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

Percentage Accurate: 89.0% → 95.8%

Time: 10.7s

Alternatives: 13

Speedup: 0.3×

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: 89.0% 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: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+212}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+212)))
     (/ (+ x (/ y t)) (+ x 1.0))
     t_1)))

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 <= -((double) INFINITY)) || !(t_1 <= 1e+212)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+212)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	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 <= -math.inf) or not (t_1 <= 1e+212):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = t_1
	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 <= Float64(-Inf)) || !(t_1 <= 1e+212))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = t_1;
	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 <= -Inf) || ~((t_1 <= 1e+212)))
		tmp = (x + (y / t)) / (x + 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[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+212]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 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 1)) < -inf.0 or 9.9999999999999991e211 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 23.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 23.9%

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

   3. Simplified 23.9%

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

   4. Taylor expanded in z around inf 79.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 9.9999999999999991e211

   1. Initial program 99.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+212}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 2: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z}{t_1}}{x + 1}\\ t_3 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;\frac{x - \frac{x}{t_1}}{x + 1}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (+ x (/ (* y z) t_1)) (+ x 1.0)))
        (t_3 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -4.4e+127)
     t_3
     (if (<= z -1.35e-105)
       t_2
       (if (<= z 8.5e-182)
         (/ (- x (/ x t_1)) (+ x 1.0))
         (if (<= z 3e+190) t_2 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + ((y * z) / t_1)) / (x + 1.0);
	double t_3 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -4.4e+127) {
		tmp = t_3;
	} else if (z <= -1.35e-105) {
		tmp = t_2;
	} else if (z <= 8.5e-182) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (z <= 3e+190) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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 = (x + ((y * z) / t_1)) / (x + 1.0d0)
    t_3 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-4.4d+127)) then
        tmp = t_3
    else if (z <= (-1.35d-105)) then
        tmp = t_2
    else if (z <= 8.5d-182) then
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    else if (z <= 3d+190) then
        tmp = t_2
    else
        tmp = t_3
    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 = (x + ((y * z) / t_1)) / (x + 1.0);
	double t_3 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -4.4e+127) {
		tmp = t_3;
	} else if (z <= -1.35e-105) {
		tmp = t_2;
	} else if (z <= 8.5e-182) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (z <= 3e+190) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + ((y * z) / t_1)) / (x + 1.0)
	t_3 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -4.4e+127:
		tmp = t_3
	elif z <= -1.35e-105:
		tmp = t_2
	elif z <= 8.5e-182:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif z <= 3e+190:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t_1)) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -4.4e+127)
		tmp = t_3;
	elseif (z <= -1.35e-105)
		tmp = t_2;
	elseif (z <= 8.5e-182)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (z <= 3e+190)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + ((y * z) / t_1)) / (x + 1.0);
	t_3 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -4.4e+127)
		tmp = t_3;
	elseif (z <= -1.35e-105)
		tmp = t_2;
	elseif (z <= 8.5e-182)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (z <= 3e+190)
		tmp = t_2;
	else
		tmp = t_3;
	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[(x + N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e+127], t$95$3, If[LessEqual[z, -1.35e-105], t$95$2, If[LessEqual[z, 8.5e-182], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+190], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4000000000000003e127 or 2.99999999999999982e190 < z

   1. Initial program 62.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 62.8%

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

   3. Simplified 62.8%

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

   4. Taylor expanded in z around inf 90.6%

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

   if -4.4000000000000003e127 < z < -1.34999999999999996e-105 or 8.5000000000000001e-182 < z < 2.99999999999999982e190

