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

Percentage Accurate: 89.5% → 95.6%

Time: 13.7s

Alternatives: 12

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ t_3 := z \cdot \left(x + 1\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+199}:\\ \;\;\;\;t_1 + \left(\frac{y}{t \cdot \left(x + 1\right)} - \frac{\frac{x}{t}}{t_3}\right)\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+302}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{\frac{y}{x + 1} - \frac{x}{t_3}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0)))
        (t_2 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0)))
        (t_3 (* z (+ x 1.0))))
   (if (<= t_2 -5e+199)
     (+ t_1 (- (/ y (* t (+ x 1.0))) (/ (/ x t) t_3)))
     (if (<= t_2 2e+302) t_2 (+ t_1 (/ (- (/ y (+ x 1.0)) (/ x t_3)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double t_3 = z * (x + 1.0);
	double tmp;
	if (t_2 <= -5e+199) {
		tmp = t_1 + ((y / (t * (x + 1.0))) - ((x / t) / t_3));
	} else if (t_2 <= 2e+302) {
		tmp = t_2;
	} else {
		tmp = t_1 + (((y / (x + 1.0)) - (x / t_3)) / 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) :: t_3
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    t_3 = z * (x + 1.0d0)
    if (t_2 <= (-5d+199)) then
        tmp = t_1 + ((y / (t * (x + 1.0d0))) - ((x / t) / t_3))
    else if (t_2 <= 2d+302) then
        tmp = t_2
    else
        tmp = t_1 + (((y / (x + 1.0d0)) - (x / t_3)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double t_3 = z * (x + 1.0);
	double tmp;
	if (t_2 <= -5e+199) {
		tmp = t_1 + ((y / (t * (x + 1.0))) - ((x / t) / t_3));
	} else if (t_2 <= 2e+302) {
		tmp = t_2;
	} else {
		tmp = t_1 + (((y / (x + 1.0)) - (x / t_3)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	t_3 = z * (x + 1.0)
	tmp = 0
	if t_2 <= -5e+199:
		tmp = t_1 + ((y / (t * (x + 1.0))) - ((x / t) / t_3))
	elif t_2 <= 2e+302:
		tmp = t_2
	else:
		tmp = t_1 + (((y / (x + 1.0)) - (x / t_3)) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	t_3 = Float64(z * Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+199)
		tmp = Float64(t_1 + Float64(Float64(y / Float64(t * Float64(x + 1.0))) - Float64(Float64(x / t) / t_3)));
	elseif (t_2 <= 2e+302)
		tmp = t_2;
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(y / Float64(x + 1.0)) - Float64(x / t_3)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	t_2 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	t_3 = z * (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+199)
		tmp = t_1 + ((y / (t * (x + 1.0))) - ((x / t) / t_3));
	elseif (t_2 <= 2e+302)
		tmp = t_2;
	else
		tmp = t_1 + (((y / (x + 1.0)) - (x / t_3)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+199], N[(t$95$1 + N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x / t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+302], t$95$2, N[(t$95$1 + N[(N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(x / t$95$3), $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 1)) < -4.9999999999999998e199

   1. Initial program 61.6%

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

      1. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   4. Taylor expanded in t around inf 93.3%

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

      1. associate--l+ 93.3%

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

      2. +-commutative 93.3%

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

      3. +-commutative 93.3%

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

      4. associate-/r* 93.3%

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

      5. +-commutative 93.3%

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

   6. Simplified 93.3%

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

   if -4.9999999999999998e199 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2.0000000000000002e302

   1. Initial program 99.8%

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

   if 2.0000000000000002e302 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 43.8%

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

      1. *-commutative 43.8%

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

   3. Simplified 43.8%

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

   4. Taylor expanded in t around -inf 86.5%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+199}:\\ \;\;\;\;\frac{x}{x + 1} + \left(\frac{y}{t \cdot \left(x + 1\right)} - \frac{\frac{x}{t}}{z \cdot \left(x + 1\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+302}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1} + \frac{\frac{y}{x + 1} - \frac{x}{z \cdot \left(x + 1\right)}}{t}\\ \end{array} \]

