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

Percentage Accurate: 89.4% → 97.2%

Time: 13.6s

Alternatives: 10

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.4% 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: 97.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{z \cdot y - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+68}:\\ \;\;\;\;\frac{x - \left(-1 - \frac{y}{\frac{t_1}{z}}\right)}{x + 1}\\ \mathbf{elif}\;t_2 \leq 10^{+302}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* z y) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -5e+68)
     (/ (- x (- -1.0 (/ y (/ t_1 z)))) (+ x 1.0))
     (if (<= t_2 1e+302) 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 + (((z * y) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+68) {
		tmp = (x - (-1.0 - (y / (t_1 / z)))) / (x + 1.0);
	} else if (t_2 <= 1e+302) {
		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 + (((z * y) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-5d+68)) then
        tmp = (x - ((-1.0d0) - (y / (t_1 / z)))) / (x + 1.0d0)
    else if (t_2 <= 1d+302) 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 + (((z * y) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -5e+68) {
		tmp = (x - (-1.0 - (y / (t_1 / z)))) / (x + 1.0);
	} else if (t_2 <= 1e+302) {
		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 + (((z * y) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -5e+68:
		tmp = (x - (-1.0 - (y / (t_1 / z)))) / (x + 1.0)
	elif t_2 <= 1e+302:
		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(z * y) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -5e+68)
		tmp = Float64(Float64(x - Float64(-1.0 - Float64(y / Float64(t_1 / z)))) / Float64(x + 1.0));
	elseif (t_2 <= 1e+302)
		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 + (((z * y) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -5e+68)
		tmp = (x - (-1.0 - (y / (t_1 / z)))) / (x + 1.0);
	elseif (t_2 <= 1e+302)
		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[(z * y), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+68], N[(N[(x - N[(-1.0 - N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+302], 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 1)) < -5.0000000000000004e68

   1. Initial program 82.4%

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

      1. sub-neg 82.4%

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

      2. +-commutative 82.4%

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

      3. neg-sub0 82.4%

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

      4. associate-+l- 82.4%

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

      5. div-sub 82.4%

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

      6. div0 82.4%

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

      7. associate-+r- 82.4%

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

      8. +-commutative 82.4%

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

      9. +-lft-identity 82.4%

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

      10. *-commutative 82.4%

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

   3. Simplified 82.4%

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

      1. div-sub 82.4%

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

      2. associate-/l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 99.9%

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

   if -5.0000000000000004e68 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.0000000000000001e302

   1. Initial program 99.4%

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

   if 1.0000000000000001e302 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 22.4%

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

      1. sub-neg 22.4%

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

      2. +-commutative 22.4%

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

      3. neg-sub0 22.4%

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

      4. associate-+l- 22.4%

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

      5. div-sub 22.4%

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

      6. div0 22.4%

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

      7. associate-+r- 22.4%

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

      8. +-commutative 22.4%

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

      9. +-lft-identity 22.4%

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

      10. *-commutative 22.4%

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

   3. Simplified 22.4%

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

   4. Taylor expanded in z around inf 86.9%

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

      1. +-commutative 86.9%

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

      2. +-commutative 86.9%

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

   6. Simplified 86.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+68}:\\ \;\;\;\;\frac{x - \left(-1 - \frac{y}{\frac{z \cdot t - x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1} \leq 10^{+302}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 95.9% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+302)))
     (/ (+ x (/ y t)) (+ x 1.0))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+302)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+302)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+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(z * y) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+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 + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+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[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+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)) < -inf.0 or 1.0000000000000001e302 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 31.0%

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

      1. sub-neg 31.0%

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

      2. +-commutative 31.0%

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

      3. neg-sub0 31.0%

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

      4. associate-+l- 31.0%

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

      5. div-sub 31.0%

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

      6. div0 31.0%

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

      7. associate-+r- 31.0%

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

      8. +-commutative 31.0%

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

      9. +-lft-identity 31.0%

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

      10. *-commutative 31.0%

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

   3. Simplified 31.0%

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

   4. Taylor expanded in z around inf 89.8%

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

      1. +-commutative 89.8%

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

      2. +-commutative 89.8%

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

   6. Simplified 89.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.0000000000000001e302

   1. Initial program 99.4%

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

4. Final simplification 98.2%

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

Alternative 3: 96.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \frac{x + \left(\frac{y}{\frac{t_1}{z}} - \frac{x}{t_1}\right)}{x + 1} \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (/ (+ x (- (/ y (/ t_1 z)) (/ x t_1))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	return (x + ((y / (t_1 / z)) - (x / t_1))) / (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
    real(8) :: t_1
    t_1 = (z * t) - x
    code = (x + ((y / (t_1 / z)) - (x / t_1))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	return (x + ((y / (t_1 / z)) - (x / t_1))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	return (x + ((y / (t_1 / z)) - (x / t_1))) / (x + 1.0)