   1. Initial program 96.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in y around inf 90.4%

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

      1. *-commutative 90.4%

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

   6. Simplified 90.4%

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

   if -1.34999999999999996e-105 < z < 8.5000000000000001e-182

   1. Initial program 99.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. +-commutative 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+127}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-105}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-182}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+190}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 68.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -0.92:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-122}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-164}:\\ \;\;\;\;1 + t \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (* y (/ z (- (* z t) x)))))
   (if (<= x -0.92)
     t_1
     (if (<= x -2.3e-49)
       t_2
       (if (<= x -4.8e-122)
         (- x (* x x))
         (if (<= x -2.65e-164)
           (+ 1.0 (* t (/ z x)))
           (if (<= x 1.5e-69) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -0.92) {
		tmp = t_1;
	} else if (x <= -2.3e-49) {
		tmp = t_2;
	} else if (x <= -4.8e-122) {
		tmp = x - (x * x);
	} else if (x <= -2.65e-164) {
		tmp = 1.0 + (t * (z / x));
	} else if (x <= 1.5e-69) {
		tmp = t_2;
	} 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 / (x + 1.0d0)
    t_2 = y * (z / ((z * t) - x))
    if (x <= (-0.92d0)) then
        tmp = t_1
    else if (x <= (-2.3d-49)) then
        tmp = t_2
    else if (x <= (-4.8d-122)) then
        tmp = x - (x * x)
    else if (x <= (-2.65d-164)) then
        tmp = 1.0d0 + (t * (z / x))
    else if (x <= 1.5d-69) then
        tmp = t_2
    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 / (x + 1.0);
	double t_2 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -0.92) {
		tmp = t_1;
	} else if (x <= -2.3e-49) {
		tmp = t_2;
	} else if (x <= -4.8e-122) {
		tmp = x - (x * x);
	} else if (x <= -2.65e-164) {
		tmp = 1.0 + (t * (z / x));
	} else if (x <= 1.5e-69) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	t_2 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -0.92:
		tmp = t_1
	elif x <= -2.3e-49:
		tmp = t_2
	elif x <= -4.8e-122:
		tmp = x - (x * x)
	elif x <= -2.65e-164:
		tmp = 1.0 + (t * (z / x))
	elif x <= 1.5e-69:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -0.92)
		tmp = t_1;
	elseif (x <= -2.3e-49)
		tmp = t_2;
	elseif (x <= -4.8e-122)
		tmp = Float64(x - Float64(x * x));
	elseif (x <= -2.65e-164)
		tmp = Float64(1.0 + Float64(t * Float64(z / x)));
	elseif (x <= 1.5e-69)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -0.92)
		tmp = t_1;
	elseif (x <= -2.3e-49)
		tmp = t_2;
	elseif (x <= -4.8e-122)
		tmp = x - (x * x);
	elseif (x <= -2.65e-164)
		tmp = 1.0 + (t * (z / x));
	elseif (x <= 1.5e-69)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.92], t$95$1, If[LessEqual[x, -2.3e-49], t$95$2, If[LessEqual[x, -4.8e-122], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.65e-164], N[(1.0 + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-69], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.92000000000000004 or 1.49999999999999995e-69 < x

   1. Initial program 84.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in t around inf 86.9%

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

      1. +-commutative 86.9%

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

   6. Simplified 86.9%

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

   if -0.92000000000000004 < x < -2.2999999999999999e-49 or -2.65000000000000016e-164 < x < 1.49999999999999995e-69

   1. Initial program 94.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 94.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. *-commutative 61.7%

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

      3. +-commutative 61.7%

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

   6. Simplified 61.7%

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

      1. *-commutative 61.7%

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

      2. times-frac 65.0%

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

      3. *-commutative 65.0%

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

   8. Applied egg-rr 65.0%

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

   9. Taylor expanded in x around 0 63.3%

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

   if -2.2999999999999999e-49 < x < -4.79999999999999975e-122

   1. Initial program 87.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in t around inf 48.5%

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

      1. +-commutative 48.5%

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

   6. Simplified 48.5%

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

   7. Taylor expanded in x around 0 48.5%

      \[\leadsto \color{blue}{-1 \cdot {x}^{2} + x} \]
   8. Step-by-step derivation

      1. +-commutative 48.5%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. neg-mul-1 48.5%

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

      3. unsub-neg 48.5%

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

      4. unpow2 48.5%

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

   9. Simplified 48.5%

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

   if -4.79999999999999975e-122 < x < -2.65000000000000016e-164

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around -inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

      3. distribute-rgt-out-- 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in y around 0 51.9%

