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

Percentage Accurate: 88.8% → 96.7%

Time: 12.8s

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: 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: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} - \frac{y}{t \cdot \left(-1 - x\right)}\right) + \frac{x}{t \cdot \left(z \cdot \left(-1 - x\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -2e+145)
     (* y (/ (/ z (+ x 1.0)) t_1))
     (if (<= t_2 5e+258)
       t_2
       (+
        (- (/ x (+ x 1.0)) (/ y (* t (- -1.0 x))))
        (/ x (* t (* z (- -1.0 x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = ((x / (x + 1.0)) - (y / (t * (-1.0 - x)))) + (x / (t * (z * (-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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-2d+145)) then
        tmp = y * ((z / (x + 1.0d0)) / t_1)
    else if (t_2 <= 5d+258) then
        tmp = t_2
    else
        tmp = ((x / (x + 1.0d0)) - (y / (t * ((-1.0d0) - x)))) + (x / (t * (z * ((-1.0d0) - x))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = ((x / (x + 1.0)) - (y / (t * (-1.0 - x)))) + (x / (t * (z * (-1.0 - x))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -2e+145:
		tmp = y * ((z / (x + 1.0)) / t_1)
	elif t_2 <= 5e+258:
		tmp = t_2
	else:
		tmp = ((x / (x + 1.0)) - (y / (t * (-1.0 - x)))) + (x / (t * (z * (-1.0 - x))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -2e+145)
		tmp = Float64(y * Float64(Float64(z / Float64(x + 1.0)) / t_1));
	elseif (t_2 <= 5e+258)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x / Float64(x + 1.0)) - Float64(y / Float64(t * Float64(-1.0 - x)))) + Float64(x / Float64(t * Float64(z * Float64(-1.0 - x)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -2e+145)
		tmp = y * ((z / (x + 1.0)) / t_1);
	elseif (t_2 <= 5e+258)
		tmp = t_2;
	else
		tmp = ((x / (x + 1.0)) - (y / (t * (-1.0 - x)))) + (x / (t * (z * (-1.0 - x))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+145], N[(y * N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+258], t$95$2, N[(N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(t * N[(z * N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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))) < -2e145

   1. Initial program 59.4%

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

      1. *-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 59.0%

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

      1. associate-/l* 85.8%

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

      2. associate-/r* 95.0%

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

      3. +-commutative 95.0%

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

   7. Simplified 95.0%

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

   if -2e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5e258

   1. Initial program 99.4%

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

   if 5e258 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 27.2%

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

      1. *-commutative 27.2%

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

   3. Simplified 27.2%

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

   5. Taylor expanded in t around inf 89.8%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} - \frac{y}{t \cdot \left(-1 - x\right)}\right) + \frac{x}{t \cdot \left(z \cdot \left(-1 - x\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -2e+145)
     (* y (/ (/ z (+ x 1.0)) t_1))
     (if (<= t_2 5e+258)
       t_2
       (- (/ x (+ x 1.0)) (/ (- (/ x (* z (+ x 1.0))) (/ y (+ x 1.0))) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-2d+145)) then
        tmp = y * ((z / (x + 1.0d0)) / t_1)
    else if (t_2 <= 5d+258) then
        tmp = t_2
    else
        tmp = (x / (x + 1.0d0)) - (((x / (z * (x + 1.0d0))) - (y / (x + 1.0d0))) / t)
    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) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -2e+145:
		tmp = y * ((z / (x + 1.0)) / t_1)
	elif t_2 <= 5e+258:
		tmp = t_2
	else:
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -2e+145)
		tmp = Float64(y * Float64(Float64(z / Float64(x + 1.0)) / t_1));
	elseif (t_2 <= 5e+258)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(Float64(x / Float64(z * Float64(x + 1.0))) - Float64(y / Float64(x + 1.0))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -2e+145)
		tmp = y * ((z / (x + 1.0)) / t_1);
	elseif (t_2 <= 5e+258)
		tmp = t_2;
	else
		tmp = (x / (x + 1.0)) - (((x / (z * (x + 1.0))) - (y / (x + 1.0))) / t);
	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[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+145], N[(y * N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+258], t$95$2, N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $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))) < -2e145