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	return Float64(Float64(x + Float64(Float64(y / Float64(t_1 / z)) - Float64(x / t_1))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = (x + ((y / (t_1 / z)) - (x / t_1))) / (x + 1.0);
end

Wolfram

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

Derivation

1. Initial program 90.3%

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

   1. sub-neg 90.3%

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

   2. +-commutative 90.3%

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

   3. neg-sub0 90.3%

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

   4. associate-+l- 90.3%

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

   5. div-sub 90.3%

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

   6. div0 90.3%

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

   7. associate-+r- 90.3%

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

   8. +-commutative 90.3%

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

   9. +-lft-identity 90.3%

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

   10. *-commutative 90.3%

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

3. Simplified 90.3%

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

   1. div-sub 90.3%

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

   2. associate-/l* 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 4: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-24} \lor \neg \left(t \leq 2.05 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{y}{\frac{x + 1}{z}}}{z \cdot t - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.3e-24) (not (<= t 2.05e-57)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (/ (/ y (/ (+ x 1.0) z)) (- (* z t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e-24) || !(t <= 2.05e-57)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / ((x + 1.0) / z)) / ((z * t) - 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 <= (-3.3d-24)) .or. (.not. (t <= 2.05d-57))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((y / ((x + 1.0d0) / z)) / ((z * t) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.3e-24) || !(t <= 2.05e-57)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((y / ((x + 1.0) / z)) / ((z * t) - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.3e-24) or not (t <= 2.05e-57):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((y / ((x + 1.0) / z)) / ((z * t) - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.3e-24) || !(t <= 2.05e-57))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(y / Float64(Float64(x + 1.0) / z)) / Float64(Float64(z * t) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.3e-24) || ~((t <= 2.05e-57)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((y / ((x + 1.0) / z)) / ((z * t) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.3e-24], N[Not[LessEqual[t, 2.05e-57]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / N[(N[(x + 1.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.29999999999999984e-24 or 2.0500000000000001e-57 < t

   1. Initial program 86.8%

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

      1. sub-neg 86.8%

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

      2. +-commutative 86.8%

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

      3. neg-sub0 86.8%

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

      4. associate-+l- 86.8%

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

      5. div-sub 86.8%

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

      6. div0 86.8%

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

      7. associate-+r- 86.8%

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

      8. +-commutative 86.8%

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

      9. +-lft-identity 86.8%

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

      10. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in z around inf 88.3%

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

      1. +-commutative 88.3%

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

      2. +-commutative 88.3%

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

   6. Simplified 88.3%

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

   if -3.29999999999999984e-24 < t < 2.0500000000000001e-57

   1. Initial program 94.3%

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

      1. sub-neg 94.3%

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

      2. +-commutative 94.3%

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

      3. neg-sub0 94.3%

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

      4. associate-+l- 94.3%

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

      5. div-sub 94.3%

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

      6. div0 94.3%

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

      7. associate-+r- 94.3%

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

      8. +-commutative 94.3%

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

      9. +-lft-identity 94.3%

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

      10. *-commutative 94.3%

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

   3. Simplified 94.3%

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

      1. div-sub 94.3%

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

      2. associate-/l* 99.1%

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

   5. Applied egg-rr 99.1%

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

   6. Taylor expanded in x around inf 88.4%

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

   7. Taylor expanded in y around 0 83.5%

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

      1. +-commutative 83.5%

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

      2. associate-/r* 83.6%

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

      3. associate-/l* 88.4%

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

      4. +-commutative 88.4%

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

   9. Simplified 88.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-24} \lor \neg \left(t \leq 2.05 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{y}{\frac{x + 1}{z}}}{z \cdot t - x}\\ \end{array} \]

Alternative 5: 81.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-69} \lor \neg \left(z \leq 5.5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot y}{z \cdot t - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e-69) (not (<= z 5.5e-11)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (/ (* z y) (- (* z t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-69) || !(z <= 5.5e-11)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((z * y) / ((z * t) - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.85d-69)) .or. (.not. (z <= 5.5d-11))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((z * y) / ((z * t) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-69) || !(z <= 5.5e-11)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + ((z * y) / ((z * t) - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e-69) or not (z <= 5.5e-11):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + ((z * y) / ((z * t) - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.85e-69) || !(z <= 5.5e-11))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(z * y) / Float64(Float64(z * t) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.85e-69) || ~((z <= 5.5e-11)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + ((z * y) / ((z * t) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.85e-69], N[Not[LessEqual[z, 5.5e-11]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(z * y), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e-69 or 5.49999999999999975e-11 < z