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

      1. div-sub 51.9%

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

      2. +-commutative 51.9%

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

      3. +-commutative 51.9%

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

      4. *-inverses 51.9%

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

      5. mul-1-neg 51.9%

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

      6. associate-/l* 51.9%

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

      7. +-commutative 51.9%

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

   9. Simplified 51.9%

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

   10. Taylor expanded in x around 0 51.9%

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

       1. associate-*r/ 51.9%

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

       2. neg-mul-1 51.9%

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

       3. distribute-rgt-neg-in 51.9%

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

   12. Simplified 51.9%

       \[\leadsto 1 - \color{blue}{t \cdot \left(-\frac{z}{x}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.92:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-49}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-122}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-164}:\\ \;\;\;\;1 + t \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 4: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-121}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-164}:\\ \;\;\;\;1 + t \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.6e+18)
   (- 1.0 (* (/ z x) (/ y x)))
   (if (<= x -1.6e-36)
     (/ (/ y (+ x 1.0)) t)
     (if (<= x -3.4e-121)
       (- x (* x x))
       (if (<= x -2.65e-164)
         (+ 1.0 (* t (/ z x)))
         (if (<= x 7.5e-70) (* y (/ z (- (* z t) x))) (/ x (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.6e+18) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= -1.6e-36) {
		tmp = (y / (x + 1.0)) / t;
	} else if (x <= -3.4e-121) {
		tmp = x - (x * x);
	} else if (x <= -2.65e-164) {
		tmp = 1.0 + (t * (z / x));
	} else if (x <= 7.5e-70) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 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 <= (-8.6d+18)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= (-1.6d-36)) then
        tmp = (y / (x + 1.0d0)) / t
    else if (x <= (-3.4d-121)) then
        tmp = x - (x * x)
    else if (x <= (-2.65d-164)) then
        tmp = 1.0d0 + (t * (z / x))
    else if (x <= 7.5d-70) then
        tmp = y * (z / ((z * t) - x))
    else
        tmp = x / (x + 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 <= -8.6e+18) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= -1.6e-36) {
		tmp = (y / (x + 1.0)) / t;
	} else if (x <= -3.4e-121) {
		tmp = x - (x * x);
	} else if (x <= -2.65e-164) {
		tmp = 1.0 + (t * (z / x));
	} else if (x <= 7.5e-70) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.6e+18:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= -1.6e-36:
		tmp = (y / (x + 1.0)) / t
	elif x <= -3.4e-121:
		tmp = x - (x * x)
	elif x <= -2.65e-164:
		tmp = 1.0 + (t * (z / x))
	elif x <= 7.5e-70:
		tmp = y * (z / ((z * t) - x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.6e+18)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= -1.6e-36)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / t);
	elseif (x <= -3.4e-121)
		tmp = Float64(x - Float64(x * x));
	elseif (x <= -2.65e-164)
		tmp = Float64(1.0 + Float64(t * Float64(z / x)));
	elseif (x <= 7.5e-70)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.6e+18)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= -1.6e-36)
		tmp = (y / (x + 1.0)) / t;
	elseif (x <= -3.4e-121)
		tmp = x - (x * x);
	elseif (x <= -2.65e-164)
		tmp = 1.0 + (t * (z / x));
	elseif (x <= 7.5e-70)
		tmp = y * (z / ((z * t) - x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.6e+18], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.6e-36], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -3.4e-121], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.65e-164], N[(1.0 + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-70], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -8.6e18

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around -inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. distribute-rgt-out-- 81.3%

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

      4. unpow2 81.3%

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

      5. times-frac 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around inf 94.9%

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

   if -8.6e18 < x < -1.60000000000000011e-36

   1. Initial program 69.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. *-commutative 69.7%

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

      3. +-commutative 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in z around inf 66.2%

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

      1. associate-/r* 66.2%

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

      2. +-commutative 66.2%

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

   9. Simplified 66.2%

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

   if -1.60000000000000011e-36 < x < -3.40000000000000001e-121

   1. Initial program 88.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around inf 43.1%

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

      1. +-commutative 43.1%

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

   6. Simplified 43.1%

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

   7. Taylor expanded in x around 0 43.1%

      \[\leadsto \color{blue}{-1 \cdot {x}^{2} + x} \]
   8. Step-by-step derivation

      1. +-commutative 43.1%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. neg-mul-1 43.1%

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

      3. unsub-neg 43.1%

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

      4. unpow2 43.1%

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

   9. Simplified 43.1%

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

   if -3.40000000000000001e-121 < x < -2.65000000000000016e-164

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around -inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

      3. distribute-rgt-out-- 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in y around 0 51.9%

