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

Percentage Accurate: 88.8% → 98.6%

Time: 11.0s

Alternatives: 10

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% 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: 98.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x}\\ t_2 := z \cdot t - x\\ t_3 := \frac{y \cdot \left(\left(\frac{z}{t\_2} + \frac{x}{y}\right) - \frac{\frac{x}{y}}{t\_2}\right)}{x + 1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-106}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ (- (* y z) x) (- x (* z t))) x) (- -1.0 x)))
        (t_2 (- (* z t) x))
        (t_3 (/ (* y (- (+ (/ z t_2) (/ x y)) (/ (/ x y) t_2))) (+ x 1.0))))
   (if (<= t_1 -1e-106)
     t_3
     (if (<= t_1 2e+213)
       t_1
       (if (<= t_1 INFINITY) t_3 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	double t_2 = (z * t) - x;
	double t_3 = (y * (((z / t_2) + (x / y)) - ((x / y) / t_2))) / (x + 1.0);
	double tmp;
	if (t_1 <= -1e-106) {
		tmp = t_3;
	} else if (t_1 <= 2e+213) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	double t_2 = (z * t) - x;
	double t_3 = (y * (((z / t_2) + (x / y)) - ((x / y) / t_2))) / (x + 1.0);
	double tmp;
	if (t_1 <= -1e-106) {
		tmp = t_3;
	} else if (t_1 <= 2e+213) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x)
	t_2 = (z * t) - x
	t_3 = (y * (((z / t_2) + (x / y)) - ((x / y) / t_2))) / (x + 1.0)
	tmp = 0
	if t_1 <= -1e-106:
		tmp = t_3
	elif t_1 <= 2e+213:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_3
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(Float64(y * z) - x) / Float64(x - Float64(z * t))) - x) / Float64(-1.0 - x))
	t_2 = Float64(Float64(z * t) - x)
	t_3 = Float64(Float64(y * Float64(Float64(Float64(z / t_2) + Float64(x / y)) - Float64(Float64(x / y) / t_2))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= -1e-106)
		tmp = t_3;
	elseif (t_1 <= 2e+213)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	t_2 = (z * t) - x;
	t_3 = (y * (((z / t_2) + (x / y)) - ((x / y) / t_2))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= -1e-106)
		tmp = t_3;
	elseif (t_1 <= 2e+213)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_3;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(N[(N[(z / t$95$2), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-106], t$95$3, If[LessEqual[t$95$1, 2e+213], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$3, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < -9.99999999999999941e-107 or 1.99999999999999997e213 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < +inf.0

   1. Initial program 71.9%

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

      1. *-commutative 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/r* 99.7%

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

   7. Simplified 99.7%

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

   if -9.99999999999999941e-107 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.99999999999999997e213

   1. Initial program 98.6%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x} \leq -1 \cdot 10^{-106}:\\ \;\;\;\;\frac{y \cdot \left(\left(\frac{z}{z \cdot t - x} + \frac{x}{y}\right) - \frac{\frac{x}{y}}{z \cdot t - x}\right)}{x + 1}\\ \mathbf{elif}\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x} \leq 2 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x}\\ \mathbf{elif}\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x} \leq \infty:\\ \;\;\;\;\frac{y \cdot \left(\left(\frac{z}{z \cdot t - x} + \frac{x}{y}\right) - \frac{\frac{x}{y}}{z \cdot t - x}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+108} \lor \neg \left(z \leq 1.85 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.15e+108) (not (<= z 1.85e+144)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- (/ (- (* y z) x) (- x (* z t))) x) (- -1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+108) || !(z <= 1.85e+144)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - 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 ((z <= (-1.15d+108)) .or. (.not. (z <= 1.85d+144))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((((y * z) - x) / (x - (z * t))) - x) / ((-1.0d0) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.15e+108) || !(z <= 1.85e+144)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.15e+108) or not (z <= 1.85e+144):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.15e+108) || !(z <= 1.85e+144))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(Float64(Float64(y * z) - x) / Float64(x - Float64(z * t))) - x) / Float64(-1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.15e+108) || ~((z <= 1.85e+144)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((((y * z) - x) / (x - (z * t))) - x) / (-1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.15e+108], N[Not[LessEqual[z, 1.85e+144]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1499999999999999e108 or 1.8499999999999998e144 < z

   1. Initial program 68.7%

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

      1. *-commutative 68.7%

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

   3. Simplified 68.7%

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

   5. Taylor expanded in z around inf 94.2%

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

   if -1.1499999999999999e108 < z < 1.8499999999999998e144

   1. Initial program 98.2%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+108} \lor \neg \left(z \leq 1.85 \cdot 10^{+144}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y \cdot z - x}{x - z \cdot t} - x}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-97} \lor \neg \left(t \leq 1.85 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.5e-97) (not (<= t 1.85e-100)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.5e-97) || !(t <= 1.85e-100)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y * (z / 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 ((t <= (-9.5d-97)) .or. (.not. (t <= 1.85d-100))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((x + 1.0d0) - (y * (z / 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 ((t <= -9.5e-97) || !(t <= 1.85e-100)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.5e-97) or not (t <= 1.85e-100):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.5e-97) || !(t <= 1.85e-100))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.5e-97) || ~((t <= 1.85e-100)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.5e-97], N[Not[LessEqual[t, 1.85e-100]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5000000000000001e-97 or 1.85000000000000009e-100 < t