Alternative 2: 95.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+199} \lor \neg \left(t_1 \leq 2 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x}{x + 1} + \left(\frac{y}{t \cdot \left(x + 1\right)} - \frac{\frac{x}{t}}{z \cdot \left(x + 1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (or (<= t_1 -5e+199) (not (<= t_1 2e+302)))
     (+ (/ x (+ x 1.0)) (- (/ y (* t (+ x 1.0))) (/ (/ x t) (* z (+ x 1.0)))))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -5e+199) || !(t_1 <= 2e+302)) {
		tmp = (x / (x + 1.0)) + ((y / (t * (x + 1.0))) - ((x / t) / (z * (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 * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if ((t_1 <= (-5d+199)) .or. (.not. (t_1 <= 2d+302))) then
        tmp = (x / (x + 1.0d0)) + ((y / (t * (x + 1.0d0))) - ((x / t) / (z * (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 * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -5e+199) || !(t_1 <= 2e+302)) {
		tmp = (x / (x + 1.0)) + ((y / (t * (x + 1.0))) - ((x / t) / (z * (x + 1.0))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if (t_1 <= -5e+199) or not (t_1 <= 2e+302):
		tmp = (x / (x + 1.0)) + ((y / (t * (x + 1.0))) - ((x / t) / (z * (x + 1.0))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if ((t_1 <= -5e+199) || !(t_1 <= 2e+302))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(Float64(y / Float64(t * Float64(x + 1.0))) - Float64(Float64(x / t) / Float64(z * Float64(x + 1.0)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if ((t_1 <= -5e+199) || ~((t_1 <= 2e+302)))
		tmp = (x / (x + 1.0)) + ((y / (t * (x + 1.0))) - ((x / t) / (z * (x + 1.0))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+199], N[Not[LessEqual[t$95$1, 2e+302]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x / t), $MachinePrecision] / N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -4.9999999999999998e199 or 2.0000000000000002e302 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 51.2%

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

      1. *-commutative 51.2%

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

   3. Simplified 51.2%

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

   4. Taylor expanded in t around inf 89.3%

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

      1. associate--l+ 89.3%

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

      2. +-commutative 89.3%

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

      3. +-commutative 89.3%

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

      4. associate-/r* 89.3%

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

      5. +-commutative 89.3%

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

   6. Simplified 89.3%

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

   if -4.9999999999999998e199 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2.0000000000000002e302

   1. Initial program 99.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+199} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x}{x + 1} + \left(\frac{y}{t \cdot \left(x + 1\right)} - \frac{\frac{x}{t}}{z \cdot \left(x + 1\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 3: 95.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+199} \lor \neg \left(t_1 \leq 2 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (or (<= t_1 -5e+199) (not (<= t_1 2e+302)))
     (/ (+ x (/ y t)) (+ x 1.0))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -5e+199) || !(t_1 <= 2e+302)) {
		tmp = (x + (y / t)) / (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 * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if ((t_1 <= (-5d+199)) .or. (.not. (t_1 <= 2d+302))) then
        tmp = (x + (y / t)) / (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 * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -5e+199) || !(t_1 <= 2e+302)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if (t_1 <= -5e+199) or not (t_1 <= 2e+302):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if ((t_1 <= -5e+199) || !(t_1 <= 2e+302))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if ((t_1 <= -5e+199) || ~((t_1 <= 2e+302)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+199], N[Not[LessEqual[t$95$1, 2e+302]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -4.9999999999999998e199 or 2.0000000000000002e302 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 51.2%

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

      1. *-commutative 51.2%

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

   3. Simplified 51.2%

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

   4. Taylor expanded in z around inf 89.1%

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

   if -4.9999999999999998e199 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2.0000000000000002e302