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

      1. div-sub 51.9%

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

      2. +-commutative 51.9%

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

      3. +-commutative 51.9%

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

      4. *-inverses 51.9%

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

      5. mul-1-neg 51.9%

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

      6. associate-/l* 51.9%

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

      7. +-commutative 51.9%

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

   9. Simplified 51.9%

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

   10. Taylor expanded in x around 0 51.9%

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

       1. associate-*r/ 51.9%

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

       2. neg-mul-1 51.9%

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

       3. distribute-rgt-neg-in 51.9%

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

   12. Simplified 51.9%

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

   if -2.65000000000000016e-164 < x < 7.49999999999999973e-70

   1. Initial program 93.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. *-commutative 59.0%

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

      3. +-commutative 59.0%

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

   6. Simplified 59.0%

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

      1. *-commutative 59.0%

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

      2. times-frac 62.6%

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

      3. *-commutative 62.6%

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

   8. Applied egg-rr 62.6%

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

   9. Taylor expanded in x around 0 62.6%

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

   if 7.49999999999999973e-70 < x

   1. Initial program 81.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around inf 84.9%

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

      1. +-commutative 84.9%

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

   6. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-121}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-164}:\\ \;\;\;\;1 + t \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 5: 67.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;1 - \frac{y}{x \cdot \frac{x}{z}}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-124}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-164}:\\ \;\;\;\;1 + t \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.6e+18)
   (- 1.0 (/ y (* x (/ x z))))
   (if (<= x -1.45e-38)
     (/ (/ y (+ x 1.0)) t)
     (if (<= x -9e-124)
       (- x (* x x))
       (if (<= x -2.65e-164)
         (+ 1.0 (* t (/ z x)))
         (if (<= x 1.5e-69) (* y (/ z (- (* z t) x))) (/ x (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.6e+18) {
		tmp = 1.0 - (y / (x * (x / z)));
	} else if (x <= -1.45e-38) {
		tmp = (y / (x + 1.0)) / t;
	} else if (x <= -9e-124) {
		tmp = x - (x * x);
	} else if (x <= -2.65e-164) {
		tmp = 1.0 + (t * (z / x));
	} else if (x <= 1.5e-69) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 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 <= (-8.6d+18)) then
        tmp = 1.0d0 - (y / (x * (x / z)))
    else if (x <= (-1.45d-38)) then
        tmp = (y / (x + 1.0d0)) / t
    else if (x <= (-9d-124)) then
        tmp = x - (x * x)
    else if (x <= (-2.65d-164)) then
        tmp = 1.0d0 + (t * (z / x))
    else if (x <= 1.5d-69) then
        tmp = y * (z / ((z * t) - x))
    else
        tmp = x / (x + 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 <= -8.6e+18) {
		tmp = 1.0 - (y / (x * (x / z)));
	} else if (x <= -1.45e-38) {
		tmp = (y / (x + 1.0)) / t;
	} else if (x <= -9e-124) {
		tmp = x - (x * x);
	} else if (x <= -2.65e-164) {
		tmp = 1.0 + (t * (z / x));
	} else if (x <= 1.5e-69) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.6e+18:
		tmp = 1.0 - (y / (x * (x / z)))
	elif x <= -1.45e-38:
		tmp = (y / (x + 1.0)) / t
	elif x <= -9e-124:
		tmp = x - (x * x)
	elif x <= -2.65e-164:
		tmp = 1.0 + (t * (z / x))
	elif x <= 1.5e-69:
		tmp = y * (z / ((z * t) - x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.6e+18)
		tmp = Float64(1.0 - Float64(y / Float64(x * Float64(x / z))));
	elseif (x <= -1.45e-38)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / t);
	elseif (x <= -9e-124)
		tmp = Float64(x - Float64(x * x));
	elseif (x <= -2.65e-164)
		tmp = Float64(1.0 + Float64(t * Float64(z / x)));
	elseif (x <= 1.5e-69)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.6e+18)
		tmp = 1.0 - (y / (x * (x / z)));
	elseif (x <= -1.45e-38)
		tmp = (y / (x + 1.0)) / t;
	elseif (x <= -9e-124)
		tmp = x - (x * x);
	elseif (x <= -2.65e-164)
		tmp = 1.0 + (t * (z / x));
	elseif (x <= 1.5e-69)
		tmp = y * (z / ((z * t) - x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.6e+18], N[(1.0 - N[(y / N[(x * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e-38], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -9e-124], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.65e-164], N[(1.0 + N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-69], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -8.6e18

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around -inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. distribute-rgt-out-- 81.3%

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

      4. unpow2 81.3%

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

      5. times-frac 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around inf 91.1%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{{x}^{2}}} \]
   8. Step-by-step derivation

      1. associate-/l* 94.8%

         \[\leadsto 1 - \color{blue}{\frac{y}{\frac{{x}^{2}}{z}}} \]

      2. unpow2 94.8%

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

      3. associate-*r/ 94.9%

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

   9. Simplified 94.9%

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

   if -8.6e18 < x < -1.44999999999999997e-38

   1. Initial program 69.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. *-commutative 69.7%

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

      3. +-commutative 69.7%

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

   6. Simplified 69.7%

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

   7. Taylor expanded in z around inf 66.2%

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

      1. associate-/r* 66.2%

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

      2. +-commutative 66.2%

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

   9. Simplified 66.2%

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

   if -1.44999999999999997e-38 < x < -8.9999999999999992e-124

   1. Initial program 88.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in t around inf 43.1%

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

      1. +-commutative 43.1%

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

   6. Simplified 43.1%

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

   7. Taylor expanded in x around 0 43.1%

      \[\leadsto \color{blue}{-1 \cdot {x}^{2} + x} \]
   8. Step-by-step derivation

      1. +-commutative 43.1%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. neg-mul-1 43.1%