   1. Initial program 59.4%

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

      1. *-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 59.0%

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

      1. associate-/l* 85.8%

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

      2. associate-/r* 95.0%

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

      3. +-commutative 95.0%

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

   7. Simplified 95.0%

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

   if -2e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5e258

   1. Initial program 99.4%

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

   if 5e258 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 27.2%

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

      1. *-commutative 27.2%

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

   3. Simplified 27.2%

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

   5. Taylor expanded in t around -inf 89.7%

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

      1. +-commutative 89.7%

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

      2. mul-1-neg 89.7%

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

      3. unsub-neg 89.7%

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

      4. +-commutative 89.7%

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

      5. sub-neg 89.7%

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

      6. mul-1-neg 89.7%

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

      7. distribute-neg-frac2 89.7%

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

      8. distribute-neg-in 89.7%

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

      9. metadata-eval 89.7%

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

      10. unsub-neg 89.7%

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

      11. mul-1-neg 89.7%

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

      12. remove-double-neg 89.7%

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

      13. +-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} - \frac{\frac{x}{z \cdot \left(x + 1\right)} - \frac{y}{x + 1}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+258}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -2e+145)
     (* y (/ (/ z (+ x 1.0)) t_1))
     (if (<= t_2 5e+258) t_2 (/ (+ x (/ y t)) (+ x 1.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (x + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-2d+145)) then
        tmp = y * ((z / (x + 1.0d0)) / t_1)
    else if (t_2 <= 5d+258) then
        tmp = t_2
    else
        tmp = (x + (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 t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -2e+145) {
		tmp = y * ((z / (x + 1.0)) / t_1);
	} else if (t_2 <= 5e+258) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -2e+145:
		tmp = y * ((z / (x + 1.0)) / t_1)
	elif t_2 <= 5e+258:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -2e+145)
		tmp = Float64(y * Float64(Float64(z / Float64(x + 1.0)) / t_1));
	elseif (t_2 <= 5e+258)
		tmp = t_2;
	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 = (z * t) - x;
	t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -2e+145)
		tmp = y * ((z / (x + 1.0)) / t_1);
	elseif (t_2 <= 5e+258)
		tmp = t_2;
	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[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+145], N[(y * N[(N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+258], t$95$2, 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))) < -2e145

   1. Initial program 59.4%

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

      1. *-commutative 59.4%

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

   3. Simplified 59.4%

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

   5. Taylor expanded in y around inf 59.0%

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

      1. associate-/l* 85.8%

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

      2. associate-/r* 95.0%

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

      3. +-commutative 95.0%

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

   7. Simplified 95.0%

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

   if -2e145 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 5e258

   1. Initial program 99.4%

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

   if 5e258 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 27.2%

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

      1. *-commutative 27.2%

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

   3. Simplified 27.2%

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

   5. Taylor expanded in z around inf 89.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -2 \cdot 10^{+145}:\\ \;\;\;\;y \cdot \frac{\frac{z}{x + 1}}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-202}:\\ \;\;\;\;1 + z \cdot \frac{\frac{y}{x}}{-1 - x}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.55e-114)
     t_1
     (if (<= t 5e-202)
       (+ 1.0 (* z (/ (/ y x) (- -1.0 x))))
       (if (<= t 7.2e-82) (* y (/ z (* (- (* z t) x) (+ x 1.0)))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.55e-114) {
		tmp = t_1;
	} else if (t <= 5e-202) {
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)));
	} else if (t <= 7.2e-82) {
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.55d-114)) then
        tmp = t_1
    else if (t <= 5d-202) then
        tmp = 1.0d0 + (z * ((y / x) / ((-1.0d0) - x)))
    else if (t <= 7.2d-82) then
        tmp = y * (z / (((z * t) - x) * (x + 1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.55e-114) {
		tmp = t_1;
	} else if (t <= 5e-202) {
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)));
	} else if (t <= 7.2e-82) {
		tmp = y * (z / (((z * t) - x) * (x + 1.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1.55e-114:
		tmp = t_1
	elif t <= 5e-202:
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)))
	elif t <= 7.2e-82:
		tmp = y * (z / (((z * t) - x) * (x + 1.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.55e-114)
		tmp = t_1;
	elseif (t <= 5e-202)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(y / x) / Float64(-1.0 - x))));
	elseif (t <= 7.2e-82)
		tmp = Float64(y * Float64(z / Float64(Float64(Float64(z * t) - x) * 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 / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.55e-114)
		tmp = t_1;
	elseif (t <= 5e-202)
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)));
	elseif (t <= 7.2e-82)
		tmp = y * (z / (((z * t) - x) * (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[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.55e-114], t$95$1, If[LessEqual[t, 5e-202], N[(1.0 + N[(z * N[(N[(y / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-82], N[(y * N[(z / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.55e-114 or 7.19999999999999996e-82 < t