   1. Initial program 99.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+199} \lor \neg \left(\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+302}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 4: 80.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x + \left(1 + \frac{z \cdot \left(t - y\right)}{x}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x + \frac{1}{\left(--1\right) - \frac{t}{\frac{x}{z}}}}{x + 1}\\ \mathbf{elif}\;z \leq 370000000:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -5.8e-60)
     t_1
     (if (<= z -4.4e-279)
       (/ (- x (/ x (- (* z t) x))) (+ x 1.0))
       (if (<= z 4.8e-197)
         (/ (+ x (+ 1.0 (/ (* z (- t y)) x))) (+ x 1.0))
         (if (<= z 4.5e-36)
           (/ (+ x (/ 1.0 (- (- -1.0) (/ t (/ x z))))) (+ x 1.0))
           (if (<= z 370000000.0)
             (/ (+ x (/ (- x (* y z)) 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 (z <= -5.8e-60) {
		tmp = t_1;
	} else if (z <= -4.4e-279) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (z <= 4.8e-197) {
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0);
	} else if (z <= 4.5e-36) {
		tmp = (x + (1.0 / (-(-1.0) - (t / (x / z))))) / (x + 1.0);
	} else if (z <= 370000000.0) {
		tmp = (x + ((x - (y * z)) / 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 (z <= (-5.8d-60)) then
        tmp = t_1
    else if (z <= (-4.4d-279)) then
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    else if (z <= 4.8d-197) then
        tmp = (x + (1.0d0 + ((z * (t - y)) / x))) / (x + 1.0d0)
    else if (z <= 4.5d-36) then
        tmp = (x + (1.0d0 / (-(-1.0d0) - (t / (x / z))))) / (x + 1.0d0)
    else if (z <= 370000000.0d0) then
        tmp = (x + ((x - (y * z)) / 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 (z <= -5.8e-60) {
		tmp = t_1;
	} else if (z <= -4.4e-279) {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	} else if (z <= 4.8e-197) {
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0);
	} else if (z <= 4.5e-36) {
		tmp = (x + (1.0 / (-(-1.0) - (t / (x / z))))) / (x + 1.0);
	} else if (z <= 370000000.0) {
		tmp = (x + ((x - (y * z)) / 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 z <= -5.8e-60:
		tmp = t_1
	elif z <= -4.4e-279:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	elif z <= 4.8e-197:
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0)
	elif z <= 4.5e-36:
		tmp = (x + (1.0 / (-(-1.0) - (t / (x / z))))) / (x + 1.0)
	elif z <= 370000000.0:
		tmp = (x + ((x - (y * z)) / 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 (z <= -5.8e-60)
		tmp = t_1;
	elseif (z <= -4.4e-279)
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	elseif (z <= 4.8e-197)
		tmp = Float64(Float64(x + Float64(1.0 + Float64(Float64(z * Float64(t - y)) / x))) / Float64(x + 1.0));
	elseif (z <= 4.5e-36)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(-(-1.0)) - Float64(t / Float64(x / z))))) / Float64(x + 1.0));
	elseif (z <= 370000000.0)
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / 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 (z <= -5.8e-60)
		tmp = t_1;
	elseif (z <= -4.4e-279)
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	elseif (z <= 4.8e-197)
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0);
	elseif (z <= 4.5e-36)
		tmp = (x + (1.0 / (-(-1.0) - (t / (x / z))))) / (x + 1.0);
	elseif (z <= 370000000.0)
		tmp = (x + ((x - (y * z)) / 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[z, -5.8e-60], t$95$1, If[LessEqual[z, -4.4e-279], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e-197], N[(N[(x + N[(1.0 + N[(N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-36], N[(N[(x + N[(1.0 / N[((--1.0) - N[(t / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 370000000.0], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.7999999999999999e-60 or 3.7e8 < z