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

      3. unsub-neg 43.1%

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

      4. unpow2 43.1%

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

   9. Simplified 43.1%

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

   if -8.9999999999999992e-124 < x < -2.65000000000000016e-164

   1. Initial program 99.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around -inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. unsub-neg 67.6%

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

      3. distribute-rgt-out-- 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in y around 0 51.9%

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

      1. div-sub 51.9%

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

      2. +-commutative 51.9%

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

      3. +-commutative 51.9%

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

      4. *-inverses 51.9%

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

      5. mul-1-neg 51.9%

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

      6. associate-/l* 51.9%

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

      7. +-commutative 51.9%

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

   9. Simplified 51.9%

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

   10. Taylor expanded in x around 0 51.9%

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

       1. associate-*r/ 51.9%

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

       2. neg-mul-1 51.9%

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

       3. distribute-rgt-neg-in 51.9%

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

   12. Simplified 51.9%

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

   if -2.65000000000000016e-164 < x < 1.49999999999999995e-69

   1. Initial program 93.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   4. Taylor expanded in y around inf 59.0%

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

      1. *-commutative 59.0%

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

      2. *-commutative 59.0%

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

      3. +-commutative 59.0%

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

   6. Simplified 59.0%

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

      1. *-commutative 59.0%

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

      2. times-frac 62.6%

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

      3. *-commutative 62.6%

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

   8. Applied egg-rr 62.6%

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

   9. Taylor expanded in x around 0 62.6%

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

   if 1.49999999999999995e-69 < x

   1. Initial program 81.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around inf 84.9%

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

      1. +-commutative 84.9%

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

   6. Simplified 84.9%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;1 - \frac{y}{x \cdot \frac{x}{z}}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-124}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-164}:\\ \;\;\;\;1 + t \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 6: 83.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-127} \lor \neg \left(t \leq 9.6 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.2e-127) (not (<= t 9.6e-70)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (/ y (/ x z)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.2e-127) || !(t <= 9.6e-70)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x / z)) / (x + 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 ((t <= (-7.2d-127)) .or. (.not. (t <= 9.6d-70))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / (x / z)) / (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.2e-127) || !(t <= 9.6e-70)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x / z)) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.2e-127) or not (t <= 9.6e-70):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / (x / z)) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.2e-127) || !(t <= 9.6e-70))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / Float64(x / z)) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.2e-127) || ~((t <= 9.6e-70)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / (x / z)) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.2e-127], N[Not[LessEqual[t, 9.6e-70]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.1999999999999999e-127 or 9.6000000000000005e-70 < t

   1. Initial program 84.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 84.9%

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

   3. Simplified 84.9%

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

   4. Taylor expanded in z around inf 87.3%

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

   if -7.1999999999999999e-127 < t < 9.6000000000000005e-70

   1. Initial program 93.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in x around -inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. distribute-rgt-out-- 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in t around 0 76.6%

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

      1. div-sub 76.6%

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

      2. +-commutative 76.6%

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

      3. +-commutative 76.6%

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

      4. *-inverses 76.6%

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

      5. associate-/l* 80.7%

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

      6. +-commutative 80.7%

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

   9. Simplified 80.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-127} \lor \neg \left(t \leq 9.6 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \]

Alternative 7: 67.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{-1}{x}\\ \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-73}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq 7.8:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ -1.0 x))))
   (if (<= x -0.95)
     t_1
     (if (<= x -4.6e-34)
       (/ y t)
       (if (<= x -3.2e-73) (- x (* x x)) (if (<= x 7.8) (/ y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (-1.0 / x);
	double tmp;
	if (x <= -0.95) {
		tmp = t_1;
	} else if (x <= -4.6e-34) {
		tmp = y / t;
	} else if (x <= -3.2e-73) {
		tmp = x - (x * x);
	} else if (x <= 7.8) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + ((-1.0d0) / x)
    if (x <= (-0.95d0)) then
        tmp = t_1
    else if (x <= (-4.6d-34)) then
        tmp = y / t
    else if (x <= (-3.2d-73)) then
        tmp = x - (x * x)
    else if (x <= 7.8d0) then
        tmp = y / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (-1.0 / x);
	double tmp;
	if (x <= -0.95) {
		tmp = t_1;
	} else if (x <= -4.6e-34) {
		tmp = y / t;
	} else if (x <= -3.2e-73) {
		tmp = x - (x * x);
	} else if (x <= 7.8) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + (-1.0 / x)
	tmp = 0
	if x <= -0.95:
		tmp = t_1
	elif x <= -4.6e-34:
		tmp = y / t
	elif x <= -3.2e-73:
		tmp = x - (x * x)
	elif x <= 7.8:
		tmp = y / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(-1.0 / x))
	tmp = 0.0
	if (x <= -0.95)
		tmp = t_1;
	elseif (x <= -4.6e-34)
		tmp = Float64(y / t);
	elseif (x <= -3.2e-73)
		tmp = Float64(x - Float64(x * x));
	elseif (x <= 7.8)
		tmp = Float64(y / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (-1.0 / x);
	tmp = 0.0;
	if (x <= -0.95)
		tmp = t_1;
	elseif (x <= -4.6e-34)
		tmp = y / t;
	elseif (x <= -3.2e-73)
		tmp = x - (x * x);
	elseif (x <= 7.8)
		tmp = y / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.95], t$95$1, If[LessEqual[x, -4.6e-34], N[(y / t), $MachinePrecision], If[LessEqual[x, -3.2e-73], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8], N[(y / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.94999999999999996 or 7.79999999999999982 < x

