0d0) then
        tmp = (x / (x + 1.0d0)) + (x / (t_1 * ((-1.0d0) - x)))
    else if (t_3 <= 5d+239) then
        tmp = t_2
    else
        tmp = 1.0d0 + (((-1.0d0) - ((-1.0d0) / x)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 0.02) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = (x / (x + 1.0)) + (x / (t_1 * (-1.0 - x)));
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (y * z) / (t_1 * (x + 1.0))
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -5e+19:
		tmp = t_2
	elif t_3 <= 0.02:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	elif t_3 <= 2.0:
		tmp = (x / (x + 1.0)) + (x / (t_1 * (-1.0 - x)))
	elif t_3 <= 5e+239:
		tmp = t_2
	else:
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(y * z) / Float64(t_1 * Float64(x + 1.0)))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 0.02)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(x / Float64(t_1 * Float64(-1.0 - x))));
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (y * z) / (t_1 * (x + 1.0));
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 0.02)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	elseif (t_3 <= 2.0)
		tmp = (x / (x + 1.0)) + (x / (t_1 * (-1.0 - x)));
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+19], t$95$2, If[LessEqual[t$95$3, 0.02], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / N[(t$95$1 * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+239], t$95$2, N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e19 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000007e239

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 89.3

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

   5. Simplified 89.3%

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

   if -5e19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.0200000000000000004

   1. Initial program 97.8%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      11. lower--.f64 N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      12. lower-/.f64 97.4

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z}} - y}{t}}{x + 1} \]

   5. Simplified 97.4%

      \[\leadsto \frac{\color{blue}{x - \frac{\frac{x}{z} - y}{t}}}{x + 1} \]

   if 0.0200000000000000004 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 99.9

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

   5. Simplified 99.9%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. associate-/l/ N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 99.9

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 99.9

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

   7. Applied egg-rr 99.9%

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

   if 5.00000000000000007e239 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 67.4

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1 - \frac{1}{x}}{x}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{1 - \frac{1}{x}}{x}} \]

      5. sub-neg N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)}}{x} \]

      6. distribute-neg-frac N/A

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{x} \]

      7. metadata-eval N/A

         \[\leadsto 1 - \frac{1 + \frac{\color{blue}{-1}}{x}}{x} \]

      8. lower-+.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \frac{-1}{x}}}{x} \]

      9. lower-/.f64 76.2

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{-1}{x}}}{x} \]

   8. Simplified 76.2%

      \[\leadsto \color{blue}{1 - \frac{1 + \frac{-1}{x}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 0.02:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x}{x + 1} + \frac{x}{\left(z \cdot t - x\right) \cdot \left(-1 - x\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+239}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{y \cdot z}{t\_1 \cdot \left(x + 1\right)}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0.02:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{\frac{x}{t\_1} - x}{-1 - x}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (* y z) (* t_1 (+ x 1.0))))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -5e+19)
     t_2
     (if (<= t_3 0.02)
       (/ (+ x (/ (- y (/ x z)) t)) (+ x 1.0))
       (if (<= t_3 2.0)
         (/ (- (/ x t_1) x) (- -1.0 x))
         (if (<= t_3 5e+239) t_2 (+ 1.0 (/ (- -1.0 (/ -1.0 x)) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 0.02) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = ((x / t_1) - x) / (-1.0 - x);
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (y * z) / (t_1 * (x + 1.0d0))
    t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_3 <= (-5d+19)) then
        tmp = t_2
    else if (t_3 <= 0.02d0) then
        tmp = (x + ((y - (x / z)) / t)) / (x + 1.0d0)
    else if (t_3 <= 2.0d0) then
        tmp = ((x / t_1) - x) / ((-1.0d0) - x)
    else if (t_3 <= 5d+239) then
        tmp = t_2
    else
        tmp = 1.0d0 + (((-1.0d0) - ((-1.0d0) / x)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 0.02) {
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = ((x / t_1) - x) / (-1.0 - x);
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (y * z) / (t_1 * (x + 1.0))
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -5e+19:
		tmp = t_2
	elif t_3 <= 0.02:
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0)
	elif t_3 <= 2.0:
		tmp = ((x / t_1) - x) / (-1.0 - x)
	elif t_3 <= 5e+239:
		tmp = t_2
	else:
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(y * z) / Float64(t_1 * Float64(x + 1.0)))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 0.02)
		tmp = Float64(Float64(x + Float64(Float64(y - Float64(x / z)) / t)) / Float64(x + 1.0));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(Float64(x / t_1) - x) / Float64(-1.0 - x));
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (y * z) / (t_1 * (x + 1.0));
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 0.02)
		tmp = (x + ((y - (x / z)) / t)) / (x + 1.0);
	elseif (t_3 <= 2.0)
		tmp = ((x / t_1) - x) / (-1.0 - x);
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+19], t$95$2, If[LessEqual[t$95$3, 0.02], N[(N[(x + N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(N[(x / t$95$1), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+239], t$95$2, N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e19 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000007e239