   1. Initial program 84.1%

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

      1. sub-neg 84.1%

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

      2. +-commutative 84.1%

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

      3. neg-sub0 84.1%

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

      4. associate-+l- 84.1%

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

      5. div-sub 84.1%

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

      6. div0 84.1%

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

      7. associate-+r- 84.1%

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

      8. +-commutative 84.1%

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

      9. +-lft-identity 84.1%

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

      10. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in z around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. +-commutative 86.3%

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

   6. Simplified 86.3%

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

   if -1.8500000000000001e-69 < z < 5.49999999999999975e-11

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. div-sub 99.9%

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

      6. div0 99.9%

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

      7. associate-+r- 99.9%

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

      8. +-commutative 99.9%

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

      9. +-lft-identity 99.9%

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

      10. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. div-sub 99.9%

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

      2. associate-/l* 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around inf 83.6%

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

   7. Taylor expanded in y around 0 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/r* 83.6%

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

      3. associate-/l* 83.5%

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

      4. +-commutative 83.5%

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

   9. Simplified 83.5%

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

   10. Taylor expanded in x around 0 81.8%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-69} \lor \neg \left(z \leq 5.5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot y}{z \cdot t - x}\\ \end{array} \]

Alternative 6: 76.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-97} \lor \neg \left(z \leq 7.6 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e-97) (not (<= z 7.6e-133)))
   (/ (+ x (/ y t)) (+ x 1.0))
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-97) || !(z <= 7.6e-133)) {
		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 ((z <= (-1.85d-97)) .or. (.not. (z <= 7.6d-133))) 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 ((z <= -1.85e-97) || !(z <= 7.6e-133)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e-97) or not (z <= 7.6e-133):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.85e-97) || !(z <= 7.6e-133))
		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 ((z <= -1.85e-97) || ~((z <= 7.6e-133)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.85e-97], N[Not[LessEqual[z, 7.6e-133]], $MachinePrecision]], 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 z < -1.84999999999999988e-97 or 7.6000000000000006e-133 < z

   1. Initial program 86.9%

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

      1. sub-neg 86.9%

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

      2. +-commutative 86.9%

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

      3. neg-sub0 86.9%

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

      4. associate-+l- 86.9%

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

      5. div-sub 86.9%

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

      6. div0 86.9%

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

      7. associate-+r- 86.9%

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

      8. +-commutative 86.9%

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

      9. +-lft-identity 86.9%

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

      10. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around inf 82.6%

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

      1. +-commutative 82.6%

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

      2. +-commutative 82.6%

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

   6. Simplified 82.6%

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

   if -1.84999999999999988e-97 < z < 7.6000000000000006e-133

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. neg-sub0 99.9%

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

      4. associate-+l- 99.9%

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

      5. div-sub 99.9%

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

      6. div0 99.9%

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

      7. associate-+r- 99.9%

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

      8. +-commutative 99.9%

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

      9. +-lft-identity 99.9%

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

      10. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 65.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-97} \lor \neg \left(z \leq 7.6 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 66.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-125} \lor \neg \left(x \leq 3.3 \cdot 10^{-162}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8.6e-125) (not (<= x 3.3e-162))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8.6e-125) || !(x <= 3.3e-162)) {
		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 <= (-8.6d-125)) .or. (.not. (x <= 3.3d-162))) 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 <= -8.6e-125) || !(x <= 3.3e-162)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8.6e-125) or not (x <= 3.3e-162):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8.6e-125) || !(x <= 3.3e-162))
		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 <= -8.6e-125) || ~((x <= 3.3e-162)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8.6e-125], N[Not[LessEqual[x, 3.3e-162]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.6000000000000004e-125 or 3.30000000000000013e-162 < 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. sub-neg 88.2%

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

      2. +-commutative 88.2%

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

      3. neg-sub0 88.2%

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

      4. associate-+l- 88.2%

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

      5. div-sub 88.2%

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

      6. div0 88.2%

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

      7. associate-+r- 88.2%

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

      8. +-commutative 88.2%

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

      9. +-lft-identity 88.2%

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

      10. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in t around inf 74.2%

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

      1. +-commutative 74.2%

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

   6. Simplified 74.2%

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

   if -8.6000000000000004e-125 < x < 3.30000000000000013e-162

   1. Initial program 95.7%

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

      1. sub-neg 95.7%

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

      2. +-commutative 95.7%

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

      3. neg-sub0 95.7%

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

      4. associate-+l- 95.7%

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

      5. div-sub 95.7%

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

      6. div0 95.7%

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

      7. associate-+r- 95.7%

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

      8. +-commutative 95.7%

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

      9. +-lft-identity 95.7%

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

      10. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in x around 0 54.8%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{-125} \lor \neg \left(x \leq 3.3 \cdot 10^{-162}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]