   1. Initial program 85.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in y around inf 85.1%

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

      1. *-commutative 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in x around inf 89.9%

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

   if -0.94999999999999996 < x < -4.60000000000000022e-34 or -3.19999999999999986e-73 < x < 7.79999999999999982

   1. Initial program 91.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in z around inf 66.2%

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

   5. Taylor expanded in x around 0 49.2%

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

   if -4.60000000000000022e-34 < x < -3.19999999999999986e-73

   1. Initial program 100.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 51.0%

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

      1. +-commutative 51.0%

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

   6. Simplified 51.0%

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

   7. Taylor expanded in x around 0 51.0%

      \[\leadsto \color{blue}{-1 \cdot {x}^{2} + x} \]
   8. Step-by-step derivation

      1. +-commutative 51.0%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. neg-mul-1 51.0%

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

      3. unsub-neg 51.0%

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

      4. unpow2 51.0%

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

   9. Simplified 51.0%

      \[\leadsto \color{blue}{x - x \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-73}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq 7.8:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]

Alternative 8: 67.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-89}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -5.2e-5)
     t_1
     (if (<= x -4.5e-35)
       (/ y t)
       (if (<= x -2.4e-89) (- x (* x x)) (if (<= x 1.05e-21) (/ y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -5.2e-5) {
		tmp = t_1;
	} else if (x <= -4.5e-35) {
		tmp = y / t;
	} else if (x <= -2.4e-89) {
		tmp = x - (x * x);
	} else if (x <= 1.05e-21) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-5.2d-5)) then
        tmp = t_1
    else if (x <= (-4.5d-35)) then
        tmp = y / t
    else if (x <= (-2.4d-89)) then
        tmp = x - (x * x)
    else if (x <= 1.05d-21) then
        tmp = y / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -5.2e-5) {
		tmp = t_1;
	} else if (x <= -4.5e-35) {
		tmp = y / t;
	} else if (x <= -2.4e-89) {
		tmp = x - (x * x);
	} else if (x <= 1.05e-21) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -5.2e-5:
		tmp = t_1
	elif x <= -4.5e-35:
		tmp = y / t
	elif x <= -2.4e-89:
		tmp = x - (x * x)
	elif x <= 1.05e-21:
		tmp = y / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -5.2e-5)
		tmp = t_1;
	elseif (x <= -4.5e-35)
		tmp = Float64(y / t);
	elseif (x <= -2.4e-89)
		tmp = Float64(x - Float64(x * x));
	elseif (x <= 1.05e-21)
		tmp = Float64(y / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -5.2e-5)
		tmp = t_1;
	elseif (x <= -4.5e-35)
		tmp = y / t;
	elseif (x <= -2.4e-89)
		tmp = x - (x * x);
	elseif (x <= 1.05e-21)
		tmp = y / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.2e-5], t$95$1, If[LessEqual[x, -4.5e-35], N[(y / t), $MachinePrecision], If[LessEqual[x, -2.4e-89], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-21], N[(y / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.19999999999999968e-5 or 1.05000000000000006e-21 < x

   1. Initial program 85.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in t around inf 88.4%

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

      1. +-commutative 88.4%

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

   6. Simplified 88.4%

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

   if -5.19999999999999968e-5 < x < -4.5000000000000001e-35 or -2.40000000000000016e-89 < x < 1.05000000000000006e-21

   1. Initial program 91.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in z around inf 66.3%

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

   5. Taylor expanded in x around 0 51.6%

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

   if -4.5000000000000001e-35 < x < -2.40000000000000016e-89

   1. Initial program 92.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in t around inf 48.0%

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

      1. +-commutative 48.0%

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

   6. Simplified 48.0%

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

   7. Taylor expanded in x around 0 48.0%

      \[\leadsto \color{blue}{-1 \cdot {x}^{2} + x} \]
   8. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. neg-mul-1 48.0%