   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. Add Preprocessing

   5. Taylor expanded in z around inf 86.9%

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

   if -9.5000000000000001e-97 < t < 1.85000000000000009e-100

   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. Add Preprocessing

   5. Taylor expanded in t around 0 75.8%

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

      1. associate-+r+ 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. +-commutative 75.8%

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

      5. associate-/l* 81.5%

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

      6. +-commutative 81.5%

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

   7. Simplified 81.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-97} \lor \neg \left(t \leq 1.85 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-63} \lor \neg \left(z \leq 5 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-63) (not (<= z 5e-70)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ x (- x (* z t)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-63) || !(z <= 5e-70)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (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 ((z <= (-2d-63)) .or. (.not. (z <= 5d-70))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (x / (x - (z * t)))) / (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 ((z <= -2e-63) || !(z <= 5e-70)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-63) or not (z <= 5e-70):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-63) || !(z <= 5e-70))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(x / Float64(x - Float64(z * t)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-63) || ~((z <= 5e-70)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (x / (x - (z * t)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-63], N[Not[LessEqual[z, 5e-70]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x / N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000013e-63 or 4.9999999999999998e-70 < z

   1. Initial program 82.4%

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

      1. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in z around inf 89.5%

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

   if -2.00000000000000013e-63 < z < 4.9999999999999998e-70

   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. Add Preprocessing

   5. Taylor expanded in y around 0 75.6%

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

      1. +-commutative 75.6%

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

   7. Simplified 75.6%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-63} \lor \neg \left(z \leq 5 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x}{x - z \cdot t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{t}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{t\_1 - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-100}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ y t))))
   (if (<= t -6.5e-96)
     (/ (- t_1 (/ x (* z t))) (+ x 1.0))
     (if (<= t 1.85e-100)
       (/ (- (+ x 1.0) (* y (/ z x))) (+ x 1.0))
       (/ t_1 (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y / t);
	double tmp;
	if (t <= -6.5e-96) {
		tmp = (t_1 - (x / (z * t))) / (x + 1.0);
	} else if (t <= 1.85e-100) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	} else {
		tmp = t_1 / (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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / t)
    if (t <= (-6.5d-96)) then
        tmp = (t_1 - (x / (z * t))) / (x + 1.0d0)
    else if (t <= 1.85d-100) then
        tmp = ((x + 1.0d0) - (y * (z / x))) / (x + 1.0d0)
    else
        tmp = t_1 / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y / t);
	double tmp;
	if (t <= -6.5e-96) {
		tmp = (t_1 - (x / (z * t))) / (x + 1.0);
	} else if (t <= 1.85e-100) {
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	} else {
		tmp = t_1 / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y / t)
	tmp = 0
	if t <= -6.5e-96:
		tmp = (t_1 - (x / (z * t))) / (x + 1.0)
	elif t <= 1.85e-100:
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0)
	else:
		tmp = t_1 / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y / t))
	tmp = 0.0
	if (t <= -6.5e-96)
		tmp = Float64(Float64(t_1 - Float64(x / Float64(z * t))) / Float64(x + 1.0));
	elseif (t <= 1.85e-100)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y * Float64(z / x))) / Float64(x + 1.0));
	else
		tmp = Float64(t_1 / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y / t);
	tmp = 0.0;
	if (t <= -6.5e-96)
		tmp = (t_1 - (x / (z * t))) / (x + 1.0);
	elseif (t <= 1.85e-100)
		tmp = ((x + 1.0) - (y * (z / x))) / (x + 1.0);
	else
		tmp = t_1 / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e-96], N[(N[(t$95$1 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-100], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000001e-96

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in t around inf 89.3%

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

   if -6.50000000000000001e-96 < t < 1.85000000000000009e-100

   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. Add Preprocessing

   5. Taylor expanded in t around 0 75.8%

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

      1. associate-+r+ 75.8%

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

      2. mul-1-neg 75.8%

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

      3. unsub-neg 75.8%

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

      4. +-commutative 75.8%

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

      5. associate-/l* 81.5%

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

      6. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   if 1.85000000000000009e-100 < t