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 89.3

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

   5. Simplified 89.3%

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

   if -5e19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.0200000000000000004

   1. Initial program 97.8%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      11. lower--.f64 N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      12. lower-/.f64 97.4

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z}} - y}{t}}{x + 1} \]

   5. Simplified 97.4%

      \[\leadsto \frac{\color{blue}{x - \frac{\frac{x}{z} - y}{t}}}{x + 1} \]

   if 0.0200000000000000004 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 99.9

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

   5. Simplified 99.9%

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

   if 5.00000000000000007e239 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 67.4

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1 - \frac{1}{x}}{x}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{1 - \frac{1}{x}}{x}} \]

      5. sub-neg N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)}}{x} \]

      6. distribute-neg-frac N/A

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{x} \]

      7. metadata-eval N/A

         \[\leadsto 1 - \frac{1 + \frac{\color{blue}{-1}}{x}}{x} \]

      8. lower-+.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \frac{-1}{x}}}{x} \]

      9. lower-/.f64 76.2

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{-1}{x}}}{x} \]

   8. Simplified 76.2%

      \[\leadsto \color{blue}{1 - \frac{1 + \frac{-1}{x}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 0.02:\\ \;\;\;\;\frac{x + \frac{y - \frac{x}{z}}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{\frac{x}{z \cdot t - x} - x}{-1 - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+239}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{y \cdot z}{t\_1 \cdot \left(x + 1\right)}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0.02:\\ \;\;\;\;\frac{x + \frac{\mathsf{fma}\left(y, z, -x\right)}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{\frac{x}{t\_1} - x}{-1 - x}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (* y z) (* t_1 (+ x 1.0))))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -5e+19)
     t_2
     (if (<= t_3 0.02)
       (/ (+ x (/ (fma y z (- x)) (* z t))) (+ x 1.0))
       (if (<= t_3 2.0)
         (/ (- (/ x t_1) x) (- -1.0 x))
         (if (<= t_3 5e+239) t_2 (+ 1.0 (/ (- -1.0 (/ -1.0 x)) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 0.02) {
		tmp = (x + (fma(y, z, -x) / (z * t))) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = ((x / t_1) - x) / (-1.0 - x);
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(y * z) / Float64(t_1 * Float64(x + 1.0)))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 0.02)
		tmp = Float64(Float64(x + Float64(fma(y, z, Float64(-x)) / Float64(z * t))) / Float64(x + 1.0));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(Float64(x / t_1) - x) / Float64(-1.0 - x));
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+19], t$95$2, If[LessEqual[t$95$3, 0.02], N[(N[(x + N[(N[(y * z + (-x)), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(N[(x / t$95$1), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+239], t$95$2, N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e19 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000007e239

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 89.3

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

   5. Simplified 89.3%

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

   if -5e19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.0200000000000000004

   1. Initial program 97.8%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. sub-neg N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-*.f64 95.4

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

   5. Simplified 95.4%

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

   if 0.0200000000000000004 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 99.9

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

   5. Simplified 99.9%

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

   if 5.00000000000000007e239 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 67.4

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1 - \frac{1}{x}}{x}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{1 - \frac{1}{x}}{x}} \]

      5. sub-neg N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)}}{x} \]

      6. distribute-neg-frac N/A

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{x} \]

      7. metadata-eval N/A

         \[\leadsto 1 - \frac{1 + \frac{\color{blue}{-1}}{x}}{x} \]

      8. lower-+.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \frac{-1}{x}}}{x} \]