Alternative 8: 68.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-38}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.36e-38) 1.0 (if (<= x 1.5e-54) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.36e-38) {
		tmp = 1.0;
	} else if (x <= 1.5e-54) {
		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 <= (-1.36d-38)) then
        tmp = 1.0d0
    else if (x <= 1.5d-54) 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 <= -1.36e-38) {
		tmp = 1.0;
	} else if (x <= 1.5e-54) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.36e-38:
		tmp = 1.0
	elif x <= 1.5e-54:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.36e-38)
		tmp = 1.0;
	elseif (x <= 1.5e-54)
		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 <= -1.36e-38)
		tmp = 1.0;
	elseif (x <= 1.5e-54)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.36e-38], 1.0, If[LessEqual[x, 1.5e-54], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.36e-38 or 1.50000000000000005e-54 < x

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. +-commutative 86.5%

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

      3. neg-sub0 86.5%

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

      4. associate-+l- 86.5%

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

      5. div-sub 86.5%

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

      6. div0 86.5%

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

      7. associate-+r- 86.5%

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

      8. +-commutative 86.5%

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

      9. +-lft-identity 86.5%

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

      10. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in x around inf 82.7%

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

   if -1.36e-38 < x < 1.50000000000000005e-54

   1. Initial program 95.4%

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

      1. sub-neg 95.4%

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

      2. +-commutative 95.4%

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

      3. neg-sub0 95.4%

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

      4. associate-+l- 95.4%

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

      5. div-sub 95.4%

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

      6. div0 95.4%

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

      7. associate-+r- 95.4%

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

      8. +-commutative 95.4%

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

      9. +-lft-identity 95.4%

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

      10. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in x around 0 46.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-38}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 55.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-46}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.32e-46) 1.0 (if (<= x 6.2e-36) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.32e-46) {
		tmp = 1.0;
	} else if (x <= 6.2e-36) {
		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 <= (-1.32d-46)) then
        tmp = 1.0d0
    else if (x <= 6.2d-36) 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 <= -1.32e-46) {
		tmp = 1.0;
	} else if (x <= 6.2e-36) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.32e-46:
		tmp = 1.0
	elif x <= 6.2e-36:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.32e-46)
		tmp = 1.0;
	elseif (x <= 6.2e-36)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.32e-46)
		tmp = 1.0;
	elseif (x <= 6.2e-36)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.32e-46], 1.0, If[LessEqual[x, 6.2e-36], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.32000000000000001e-46 or 6.1999999999999997e-36 < x

   1. Initial program 85.6%

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

      1. sub-neg 85.6%

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

      2. +-commutative 85.6%

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

      3. neg-sub0 85.6%

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

      4. associate-+l- 85.6%

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

      5. div-sub 85.6%

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

      6. div0 85.6%

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

      7. associate-+r- 85.6%

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

      8. +-commutative 85.6%

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

      9. +-lft-identity 85.6%

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

      10. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in x around inf 84.3%

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

   if -1.32000000000000001e-46 < x < 6.1999999999999997e-36

   1. Initial program 96.4%

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

      1. sub-neg 96.4%

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

      2. +-commutative 96.4%

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

      3. neg-sub0 96.4%

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

      4. associate-+l- 96.4%

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

      5. div-sub 96.4%

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

      6. div0 96.4%

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

      7. associate-+r- 96.4%

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

      8. +-commutative 96.4%

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

      9. +-lft-identity 96.4%

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

      10. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around inf 23.4%

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

      1. +-commutative 23.4%

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

   6. Simplified 23.4%

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

   7. Taylor expanded in x around 0 23.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-46}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 53.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.3%

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

   1. sub-neg 90.3%

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

   2. +-commutative 90.3%

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

   3. neg-sub0 90.3%

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

   4. associate-+l- 90.3%

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

   5. div-sub 90.3%

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

   6. div0 90.3%

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

   7. associate-+r- 90.3%

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

   8. +-commutative 90.3%

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

   9. +-lft-identity 90.3%

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

   10. *-commutative 90.3%

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

3. Simplified 90.3%

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

4. Taylor expanded in x around inf 52.9%

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

5. Final simplification 52.9%

   \[\leadsto 1 \]

Developer target: 99.4% 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 2023326 
(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)))