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in z around inf 85.8%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-96}:\\ \;\;\;\;\frac{\left(x + \frac{y}{t}\right) - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-100}:\\ \;\;\;\;\frac{\left(x + 1\right) - y \cdot \frac{z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.66 \cdot 10^{+65}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.25e+56)
   1.0
   (if (<= x 1.66e+65) (/ (+ x (/ y t)) (+ x 1.0)) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.25e+56) {
		tmp = 1.0;
	} else if (x <= 1.66e+65) {
		tmp = (x + (y / t)) / (x + 1.0);
	} 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 <= (-1.25d+56)) then
        tmp = 1.0d0
    else if (x <= 1.66d+65) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    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 <= -1.25e+56) {
		tmp = 1.0;
	} else if (x <= 1.66e+65) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.25e+56:
		tmp = 1.0
	elif x <= 1.66e+65:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.25e+56)
		tmp = 1.0;
	elseif (x <= 1.66e+65)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	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 <= -1.25e+56)
		tmp = 1.0;
	elseif (x <= 1.66e+65)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.25e+56], 1.0, If[LessEqual[x, 1.66e+65], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.25000000000000006e56

   1. Initial program 81.2%

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

      1. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in z around inf 76.9%

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

   6. Taylor expanded in x around inf 95.2%

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

   if -1.25000000000000006e56 < x < 1.6600000000000001e65

   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. Add Preprocessing

   5. Taylor expanded in z around inf 72.8%

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

   if 1.6600000000000001e65 < x

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 96.7%

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

      1. +-commutative 96.7%

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

   7. Simplified 96.7%

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

Alternative 7: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-144} \lor \neg \left(x \leq 1.9 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.2e-144) (not (<= x 1.9e-166)))
   (/ x (+ x 1.0))
   (/ y (* t (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.2e-144) || !(x <= 1.9e-166)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t * (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 <= (-3.2d-144)) .or. (.not. (x <= 1.9d-166))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / (t * (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 <= -3.2e-144) || !(x <= 1.9e-166)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t * (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.2e-144) or not (x <= 1.9e-166):
		tmp = x / (x + 1.0)
	else:
		tmp = y / (t * (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.2e-144) || !(x <= 1.9e-166))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.2e-144) || ~((x <= 1.9e-166)))
		tmp = x / (x + 1.0);
	else
		tmp = y / (t * (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.2e-144], N[Not[LessEqual[x, 1.9e-166]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999973e-144 or 1.89999999999999991e-166 < x

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in t around inf 72.3%

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

      1. +-commutative 72.3%

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

   7. Simplified 72.3%

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

   if -3.19999999999999973e-144 < x < 1.89999999999999991e-166

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in y around inf 56.2%

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

      1. associate-/l* 63.1%

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

      2. +-commutative 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in z around inf 63.4%

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

      1. +-commutative 63.4%

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

   10. Simplified 63.4%

       \[\leadsto \color{blue}{\frac{y}{t \cdot \left(x + 1\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-144} \lor \neg \left(x \leq 1.9 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-146} \lor \neg \left(x \leq 1.9 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.6e-146) (not (<= x 1.9e-166))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.6e-146) || !(x <= 1.9e-166)) {
		tmp = x / (x + 1.0);
	} 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 <= (-5.6d-146)) .or. (.not. (x <= 1.9d-166))) then
        tmp = x / (x + 1.0d0)
    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 <= -5.6e-146) || !(x <= 1.9e-166)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.6e-146) or not (x <= 1.9e-166):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.6e-146) || !(x <= 1.9e-166))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.6e-146) || ~((x <= 1.9e-166)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.6e-146], N[Not[LessEqual[x, 1.9e-166]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.60000000000000006e-146 or 1.89999999999999991e-166 < x

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in t around inf 72.3%

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

      1. +-commutative 72.3%

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

   7. Simplified 72.3%

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

   if -5.60000000000000006e-146 < x < 1.89999999999999991e-166

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in z around inf 78.3%

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

   6. Taylor expanded in x around 0 63.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-146} \lor \neg \left(x \leq 1.9 \cdot 10^{-166}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{-23}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.2e-23) 1.0 (if (<= x 1.3e-88) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.2e-23) {
		tmp = 1.0;
	} else if (x <= 1.3e-88) {
		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 <= (-5.2d-23)) then
        tmp = 1.0d0
    else if (x <= 1.3d-88) 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 <= -5.2e-23) {
		tmp = 1.0;
	} else if (x <= 1.3e-88) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.2e-23:
		tmp = 1.0
	elif x <= 1.3e-88:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.2e-23)
		tmp = 1.0;
	elseif (x <= 1.3e-88)
		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 <= -5.2e-23)
		tmp = 1.0;
	elseif (x <= 1.3e-88)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.2e-23], 1.0, If[LessEqual[x, 1.3e-88], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2e-23 or 1.30000000000000007e-88 < x

   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. Add Preprocessing

   5. Taylor expanded in z around inf 75.6%

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

   6. Taylor expanded in x around inf 78.9%

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

   if -5.2e-23 < x < 1.30000000000000007e-88

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around inf 75.2%

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

   6. Taylor expanded in x around 0 48.8%

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

Alternative 10: 52.8% 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 88.3%

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

   1. *-commutative 88.3%

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

3. Simplified 88.3%

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

5. Taylor expanded in z around inf 75.4%

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

6. Taylor expanded in x around inf 48.5%

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

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 2024108 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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