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -5.7999999999999999e-60 < z < -4.40000000000000001e-279

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 87.6%

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

      1. +-commutative 87.6%

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

   6. Simplified 87.6%

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

   if -4.40000000000000001e-279 < z < 4.8000000000000002e-197

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 93.0%

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

      1. associate--l+ 93.0%

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

      2. associate-*r/ 93.0%

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

      3. associate-*r/ 93.0%

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

      4. div-sub 93.0%

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

      5. distribute-lft-out-- 93.0%

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

      6. associate-*r/ 93.0%

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

      7. mul-1-neg 93.0%

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

      8. unsub-neg 93.0%

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

      9. distribute-rgt-out-- 93.0%

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

   6. Simplified 93.0%

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

   if 4.8000000000000002e-197 < z < 4.50000000000000024e-36

   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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. fma-neg 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. *-commutative 99.9%

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

      3. fma-neg 99.9%

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

      4. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. div-sub 87.0%

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

      3. sub-neg 87.0%

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

      4. associate-/l* 87.1%

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

      5. *-inverses 87.1%

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

      6. metadata-eval 87.1%

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

   10. Simplified 87.1%

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

   if 4.50000000000000024e-36 < z < 3.7e8

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 91.0%

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

      1. fma-neg 91.0%

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

      2. associate-*r/ 91.0%

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

      3. neg-mul-1 91.0%

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

      4. neg-sub0 91.0%

         \[\leadsto \frac{x + \frac{\color{blue}{0 - \mathsf{fma}\left(y, z, -x\right)}}{x}}{x + 1} \]

      5. fma-def 91.0%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{x}}{x + 1} \]

      6. +-commutative 91.0%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{x}}{x + 1} \]

      7. associate--r+ 91.0%

         \[\leadsto \frac{x + \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{x}}{x + 1} \]

      8. neg-sub0 91.0%

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

      9. remove-double-neg 91.0%

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

      10. *-commutative 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-279}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x + \left(1 + \frac{z \cdot \left(t - y\right)}{x}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x + \frac{1}{\left(--1\right) - \frac{t}{\frac{x}{z}}}}{x + 1}\\ \mathbf{elif}\;z \leq 370000000:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 5: 80.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ t_3 := \frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 380000000000:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))))
   (if (<= z -1.32e-61)
     t_2
     (if (<= z -4e-290)
       t_1
       (if (<= z 1.75e-183)
         t_3
         (if (<= z 6.5e-36) t_1 (if (<= z 380000000000.0) t_3 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double t_3 = (x + ((x - (y * z)) / x)) / (x + 1.0);
	double tmp;
	if (z <= -1.32e-61) {
		tmp = t_2;
	} else if (z <= -4e-290) {
		tmp = t_1;
	} else if (z <= 1.75e-183) {
		tmp = t_3;
	} else if (z <= 6.5e-36) {
		tmp = t_1;
	} else if (z <= 380000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    t_2 = (x + (y / t)) / (x + 1.0d0)
    t_3 = (x + ((x - (y * z)) / x)) / (x + 1.0d0)
    if (z <= (-1.32d-61)) then
        tmp = t_2
    else if (z <= (-4d-290)) then
        tmp = t_1
    else if (z <= 1.75d-183) then
        tmp = t_3
    else if (z <= 6.5d-36) then
        tmp = t_1
    else if (z <= 380000000000.0d0) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double t_3 = (x + ((x - (y * z)) / x)) / (x + 1.0);
	double tmp;
	if (z <= -1.32e-61) {
		tmp = t_2;
	} else if (z <= -4e-290) {
		tmp = t_1;
	} else if (z <= 1.75e-183) {
		tmp = t_3;
	} else if (z <= 6.5e-36) {
		tmp = t_1;
	} else if (z <= 380000000000.0) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0)
	t_2 = (x + (y / t)) / (x + 1.0)
	t_3 = (x + ((x - (y * z)) / x)) / (x + 1.0)
	tmp = 0
	if z <= -1.32e-61:
		tmp = t_2
	elif z <= -4e-290:
		tmp = t_1
	elif z <= 1.75e-183:
		tmp = t_3
	elif z <= 6.5e-36:
		tmp = t_1
	elif z <= 380000000000.0:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -1.32e-61)
		tmp = t_2;
	elseif (z <= -4e-290)
		tmp = t_1;
	elseif (z <= 1.75e-183)
		tmp = t_3;
	elseif (z <= 6.5e-36)
		tmp = t_1;
	elseif (z <= 380000000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	t_2 = (x + (y / t)) / (x + 1.0);
	t_3 = (x + ((x - (y * z)) / x)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -1.32e-61)
		tmp = t_2;
	elseif (z <= -4e-290)
		tmp = t_1;
	elseif (z <= 1.75e-183)
		tmp = t_3;
	elseif (z <= 6.5e-36)
		tmp = t_1;
	elseif (z <= 380000000000.0)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.32e-61], t$95$2, If[LessEqual[z, -4e-290], t$95$1, If[LessEqual[z, 1.75e-183], t$95$3, If[LessEqual[z, 6.5e-36], t$95$1, If[LessEqual[z, 380000000000.0], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.32000000000000002e-61 or 3.8e11 < z