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

      3. unsub-neg 48.0%

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

      4. unpow2 48.0%

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

   9. Simplified 48.0%

      \[\leadsto \color{blue}{x - x \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-89}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 9: 66.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-51}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.6e+18)
   1.0
   (if (<= x -8e-51)
     (/ (/ y (+ x 1.0)) t)
     (if (<= x -1.02e-85)
       (- x (* x x))
       (if (<= x 3.05e-27) (/ y t) (/ x (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.6e+18) {
		tmp = 1.0;
	} else if (x <= -8e-51) {
		tmp = (y / (x + 1.0)) / t;
	} else if (x <= -1.02e-85) {
		tmp = x - (x * x);
	} else if (x <= 3.05e-27) {
		tmp = y / t;
	} else {
		tmp = x / (x + 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 <= (-8.6d+18)) then
        tmp = 1.0d0
    else if (x <= (-8d-51)) then
        tmp = (y / (x + 1.0d0)) / t
    else if (x <= (-1.02d-85)) then
        tmp = x - (x * x)
    else if (x <= 3.05d-27) then
        tmp = y / t
    else
        tmp = x / (x + 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 <= -8.6e+18) {
		tmp = 1.0;
	} else if (x <= -8e-51) {
		tmp = (y / (x + 1.0)) / t;
	} else if (x <= -1.02e-85) {
		tmp = x - (x * x);
	} else if (x <= 3.05e-27) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.6e+18:
		tmp = 1.0
	elif x <= -8e-51:
		tmp = (y / (x + 1.0)) / t
	elif x <= -1.02e-85:
		tmp = x - (x * x)
	elif x <= 3.05e-27:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.6e+18)
		tmp = 1.0;
	elseif (x <= -8e-51)
		tmp = Float64(Float64(y / Float64(x + 1.0)) / t);
	elseif (x <= -1.02e-85)
		tmp = Float64(x - Float64(x * x));
	elseif (x <= 3.05e-27)
		tmp = Float64(y / t);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.6e+18)
		tmp = 1.0;
	elseif (x <= -8e-51)
		tmp = (y / (x + 1.0)) / t;
	elseif (x <= -1.02e-85)
		tmp = x - (x * x);
	elseif (x <= 3.05e-27)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.6e+18], 1.0, If[LessEqual[x, -8e-51], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, -1.02e-85], N[(x - N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.05e-27], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8.6e18

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in y around inf 92.7%

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

      1. *-commutative 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in x around inf 94.5%

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

   if -8.6e18 < x < -8.0000000000000001e-51

   1. Initial program 74.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 74.7%

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

   3. Simplified 74.7%

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

   4. Taylor expanded in y around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. *-commutative 66.8%

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

      3. +-commutative 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in z around inf 55.7%

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

      1. associate-/r* 55.7%

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

      2. +-commutative 55.7%

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

   9. Simplified 55.7%

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

   if -8.0000000000000001e-51 < x < -1.02000000000000001e-85

   1. Initial program 90.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 56.3%

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

      1. +-commutative 56.3%

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

   6. Simplified 56.3%

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

   7. Taylor expanded in x around 0 56.3%

      \[\leadsto \color{blue}{-1 \cdot {x}^{2} + x} \]
   8. Step-by-step derivation

      1. +-commutative 56.3%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. neg-mul-1 56.3%

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

      3. unsub-neg 56.3%

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

      4. unpow2 56.3%

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

   9. Simplified 56.3%

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

   if -1.02000000000000001e-85 < x < 3.05e-27

   1. Initial program 91.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in z around inf 65.0%

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

   5. Taylor expanded in x around 0 49.7%

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

   if 3.05e-27 < x

   1. Initial program 83.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in t around inf 88.3%

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

      1. +-commutative 88.3%

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

   6. Simplified 88.3%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-51}:\\ \;\;\;\;\frac{\frac{y}{x + 1}}{t}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-85}:\\ \;\;\;\;x - x \cdot x\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 10: 77.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;1 - \frac{y}{x \cdot \frac{x}{z}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.9e+23)
   (- 1.0 (/ y (* x (/ x z))))
   (if (<= x 2.5e+56)
     (/ (+ x (/ y t)) (+ x 1.0))
     (- 1.0 (* (/ z x) (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+23) {
		tmp = 1.0 - (y / (x * (x / z)));
	} else if (x <= 2.5e+56) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / x) * (y / 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) :: tmp
    if (x <= (-2.9d+23)) then
        tmp = 1.0d0 - (y / (x * (x / z)))
    else if (x <= 2.5d+56) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z / x) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+23) {
		tmp = 1.0 - (y / (x * (x / z)));
	} else if (x <= 2.5e+56) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z / x) * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.9e+23:
		tmp = 1.0 - (y / (x * (x / z)))
	elif x <= 2.5e+56:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((z / x) * (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.9e+23)
		tmp = Float64(1.0 - Float64(y / Float64(x * Float64(x / z))));
	elseif (x <= 2.5e+56)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.9e+23)
		tmp = 1.0 - (y / (x * (x / z)));
	elseif (x <= 2.5e+56)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((z / x) * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.9e+23], N[(1.0 - N[(y / N[(x * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+56], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.90000000000000013e23