      9. lower-/.f64 76.2

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{-1}{x}}}{x} \]

   8. Simplified 76.2%

      \[\leadsto \color{blue}{1 - \frac{1 + \frac{-1}{x}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 0.02:\\ \;\;\;\;\frac{x + \frac{\mathsf{fma}\left(y, z, -x\right)}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{\frac{x}{z \cdot t - x} - x}{-1 - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+239}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{y \cdot z}{t\_1 \cdot \left(x + 1\right)}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;\frac{\frac{x}{t\_1} - x}{-1 - x}\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (* y z) (* t_1 (+ x 1.0))))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -5e+19)
     t_2
     (if (<= t_3 -2e-303)
       (/ (+ x (/ y t)) (+ x 1.0))
       (if (<= t_3 2.0)
         (/ (- (/ x t_1) x) (- -1.0 x))
         (if (<= t_3 5e+239) t_2 (+ 1.0 (/ (- -1.0 (/ -1.0 x)) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= -2e-303) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = ((x / t_1) - x) / (-1.0 - x);
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (y * z) / (t_1 * (x + 1.0d0))
    t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_3 <= (-5d+19)) then
        tmp = t_2
    else if (t_3 <= (-2d-303)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (t_3 <= 2.0d0) then
        tmp = ((x / t_1) - x) / ((-1.0d0) - x)
    else if (t_3 <= 5d+239) then
        tmp = t_2
    else
        tmp = 1.0d0 + (((-1.0d0) - ((-1.0d0) / x)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= -2e-303) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = ((x / t_1) - x) / (-1.0 - x);
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (y * z) / (t_1 * (x + 1.0))
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -5e+19:
		tmp = t_2
	elif t_3 <= -2e-303:
		tmp = (x + (y / t)) / (x + 1.0)
	elif t_3 <= 2.0:
		tmp = ((x / t_1) - x) / (-1.0 - x)
	elif t_3 <= 5e+239:
		tmp = t_2
	else:
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(y * z) / Float64(t_1 * Float64(x + 1.0)))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= -2e-303)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (t_3 <= 2.0)
		tmp = Float64(Float64(Float64(x / t_1) - x) / Float64(-1.0 - x));
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (y * z) / (t_1 * (x + 1.0));
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= -2e-303)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (t_3 <= 2.0)
		tmp = ((x / t_1) - x) / (-1.0 - x);
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+19], t$95$2, If[LessEqual[t$95$3, -2e-303], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], N[(N[(N[(x / t$95$1), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 5e+239], t$95$2, N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e19 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000007e239

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 89.3

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

   5. Simplified 89.3%

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

   if -5e19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -1.99999999999999986e-303

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 86.0

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

   5. Simplified 86.0%

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

   if -1.99999999999999986e-303 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 98.2

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

   5. Simplified 98.2%

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

   if 5.00000000000000007e239 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 67.4

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1 - \frac{1}{x}}{x}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{1 - \frac{1}{x}}{x}} \]

      5. sub-neg N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)}}{x} \]

      6. distribute-neg-frac N/A

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{x} \]

      7. metadata-eval N/A

         \[\leadsto 1 - \frac{1 + \frac{\color{blue}{-1}}{x}}{x} \]

      8. lower-+.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \frac{-1}{x}}}{x} \]

      9. lower-/.f64 76.2

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{-1}{x}}}{x} \]