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -1.32000000000000002e-61 < z < -4.0000000000000003e-290 or 1.74999999999999996e-183 < z < 6.50000000000000012e-36

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 89.1%

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

      1. +-commutative 89.1%

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

   6. Simplified 89.1%

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

   if -4.0000000000000003e-290 < z < 1.74999999999999996e-183 or 6.50000000000000012e-36 < z < 3.8e11

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 88.7%

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

      1. fma-neg 88.7%

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

      2. associate-*r/ 88.7%

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

      3. neg-mul-1 88.7%

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

      4. neg-sub0 88.7%

         \[\leadsto \frac{x + \frac{\color{blue}{0 - \mathsf{fma}\left(y, z, -x\right)}}{x}}{x + 1} \]

      5. fma-def 88.7%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{x}}{x + 1} \]

      6. +-commutative 88.7%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{x}}{x + 1} \]

      7. associate--r+ 88.7%

         \[\leadsto \frac{x + \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{x}}{x + 1} \]

      8. neg-sub0 88.7%

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

      9. remove-double-neg 88.7%

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

      10. *-commutative 88.7%

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

   6. Simplified 88.7%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-61}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-290}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-183}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 380000000000:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 6: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x + \left(1 + \frac{z \cdot \left(t - y\right)}{x}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 26000000:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -3.2e-65)
     t_2
     (if (<= z -2.8e-286)
       t_1
       (if (<= z 4.8e-197)
         (/ (+ x (+ 1.0 (/ (* z (- t y)) x))) (+ x 1.0))
         (if (<= z 6.8e-36)
           t_1
           (if (<= z 26000000.0)
             (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))
             t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -3.2e-65) {
		tmp = t_2;
	} else if (z <= -2.8e-286) {
		tmp = t_1;
	} else if (z <= 4.8e-197) {
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0);
	} else if (z <= 6.8e-36) {
		tmp = t_1;
	} else if (z <= 26000000.0) {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-3.2d-65)) then
        tmp = t_2
    else if (z <= (-2.8d-286)) then
        tmp = t_1
    else if (z <= 4.8d-197) then
        tmp = (x + (1.0d0 + ((z * (t - y)) / x))) / (x + 1.0d0)
    else if (z <= 6.8d-36) then
        tmp = t_1
    else if (z <= 26000000.0d0) then
        tmp = (x + ((x - (y * z)) / x)) / (x + 1.0d0)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -3.2e-65) {
		tmp = t_2;
	} else if (z <= -2.8e-286) {
		tmp = t_1;
	} else if (z <= 4.8e-197) {
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0);
	} else if (z <= 6.8e-36) {
		tmp = t_1;
	} else if (z <= 26000000.0) {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0)
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -3.2e-65:
		tmp = t_2
	elif z <= -2.8e-286:
		tmp = t_1
	elif z <= 4.8e-197:
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0)
	elif z <= 6.8e-36:
		tmp = t_1
	elif z <= 26000000.0:
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -3.2e-65)
		tmp = t_2;
	elseif (z <= -2.8e-286)
		tmp = t_1;
	elseif (z <= 4.8e-197)
		tmp = Float64(Float64(x + Float64(1.0 + Float64(Float64(z * Float64(t - y)) / x))) / Float64(x + 1.0));
	elseif (z <= 6.8e-36)
		tmp = t_1;
	elseif (z <= 26000000.0)
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -3.2e-65)
		tmp = t_2;
	elseif (z <= -2.8e-286)
		tmp = t_1;
	elseif (z <= 4.8e-197)
		tmp = (x + (1.0 + ((z * (t - y)) / x))) / (x + 1.0);
	elseif (z <= 6.8e-36)
		tmp = t_1;
	elseif (z <= 26000000.0)
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-65], t$95$2, If[LessEqual[z, -2.8e-286], t$95$1, If[LessEqual[z, 4.8e-197], N[(N[(x + N[(1.0 + N[(N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-36], t$95$1, If[LessEqual[z, 26000000.0], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1999999999999999e-65 or 2.6e7 < z