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around inf 88.2%

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

   if -1.55e-114 < t < 4.99999999999999973e-202

   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 z around 0 84.2%

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

   6. Taylor expanded in y around inf 84.2%

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

      1. associate-/r* 85.8%

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

      2. +-commutative 85.8%

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

      3. associate-*r/ 85.8%

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

      4. associate-*r/ 85.8%

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

      5. neg-mul-1 85.8%

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

      6. +-commutative 85.8%

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

   8. Simplified 85.8%

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

   if 4.99999999999999973e-202 < t < 7.19999999999999996e-82

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in y around inf 72.5%

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

      1. associate-/l* 76.9%

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

      2. +-commutative 76.9%

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

   7. Simplified 76.9%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-114}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-202}:\\ \;\;\;\;1 + z \cdot \frac{\frac{y}{x}}{-1 - x}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-111} \lor \neg \left(t \leq 4.15 \cdot 10^{-116}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.55e-111) (not (<= t 4.15e-116)))
   (/ (+ 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 <= -2.55e-111) || !(t <= 4.15e-116)) {
		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 <= (-2.55d-111)) .or. (.not. (t <= 4.15d-116))) 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 <= -2.55e-111) || !(t <= 4.15e-116)) {
		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 <= -2.55e-111) or not (t <= 4.15e-116):
		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 <= -2.55e-111) || !(t <= 4.15e-116))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(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 <= -2.55e-111) || ~((t <= 4.15e-116)))
		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, -2.55e-111], N[Not[LessEqual[t, 4.15e-116]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.55000000000000016e-111 or 4.1499999999999998e-116 < t

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around inf 87.5%

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

   if -2.55000000000000016e-111 < t < 4.1499999999999998e-116

   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. Add Preprocessing

   5. Taylor expanded in t around 0 74.6%

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

      1. associate-+r+ 74.6%

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

      2. +-commutative 74.6%

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

      3. associate-+l+ 74.6%

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

      4. mul-1-neg 74.6%

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

      5. unsub-neg 74.6%

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

      6. associate-/l* 80.5%

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

      7. +-commutative 80.5%

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

   7. Simplified 80.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-111} \lor \neg \left(t \leq 4.15 \cdot 10^{-116}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - y \cdot \frac{z}{x}\right)}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-111} \lor \neg \left(t \leq 1.52 \cdot 10^{-183}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{\frac{y}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.55e-111) (not (<= t 1.52e-183)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* z (/ (/ y x) (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.55e-111) || !(t <= 1.52e-183)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z * ((y / 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 ((t <= (-2.55d-111)) .or. (.not. (t <= 1.52d-183))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (z * ((y / 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 ((t <= -2.55e-111) || !(t <= 1.52e-183)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.55e-111) or not (t <= 1.52e-183):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.55e-111) || !(t <= 1.52e-183))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(z * Float64(Float64(y / x) / Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.55e-111) || ~((t <= 1.52e-183)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (z * ((y / x) / (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.55e-111], N[Not[LessEqual[t, 1.52e-183]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(z * N[(N[(y / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.55000000000000016e-111 or 1.52000000000000007e-183 < t

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in z around inf 84.5%

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

   if -2.55000000000000016e-111 < t < 1.52000000000000007e-183

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in z around 0 84.7%

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

   6. Taylor expanded in y around inf 84.7%

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

      1. associate-/r* 86.2%

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

      2. +-commutative 86.2%

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

      3. associate-*r/ 86.2%

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

      4. associate-*r/ 86.2%

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

      5. neg-mul-1 86.2%

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

      6. +-commutative 86.2%

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

   8. Simplified 86.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-111} \lor \neg \left(t \leq 1.52 \cdot 10^{-183}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + z \cdot \frac{\frac{y}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.7e+35) 1.0 (if (<= x 1.6e+36) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.7e+35) {
		tmp = 1.0;
	} else if (x <= 1.6e+36) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.7d+35)) then
        tmp = 1.0d0
    else if (x <= 1.6d+36) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.7e+35) {
		tmp = 1.0;
	} else if (x <= 1.6e+36) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.7e+35:
		tmp = 1.0
	elif x <= 1.6e+36:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.7e+35)
		tmp = 1.0;
	elseif (x <= 1.6e+36)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.7e+35)
		tmp = 1.0;
	elseif (x <= 1.6e+36)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.7e+35], 1.0, If[LessEqual[x, 1.6e+36], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7000000000000001e35 or 1.5999999999999999e36 < x

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around inf 69.1%

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

   6. Taylor expanded in x around inf 89.0%

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

   if -1.7000000000000001e35 < x < 1.5999999999999999e36

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in z around inf 73.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.5e-114)
   (/ x (+ x 1.0))
   (if (<= x 1.7e+33) (/ y (* t (+ x 1.0))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-114) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.7e+33) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.5d-114)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.7d+33) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-114) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.7e+33) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.5e-114:
		tmp = x / (x + 1.0)
	elif x <= 1.7e+33:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.5e-114)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.7e+33)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.5e-114)
		tmp = x / (x + 1.0);
	elseif (x <= 1.7e+33)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.5e-114], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+33], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999995e-114