   8. Simplified 76.2%

      \[\leadsto \color{blue}{1 - \frac{1 + \frac{-1}{x}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{-303}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{\frac{x}{z \cdot t - x} - x}{-1 - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+239}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{y \cdot z}{t\_1 \cdot \left(x + 1\right)}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0.9999999988903038:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t\_3 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+239}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (* y z) (* t_1 (+ x 1.0))))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -5e+19)
     t_2
     (if (<= t_3 0.9999999988903038)
       (/ (+ x (/ y t)) (+ x 1.0))
       (if (<= t_3 2.0)
         1.0
         (if (<= t_3 5e+239) t_2 (+ 1.0 (/ (- -1.0 (/ -1.0 x)) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 0.9999999988903038) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (y * z) / (t_1 * (x + 1.0d0))
    t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_3 <= (-5d+19)) then
        tmp = t_2
    else if (t_3 <= 0.9999999988903038d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (t_3 <= 2.0d0) then
        tmp = 1.0d0
    else if (t_3 <= 5d+239) then
        tmp = t_2
    else
        tmp = 1.0d0 + (((-1.0d0) - ((-1.0d0) / x)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (y * z) / (t_1 * (x + 1.0));
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+19) {
		tmp = t_2;
	} else if (t_3 <= 0.9999999988903038) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (t_3 <= 2.0) {
		tmp = 1.0;
	} else if (t_3 <= 5e+239) {
		tmp = t_2;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (y * z) / (t_1 * (x + 1.0))
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -5e+19:
		tmp = t_2
	elif t_3 <= 0.9999999988903038:
		tmp = (x + (y / t)) / (x + 1.0)
	elif t_3 <= 2.0:
		tmp = 1.0
	elif t_3 <= 5e+239:
		tmp = t_2
	else:
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(y * z) / Float64(t_1 * Float64(x + 1.0)))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 0.9999999988903038)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (y * z) / (t_1 * (x + 1.0));
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -5e+19)
		tmp = t_2;
	elseif (t_3 <= 0.9999999988903038)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (t_3 <= 2.0)
		tmp = 1.0;
	elseif (t_3 <= 5e+239)
		tmp = t_2;
	else
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+19], t$95$2, If[LessEqual[t$95$3, 0.9999999988903038], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2.0], 1.0, If[LessEqual[t$95$3, 5e+239], t$95$2, N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -5e19 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000007e239

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 89.3

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

   5. Simplified 89.3%

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

   if -5e19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999998890303776

   1. Initial program 97.9%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 80.2

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

   5. Simplified 80.2%

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

   if 0.999999998890303776 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 99.1%

      \[\leadsto \color{blue}{1} \]

   if 5.00000000000000007e239 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 26.2%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 67.4

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1 - \frac{1}{x}}{x}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{1 - \frac{1}{x}}{x}} \]

      5. sub-neg N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)}}{x} \]

      6. distribute-neg-frac N/A

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{x} \]

      7. metadata-eval N/A

         \[\leadsto 1 - \frac{1 + \frac{\color{blue}{-1}}{x}}{x} \]

      8. lower-+.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \frac{-1}{x}}}{x} \]

      9. lower-/.f64 76.2

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{-1}{x}}}{x} \]

   8. Simplified 76.2%

      \[\leadsto \color{blue}{1 - \frac{1 + \frac{-1}{x}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 0.9999999988903038:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+239}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (fma x t t)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_2 -4e-181)
     t_1
     (if (<= t_2 5e-5)
       (* x (+ 1.0 (/ -1.0 (* z t))))
       (if (<= t_2 2.0)
         1.0
         (if (<= t_2 5e+182) t_1 (+ 1.0 (/ (- -1.0 (/ -1.0 x)) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / fma(x, t, t);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e-181) {
		tmp = t_1;
	} else if (t_2 <= 5e-5) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+182) {
		tmp = t_1;
	} else {
		tmp = 1.0 + ((-1.0 - (-1.0 / x)) / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y / fma(x, t, t))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -4e-181)
		tmp = t_1;
	elseif (t_2 <= 5e-5)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+182)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(Float64(-1.0 - Float64(-1.0 / x)) / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(x * t + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-181], t$95$1, If[LessEqual[t$95$2, 5e-5], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, If[LessEqual[t$95$2, 5e+182], t$95$1, N[(1.0 + N[(N[(-1.0 - N[(-1.0 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.00000000000000019e-181 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999973e182

   1. Initial program 92.5%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      11. lower--.f64 N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      12. lower-/.f64 70.2

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z}} - y}{t}}{x + 1} \]

   5. Simplified 70.2%

      \[\leadsto \frac{\color{blue}{x - \frac{\frac{x}{z} - y}{t}}}{x + 1} \]

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 57.3

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

   8. Simplified 57.3%

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

   if -4.00000000000000019e-181 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000024e-5

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 86.8

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

   5. Simplified 86.8%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 84.8

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

   8. Simplified 84.8%

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

   if 5.00000000000000024e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 97.2%

      \[\leadsto \color{blue}{1} \]

   if 4.99999999999999973e182 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 40.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 54.3