   1. Initial program 92.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in x around -inf 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. distribute-rgt-out-- 81.3%

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

      4. unpow2 81.3%

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

      5. times-frac 90.8%

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

   6. Simplified 90.8%

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

   7. Taylor expanded in y around inf 91.1%

      \[\leadsto 1 - \color{blue}{\frac{y \cdot z}{{x}^{2}}} \]
   8. Step-by-step derivation

      1. associate-/l* 94.8%

         \[\leadsto 1 - \color{blue}{\frac{y}{\frac{{x}^{2}}{z}}} \]

      2. unpow2 94.8%

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

      3. associate-*r/ 94.9%

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

   9. Simplified 94.9%

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

   if -2.90000000000000013e23 < x < 2.50000000000000012e56

   1. Initial program 88.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around inf 67.4%

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

   if 2.50000000000000012e56 < x

   1. Initial program 83.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 83.7%

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

   3. Simplified 83.7%

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

   4. Taylor expanded in x around -inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. distribute-rgt-out-- 73.7%

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

      4. unpow2 73.7%

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

      5. times-frac 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in y around inf 93.2%

      \[\leadsto 1 - \frac{z}{x} \cdot \color{blue}{\frac{y}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;1 - \frac{y}{x \cdot \frac{x}{z}}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \end{array} \]

Alternative 11: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.95 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.95) (not (<= x 1.4))) (+ 1.0 (/ -1.0 x)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.95) || !(x <= 1.4)) {
		tmp = 1.0 + (-1.0 / x);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-0.95d0)) .or. (.not. (x <= 1.4d0))) then
        tmp = 1.0d0 + ((-1.0d0) / x)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.95) || !(x <= 1.4)) {
		tmp = 1.0 + (-1.0 / x);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.95) or not (x <= 1.4):
		tmp = 1.0 + (-1.0 / x)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.95) || !(x <= 1.4))
		tmp = Float64(1.0 + Float64(-1.0 / x));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -0.95) || ~((x <= 1.4)))
		tmp = 1.0 + (-1.0 / x);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.95], N[Not[LessEqual[x, 1.4]], $MachinePrecision]], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.94999999999999996 or 1.3999999999999999 < x

   1. Initial program 85.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in y around inf 85.1%

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

      1. *-commutative 85.1%

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

   6. Simplified 85.1%

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

   7. Taylor expanded in x around inf 89.9%

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

   if -0.94999999999999996 < x < 1.3999999999999999

   1. Initial program 91.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around inf 65.5%

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

   5. Taylor expanded in x around 0 45.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.95 \lor \neg \left(x \leq 1.4\right):\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]

Alternative 12: 67.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.92:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.92) 1.0 (if (<= x 3.9e-26) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.92) {
		tmp = 1.0;
	} else if (x <= 3.9e-26) {
		tmp = y / t;
	} 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 <= (-0.92d0)) then
        tmp = 1.0d0
    else if (x <= 3.9d-26) then
        tmp = y / t
    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 <= -0.92) {
		tmp = 1.0;
	} else if (x <= 3.9e-26) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.92:
		tmp = 1.0
	elif x <= 3.9e-26:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.92)
		tmp = 1.0;
	elseif (x <= 3.9e-26)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.92)
		tmp = 1.0;
	elseif (x <= 3.9e-26)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.92], 1.0, If[LessEqual[x, 3.9e-26], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.92000000000000004 or 3.89999999999999986e-26 < x

   1. Initial program 85.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in x around inf 87.8%

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

   if -0.92000000000000004 < x < 3.89999999999999986e-26

   1. Initial program 91.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in z around inf 65.4%

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

   5. Taylor expanded in x around 0 46.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.92:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-26}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 53.2% accurate, 17.0× 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 88.2%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Step-by-step derivation

   1. *-commutative 88.2%

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

3. Simplified 88.2%

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

4. Taylor expanded in y around inf 77.7%

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

   1. *-commutative 77.7%

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

6. Simplified 77.7%

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

7. Taylor expanded in x around inf 55.9%

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

8. Final simplification 55.9%

   \[\leadsto 1 \]

Developer target: 99.6% accurate, 0.8× 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 2023178 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

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