   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. Add Preprocessing

   5. Taylor expanded in t around inf 76.1%

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

      1. +-commutative 76.1%

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

   7. Simplified 76.1%

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

   if -2.49999999999999995e-114 < x < 1.7e33

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in y around inf 49.8%

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

      1. associate-/l* 57.6%

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

      2. +-commutative 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in z around inf 51.8%

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

   if 1.7e33 < x

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 67.5%

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

   6. Taylor expanded in x around inf 89.6%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-113} \lor \neg \left(x \leq 3.2 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.4e-113) (not (<= x 3.2e-43))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.4e-113) || !(x <= 3.2e-43)) {
		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 <= (-4.4d-113)) .or. (.not. (x <= 3.2d-43))) 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 <= -4.4e-113) || !(x <= 3.2e-43)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.4e-113) or not (x <= 3.2e-43):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.4e-113) || !(x <= 3.2e-43))
		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 <= -4.4e-113) || ~((x <= 3.2e-43)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.4e-113], N[Not[LessEqual[x, 3.2e-43]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.40000000000000008e-113 or 3.19999999999999985e-43 < 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 t around inf 75.9%

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

      1. +-commutative 75.9%

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

   7. Simplified 75.9%

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

   if -4.40000000000000008e-113 < x < 3.19999999999999985e-43

   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 74.6%

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

   6. Taylor expanded in x around 0 54.0%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-113} \lor \neg \left(x \leq 3.2 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.2) 1.0 (if (<= x 1.06e-15) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.2) {
		tmp = 1.0;
	} else if (x <= 1.06e-15) {
		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 <= (-0.2d0)) then
        tmp = 1.0d0
    else if (x <= 1.06d-15) 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 <= -0.2) {
		tmp = 1.0;
	} else if (x <= 1.06e-15) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.2:
		tmp = 1.0
	elif x <= 1.06e-15:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.2)
		tmp = 1.0;
	elseif (x <= 1.06e-15)
		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 <= -0.2)
		tmp = 1.0;
	elseif (x <= 1.06e-15)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.2], 1.0, If[LessEqual[x, 1.06e-15], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.20000000000000001 or 1.06000000000000007e-15 < x

   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 68.5%

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

   6. Taylor expanded in x around inf 82.8%

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

   if -0.20000000000000001 < x < 1.06000000000000007e-15

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 74.3%

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

   6. Taylor expanded in x around 0 49.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.2:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.0) (+ 1.0 (/ -1.0 x)) (if (<= x 8e-17) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0 + (-1.0 / x);
	} else if (x <= 8e-17) {
		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 <= (-1.0d0)) then
        tmp = 1.0d0 + ((-1.0d0) / x)
    else if (x <= 8d-17) 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 <= -1.0) {
		tmp = 1.0 + (-1.0 / x);
	} else if (x <= 8e-17) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.0:
		tmp = 1.0 + (-1.0 / x)
	elif x <= 8e-17:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(1.0 + Float64(-1.0 / x));
	elseif (x <= 8e-17)
		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 <= -1.0)
		tmp = 1.0 + (-1.0 / x);
	elseif (x <= 8e-17)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.0], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e-17], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   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 t around inf 85.8%

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

      1. +-commutative 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in x around inf 85.7%

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

   if -1 < x < 8.00000000000000057e-17

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 74.3%

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

   6. Taylor expanded in x around 0 49.2%

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

   if 8.00000000000000057e-17 < x

   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 66.0%

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

   6. Taylor expanded in x around inf 80.0%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1 + \frac{-1}{x}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0027:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -0.0027) 1.0 (if (<= x 1.8e-13) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.0027) {
		tmp = 1.0;
	} else if (x <= 1.8e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-0.0027d0)) then
        tmp = 1.0d0
    else if (x <= 1.8d-13) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -0.0027) {
		tmp = 1.0;
	} else if (x <= 1.8e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -0.0027:
		tmp = 1.0
	elif x <= 1.8e-13:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -0.0027)
		tmp = 1.0;
	elseif (x <= 1.8e-13)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -0.0027)
		tmp = 1.0;
	elseif (x <= 1.8e-13)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -0.0027], 1.0, If[LessEqual[x, 1.8e-13], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0027000000000000001 or 1.7999999999999999e-13 < x

   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 68.5%

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

   6. Taylor expanded in x around inf 82.7%

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

   if -0.0027000000000000001 < x < 1.7999999999999999e-13

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in t around inf 29.6%

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

      1. +-commutative 29.6%

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

   7. Simplified 29.6%

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

   8. Taylor expanded in x around 0 28.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0027:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.3% 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. Add Preprocessing

5. Taylor expanded in z around inf 71.6%

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

6. Taylor expanded in x around inf 47.4%

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

7. Final simplification 47.4%

   \[\leadsto 1 \]
8. Add Preprocessing

Developer target: 99.5% 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 2024071 
(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)))