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{1 - \frac{1}{x}}{x}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{1 - \frac{1}{x}}{x}} \]

      4. lower-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{1 - \frac{1}{x}}{x}} \]

      5. sub-neg N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \left(\mathsf{neg}\left(\frac{1}{x}\right)\right)}}{x} \]

      6. distribute-neg-frac N/A

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{x}}}{x} \]

      7. metadata-eval N/A

         \[\leadsto 1 - \frac{1 + \frac{\color{blue}{-1}}{x}}{x} \]

      8. lower-+.f64 N/A

         \[\leadsto 1 - \frac{\color{blue}{1 + \frac{-1}{x}}}{x} \]

      9. lower-/.f64 62.2

         \[\leadsto 1 - \frac{1 + \color{blue}{\frac{-1}{x}}}{x} \]

   8. Simplified 62.2%

      \[\leadsto \color{blue}{1 - \frac{1 + \frac{-1}{x}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1 - \frac{-1}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (fma x t t)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_2 -4e-181)
     t_1
     (if (<= t_2 5e-5)
       (* x (+ 1.0 (/ -1.0 (* z t))))
       (if (<= t_2 2.0) 1.0 (if (<= t_2 5e+182) t_1 (+ 1.0 (/ -1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / fma(x, t, t);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e-181) {
		tmp = t_1;
	} else if (t_2 <= 5e-5) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+182) {
		tmp = t_1;
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y / fma(x, t, t))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -4e-181)
		tmp = t_1;
	elseif (t_2 <= 5e-5)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+182)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(x * t + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-181], t$95$1, If[LessEqual[t$95$2, 5e-5], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, If[LessEqual[t$95$2, 5e+182], t$95$1, N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.00000000000000019e-181 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999973e182

   1. Initial program 92.5%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      11. lower--.f64 N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      12. lower-/.f64 70.2

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z}} - y}{t}}{x + 1} \]

   5. Simplified 70.2%

      \[\leadsto \frac{\color{blue}{x - \frac{\frac{x}{z} - y}{t}}}{x + 1} \]

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 57.3

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

   8. Simplified 57.3%

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

   if -4.00000000000000019e-181 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000024e-5

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 86.8

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

   5. Simplified 86.8%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 84.8

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

   8. Simplified 84.8%

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

   if 5.00000000000000024e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 97.2%

      \[\leadsto \color{blue}{1} \]

   if 4.99999999999999973e182 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 40.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 54.3

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. distribute-neg-frac N/A

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

      3. metadata-eval N/A

         \[\leadsto 1 + \frac{\color{blue}{-1}}{x} \]

      4. lower-+.f64 N/A

         \[\leadsto \color{blue}{1 + \frac{-1}{x}} \]

      5. lower-/.f64 55.2

         \[\leadsto 1 + \color{blue}{\frac{-1}{x}} \]

   8. Simplified 55.2%

      \[\leadsto \color{blue}{1 + \frac{-1}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (fma x t t)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_2 -4e-181)
     t_1
     (if (<= t_2 5e-5)
       (- x (/ x (* z t)))
       (if (<= t_2 2.0) 1.0 (if (<= t_2 5e+182) t_1 (+ 1.0 (/ -1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / fma(x, t, t);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e-181) {
		tmp = t_1;
	} else if (t_2 <= 5e-5) {
		tmp = x - (x / (z * t));
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+182) {
		tmp = t_1;
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y / fma(x, t, t))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -4e-181)
		tmp = t_1;
	elseif (t_2 <= 5e-5)
		tmp = Float64(x - Float64(x / Float64(z * t)));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+182)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(x * t + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-181], t$95$1, If[LessEqual[t$95$2, 5e-5], N[(x - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, If[LessEqual[t$95$2, 5e+182], t$95$1, N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.00000000000000019e-181 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999973e182

   1. Initial program 92.5%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      11. lower--.f64 N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      12. lower-/.f64 70.2

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z}} - y}{t}}{x + 1} \]

   5. Simplified 70.2%

      \[\leadsto \frac{\color{blue}{x - \frac{\frac{x}{z} - y}{t}}}{x + 1} \]

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 57.3

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

   8. Simplified 57.3%

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

   if -4.00000000000000019e-181 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.00000000000000024e-5