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -3.1999999999999999e-65 < z < -2.8e-286 or 4.8000000000000002e-197 < z < 6.8000000000000005e-36

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 87.3%

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

      1. +-commutative 87.3%

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

   6. Simplified 87.3%

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

   if -2.8e-286 < z < 4.8000000000000002e-197

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 93.0%

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

      1. associate--l+ 93.0%

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

      2. associate-*r/ 93.0%

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

      3. associate-*r/ 93.0%

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

      4. div-sub 93.0%

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

      5. distribute-lft-out-- 93.0%

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

      6. associate-*r/ 93.0%

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

      7. mul-1-neg 93.0%

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

      8. unsub-neg 93.0%

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

      9. distribute-rgt-out-- 93.0%

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

   6. Simplified 93.0%

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

   if 6.8000000000000005e-36 < z < 2.6e7

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 91.0%

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

      1. fma-neg 91.0%

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

      2. associate-*r/ 91.0%

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

      3. neg-mul-1 91.0%

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

      4. neg-sub0 91.0%

         \[\leadsto \frac{x + \frac{\color{blue}{0 - \mathsf{fma}\left(y, z, -x\right)}}{x}}{x + 1} \]

      5. fma-def 91.0%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{x}}{x + 1} \]

      6. +-commutative 91.0%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{x}}{x + 1} \]

      7. associate--r+ 91.0%

         \[\leadsto \frac{x + \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{x}}{x + 1} \]

      8. neg-sub0 91.0%

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

      9. remove-double-neg 91.0%

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

      10. *-commutative 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-65}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-286}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x + \left(1 + \frac{z \cdot \left(t - y\right)}{x}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 26000000:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 7: 84.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+32} \lor \neg \left(t \leq 1.3 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{y \cdot z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7e+32) (not (<= t 1.3e-14)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ 1.0 (/ (- (* z t) x) (* y z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e+32) || !(t <= 1.3e-14)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 / (((z * t) - x) / (y * z)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-7d+32)) .or. (.not. (t <= 1.3d-14))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (1.0d0 / (((z * t) - x) / (y * z)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7e+32) || !(t <= 1.3e-14)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 / (((z * t) - x) / (y * z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7e+32) or not (t <= 1.3e-14):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (1.0 / (((z * t) - x) / (y * z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7e+32) || !(t <= 1.3e-14))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(Float64(z * t) - x) / Float64(y * z)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7e+32) || ~((t <= 1.3e-14)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (1.0 / (((z * t) - x) / (y * z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7e+32], N[Not[LessEqual[t, 1.3e-14]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0000000000000002e32 or 1.29999999999999998e-14 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 90.1%