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 86.8

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

   5. Simplified 86.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 86.9

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 86.9

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

   7. Applied egg-rr 86.9%

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

   8. Taylor expanded in x around 0

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

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. *-rgt-identity N/A

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

      4. distribute-neg-frac N/A

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

      5. metadata-eval N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. associate-*r/ N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 84.8

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

   10. Simplified 84.8%

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

   if 5.00000000000000024e-5 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 97.2%

      \[\leadsto \color{blue}{1} \]

   if 4.99999999999999973e182 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 40.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 54.3

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. distribute-neg-frac N/A

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

      3. metadata-eval N/A

         \[\leadsto 1 + \frac{\color{blue}{-1}}{x} \]

      4. lower-+.f64 N/A

         \[\leadsto \color{blue}{1 + \frac{-1}{x}} \]

      5. lower-/.f64 55.2

         \[\leadsto 1 + \color{blue}{\frac{-1}{x}} \]

   8. Simplified 55.2%

      \[\leadsto \color{blue}{1 + \frac{-1}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{x}{z \cdot t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ t_2 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0.9999999988903038:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+182}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (fma x t t)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_2 -4e-181)
     t_1
     (if (<= t_2 0.9999999988903038)
       (/ x (+ x 1.0))
       (if (<= t_2 2.0) 1.0 (if (<= t_2 5e+182) t_1 (+ 1.0 (/ -1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / fma(x, t, t);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= -4e-181) {
		tmp = t_1;
	} else if (t_2 <= 0.9999999988903038) {
		tmp = x / (x + 1.0);
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else if (t_2 <= 5e+182) {
		tmp = t_1;
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y / fma(x, t, t))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -4e-181)
		tmp = t_1;
	elseif (t_2 <= 0.9999999988903038)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	elseif (t_2 <= 5e+182)
		tmp = t_1;
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(x * t + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-181], t$95$1, If[LessEqual[t$95$2, 0.9999999988903038], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2.0], 1.0, If[LessEqual[t$95$2, 5e+182], t$95$1, N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.00000000000000019e-181 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 4.99999999999999973e182

   1. Initial program 92.5%

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

   3. Taylor expanded in t around -inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. sub-neg N/A

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

      5. mul-1-neg N/A

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

      6. remove-double-neg N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. mul-1-neg N/A

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

      10. unsub-neg N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      11. lower--.f64 N/A

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z} - y}}{t}}{x + 1} \]

      12. lower-/.f64 70.2

          \[\leadsto \frac{x - \frac{\color{blue}{\frac{x}{z}} - y}{t}}{x + 1} \]

   5. Simplified 70.2%

      \[\leadsto \frac{\color{blue}{x - \frac{\frac{x}{z} - y}{t}}}{x + 1} \]

   6. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 57.3

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

   8. Simplified 57.3%

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

   if -4.00000000000000019e-181 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999998890303776

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 64.2

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if 0.999999998890303776 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 99.1%

      \[\leadsto \color{blue}{1} \]

   if 4.99999999999999973e182 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 40.9%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 54.3

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 54.3%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around inf

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

      1. sub-neg N/A

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

      2. distribute-neg-frac N/A

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

      3. metadata-eval N/A

         \[\leadsto 1 + \frac{\color{blue}{-1}}{x} \]

      4. lower-+.f64 N/A

         \[\leadsto \color{blue}{1 + \frac{-1}{x}} \]

      5. lower-/.f64 55.2

         \[\leadsto 1 + \color{blue}{\frac{-1}{x}} \]

   8. Simplified 55.2%

      \[\leadsto \color{blue}{1 + \frac{-1}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 0.9999999988903038:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+182}:\\ \;\;\;\;\frac{y}{\mathsf{fma}\left(x, t, t\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_2 \leq 0.9999999988903038:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_2 0.9999999988903038) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.9999999988903038) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_2 <= 0.9999999988903038d0) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    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 / t)) / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_2 <= 0.9999999988903038) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_2 <= 0.9999999988903038:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= 0.9999999988903038)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= 0.9999999988903038)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 0.9999999988903038], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999998890303776 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 68.7