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

   if -7.0000000000000002e32 < t < 1.29999999999999998e-14

   1. Initial program 96.3%

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

      1. *-commutative 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 96.3%

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

      2. inv-pow 96.3%

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

      3. fma-neg 96.3%

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

   5. Applied egg-rr 96.3%

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

      1. unpow-1 96.3%

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

      2. *-commutative 96.3%

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

      3. fma-neg 96.3%

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

      4. *-commutative 96.3%

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

   7. Simplified 96.3%

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

   8. Taylor expanded in y around inf 83.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+32} \lor \neg \left(t \leq 1.3 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{y \cdot z}}}{x + 1}\\ \end{array} \]

Alternative 8: 79.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-178} \lor \neg \left(z \leq 430000000\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6e-178) (not (<= z 430000000.0)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- x (* y z)) x)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6e-178) || !(z <= 430000000.0)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (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 ((z <= (-6d-178)) .or. (.not. (z <= 430000000.0d0))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + ((x - (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 ((z <= -6e-178) || !(z <= 430000000.0)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6e-178) or not (z <= 430000000.0):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6e-178) || !(z <= 430000000.0))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(x - Float64(y * z)) / x)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6e-178) || ~((z <= 430000000.0)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + ((x - (y * z)) / x)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6e-178], N[Not[LessEqual[z, 430000000.0]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9999999999999997e-178 or 4.3e8 < z

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in z around inf 83.7%

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

   if -5.9999999999999997e-178 < z < 4.3e8

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 81.1%

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

      1. fma-neg 81.1%

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

      2. associate-*r/ 81.1%

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

      3. neg-mul-1 81.1%

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

      4. neg-sub0 81.1%

         \[\leadsto \frac{x + \frac{\color{blue}{0 - \mathsf{fma}\left(y, z, -x\right)}}{x}}{x + 1} \]

      5. fma-def 81.1%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(y \cdot z + \left(-x\right)\right)}}{x}}{x + 1} \]

      6. +-commutative 81.1%

         \[\leadsto \frac{x + \frac{0 - \color{blue}{\left(\left(-x\right) + y \cdot z\right)}}{x}}{x + 1} \]

      7. associate--r+ 81.1%

         \[\leadsto \frac{x + \frac{\color{blue}{\left(0 - \left(-x\right)\right) - y \cdot z}}{x}}{x + 1} \]

      8. neg-sub0 81.1%

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

      9. remove-double-neg 81.1%

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

      10. *-commutative 81.1%

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

   6. Simplified 81.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-178} \lor \neg \left(z \leq 430000000\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{x - y \cdot z}{x}}{x + 1}\\ \end{array} \]

Alternative 9: 77.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.85e+73)
   1.0
   (if (<= x 2.05e+15) (/ (+ x (/ y t)) (+ x 1.0)) (+ 1.0 (/ -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.85e+73) {
		tmp = 1.0;
	} else if (x <= 2.05e+15) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-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 (x <= (-1.85d+73)) then
        tmp = 1.0d0
    else if (x <= 2.05d+15) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((-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 (x <= -1.85e+73) {
		tmp = 1.0;
	} else if (x <= 2.05e+15) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.85e+73:
		tmp = 1.0
	elif x <= 2.05e+15:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (-1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.85e+73)
		tmp = 1.0;
	elseif (x <= 2.05e+15)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.85e+73)
		tmp = 1.0;
	elseif (x <= 2.05e+15)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.85e+73], 1.0, If[LessEqual[x, 2.05e+15], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.84999999999999987e73