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

   5. Simplified 68.7%

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

   if 0.999999998890303776 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 99.1%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 0.9999999988903038:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 0.9999999988903038:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -4e-181)
     (/ y t)
     (if (<= t_1 0.9999999988903038) (/ x (+ x 1.0)) 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -4e-181) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999988903038) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= (-4d-181)) then
        tmp = y / t
    else if (t_1 <= 0.9999999988903038d0) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -4e-181) {
		tmp = y / t;
	} else if (t_1 <= 0.9999999988903038) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -4e-181:
		tmp = y / t
	elif t_1 <= 0.9999999988903038:
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -4e-181)
		tmp = Float64(y / t);
	elseif (t_1 <= 0.9999999988903038)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -4e-181)
		tmp = y / t;
	elseif (t_1 <= 0.9999999988903038)
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-181], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 0.9999999988903038], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.00000000000000019e-181

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 54.8

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

   5. Simplified 54.8%

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

   if -4.00000000000000019e-181 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 0.999999998890303776

   1. Initial program 97.1%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 64.2

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   if 0.999999998890303776 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 94.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 87.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 0.9999999988903038:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 -4e-181) (/ y t) (if (<= t_1 5e-19) x 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -4e-181) {
		tmp = y / t;
	} else if (t_1 <= 5e-19) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= (-4d-181)) then
        tmp = y / t
    else if (t_1 <= 5d-19) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= -4e-181) {
		tmp = y / t;
	} else if (t_1 <= 5e-19) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= -4e-181:
		tmp = y / t
	elif t_1 <= 5e-19:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -4e-181)
		tmp = Float64(y / t);
	elseif (t_1 <= 5e-19)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -4e-181)
		tmp = y / t;
	elseif (t_1 <= 5e-19)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-181], N[(y / t), $MachinePrecision], If[LessEqual[t$95$1, 5e-19], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -4.00000000000000019e-181

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 54.8

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

   5. Simplified 54.8%

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

   if -4.00000000000000019e-181 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e-19

   1. Initial program 96.5%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 68.1

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 68.1%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around 0

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

   8. Simplified 68.1%

      \[\leadsto \frac{x}{\color{blue}{1}} \]

   if 5.0000000000000004e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 85.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -4 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 92.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (y * ((z / ((z * t) - x)) + (x / (y * (x - (z * t))))))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in y around inf

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

   1. lower-*.f64 N/A

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

   2. +-commutative N/A

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

   3. mul-1-neg N/A

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

   4. sub-neg N/A

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

   5. lower--.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower--.f64 N/A

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

   8. lower-*.f64 N/A

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

   9. lower-/.f64 N/A

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

   10. lower-*.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lower-*.f64 96.2

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

5. Simplified 96.2%

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

6. Final simplification 96.2%

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

Alternative 15: 61.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0)) 5e-19)
   (- x (* x x))
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= 5e-19) {
		tmp = x - (x * x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)) <= 5d-19) then
        tmp = x - (x * x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= 5e-19) {
		tmp = x - (x * x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= 5e-19:
		tmp = x - (x * x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0)) <= 5e-19)
		tmp = Float64(x - Float64(x * x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)) <= 5e-19)
		tmp = x - (x * x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 5e-19], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5.0000000000000004e-19

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{1 + x}} \]

      2. +-commutative N/A

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

      3. lower-+.f64 33.5

         \[\leadsto \frac{x}{\color{blue}{x + 1}} \]

   5. Simplified 33.5%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]

   6. Taylor expanded in x around 0

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

      1. distribute-rgt-in N/A

         \[\leadsto \color{blue}{1 \cdot x + \left(-1 \cdot x\right) \cdot x} \]

      2. *-lft-identity N/A

         \[\leadsto \color{blue}{x} + \left(-1 \cdot x\right) \cdot x \]

      3. mul-1-neg N/A

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} \cdot x \]

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

         \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(x \cdot x\right)\right)} \]

      5. unpow2 N/A

         \[\leadsto x + \left(\mathsf{neg}\left(\color{blue}{{x}^{2}}\right)\right) \]

      6. unsub-neg N/A

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

      7. lower--.f64 N/A

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

      8. unpow2 N/A

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

      9. lower-*.f64 31.6

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

   8. Simplified 31.6%

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

   if 5.0000000000000004e-19 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 94.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 85.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.0% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Simplified 59.4%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 99.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024208 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1)))

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