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around inf 74.5%

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

      1. +-commutative 74.5%

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

      2. div-inv 74.5%

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

      3. fma-def 74.5%

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

   6. Applied egg-rr 74.5%

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

   7. Taylor expanded in x around inf 95.6%

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

   if -1.84999999999999987e73 < x < 2.05e15

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around inf 69.8%

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

   if 2.05e15 < x

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around inf 75.0%

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

   5. Taylor expanded in x around -inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. unsub-neg 75.0%

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

      3. mul-1-neg 75.0%

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

      4. sub-neg 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in y around 0 92.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+73}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]

Alternative 10: 67.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.55e-43) 1.0 (if (<= x 4.4e-117) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.55e-43) {
		tmp = 1.0;
	} else if (x <= 4.4e-117) {
		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 <= (-2.55d-43)) then
        tmp = 1.0d0
    else if (x <= 4.4d-117) 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 <= -2.55e-43) {
		tmp = 1.0;
	} else if (x <= 4.4e-117) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.55e-43:
		tmp = 1.0
	elif x <= 4.4e-117:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.55e-43)
		tmp = 1.0;
	elseif (x <= 4.4e-117)
		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 <= -2.55e-43)
		tmp = 1.0;
	elseif (x <= 4.4e-117)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.55e-43], 1.0, If[LessEqual[x, 4.4e-117], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5499999999999998e-43 or 4.4000000000000002e-117 < x

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. +-commutative 70.0%

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

      2. div-inv 70.0%

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

      3. fma-def 70.0%

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

   6. Applied egg-rr 70.0%

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

   7. Taylor expanded in x around inf 75.4%

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

   if -2.5499999999999998e-43 < x < 4.4000000000000002e-117

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

   3. Simplified 91.2%

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

      1. clear-num 91.2%

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

      2. inv-pow 91.2%

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

      3. fma-neg 91.2%

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

   5. Applied egg-rr 91.2%

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

      1. unpow-1 91.2%

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

      2. *-commutative 91.2%

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

      3. fma-neg 91.2%

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

      4. *-commutative 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in x around 0 57.8%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 67.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.8e-58) (/ x (+ x 1.0)) (if (<= x 4.5e-118) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-58) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.5e-118) {
		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 <= (-3.8d-58)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 4.5d-118) 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 <= -3.8e-58) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.5e-118) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.8e-58:
		tmp = x / (x + 1.0)
	elif x <= 4.5e-118:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.8e-58)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 4.5e-118)
		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 <= -3.8e-58)
		tmp = x / (x + 1.0);
	elseif (x <= 4.5e-118)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.8e-58], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e-118], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999997e-58

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around inf 77.5%

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

      1. +-commutative 77.5%

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

   6. Simplified 77.5%

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

   if -3.7999999999999997e-58 < x < 4.5e-118

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.7%

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

      2. inv-pow 92.7%

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

      3. fma-neg 92.7%

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

   5. Applied egg-rr 92.7%

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

      1. unpow-1 92.7%

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

      2. *-commutative 92.7%

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

      3. fma-neg 92.7%

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

      4. *-commutative 92.7%

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

   7. Simplified 92.7%

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

   8. Taylor expanded in x around 0 60.1%

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

   if 4.5e-118 < x

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in z around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. div-inv 68.4%

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

      3. fma-def 68.4%

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

   6. Applied egg-rr 68.4%

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

   7. Taylor expanded in x around inf 75.8%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-118}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 53.7% 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 93.0%

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

   1. *-commutative 93.0%

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

3. Simplified 93.0%

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

4. Taylor expanded in z around inf 71.8%

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

   1. +-commutative 71.8%

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

   2. div-inv 71.8%

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

   3. fma-def 71.8%

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

6. Applied egg-rr 71.8%

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

7. Taylor expanded in x around inf 51.8%

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

8. Final simplification 51.8%

   \[\leadsto 1 \]

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 2023320 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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