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

Percentage Accurate: 89.6% → 96.3%

Time: 14.7s

Alternatives: 10

Speedup: 0.2×

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: 89.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{z}{\frac{t_1}{y}}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_3 \leq -6 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (+ x (/ z (/ t_1 y))) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -6e-46)
     t_2
     (if (<= t_3 4e+265)
       t_3
       (if (<= t_3 INFINITY) 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 / (t_1 / y))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -6e-46) {
		tmp = t_2;
	} else if (t_3 <= 4e+265) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (z / (t_1 / y))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -6e-46) {
		tmp = t_2;
	} else if (t_3 <= 4e+265) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		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 / (t_1 / y))) / (x + 1.0)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -6e-46:
		tmp = t_2
	elif t_3 <= 4e+265:
		tmp = t_3
	elif t_3 <= math.inf:
		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(z / Float64(t_1 / y))) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -6e-46)
		tmp = t_2;
	elseif (t_3 <= 4e+265)
		tmp = t_3;
	elseif (t_3 <= Inf)
		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 / (t_1 / y))) / (x + 1.0);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -6e-46)
		tmp = t_2;
	elseif (t_3 <= 4e+265)
		tmp = t_3;
	elseif (t_3 <= Inf)
		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[(z / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -6e-46], t$95$2, If[LessEqual[t$95$3, 4e+265], t$95$3, If[LessEqual[t$95$3, Infinity], 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)) < -5.99999999999999975e-46 or 4.00000000000000027e265 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < +inf.0

   1. Initial program 67.3%

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

      1. *-commutative 67.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in y around inf 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*l/ 97.9%

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

      3. *-commutative 97.9%

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

      4. *-commutative 97.9%

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

   6. Simplified 97.9%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.1%

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

      3. *-commutative 98.1%

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

   8. Applied egg-rr 98.1%

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

   if -5.99999999999999975e-46 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 4.00000000000000027e265

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -6 \cdot 10^{-46}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{z \cdot t - x}{y}}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 4 \cdot 10^{+265}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{x + \frac{z}{\frac{z \cdot t - x}{y}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 74.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-288}:\\ \;\;\;\;\frac{x - z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-285}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.16e-143)
     t_1
     (if (<= t -1.2e-288)
       (/ (- x (* z (/ y x))) (+ x 1.0))
       (if (<= t 5.6e-285)
         1.0
         (if (<= t 1.5e-201)
           (* (/ y (+ x 1.0)) (/ z (- (* z t) x)))
           (if (<= t 5.4e-151) 1.0 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.16e-143) {
		tmp = t_1;
	} else if (t <= -1.2e-288) {
		tmp = (x - (z * (y / x))) / (x + 1.0);
	} else if (t <= 5.6e-285) {
		tmp = 1.0;
	} else if (t <= 1.5e-201) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 5.4e-151) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.16d-143)) then
        tmp = t_1
    else if (t <= (-1.2d-288)) then
        tmp = (x - (z * (y / x))) / (x + 1.0d0)
    else if (t <= 5.6d-285) then
        tmp = 1.0d0
    else if (t <= 1.5d-201) then
        tmp = (y / (x + 1.0d0)) * (z / ((z * t) - x))
    else if (t <= 5.4d-151) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -1.16e-143) {
		tmp = t_1;
	} else if (t <= -1.2e-288) {
		tmp = (x - (z * (y / x))) / (x + 1.0);
	} else if (t <= 5.6e-285) {
		tmp = 1.0;
	} else if (t <= 1.5e-201) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 5.4e-151) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -1.16e-143:
		tmp = t_1
	elif t <= -1.2e-288:
		tmp = (x - (z * (y / x))) / (x + 1.0)
	elif t <= 5.6e-285:
		tmp = 1.0
	elif t <= 1.5e-201:
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x))
	elif t <= 5.4e-151:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -1.16e-143)
		tmp = t_1;
	elseif (t <= -1.2e-288)
		tmp = Float64(Float64(x - Float64(z * Float64(y / x))) / Float64(x + 1.0));
	elseif (t <= 5.6e-285)
		tmp = 1.0;
	elseif (t <= 1.5e-201)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / Float64(Float64(z * t) - x)));
	elseif (t <= 5.4e-151)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -1.16e-143)
		tmp = t_1;
	elseif (t <= -1.2e-288)
		tmp = (x - (z * (y / x))) / (x + 1.0);
	elseif (t <= 5.6e-285)
		tmp = 1.0;
	elseif (t <= 1.5e-201)
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	elseif (t <= 5.4e-151)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.16e-143], t$95$1, If[LessEqual[t, -1.2e-288], N[(N[(x - N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-285], 1.0, If[LessEqual[t, 1.5e-201], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-151], 1.0, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.16000000000000008e-143 or 5.40000000000000014e-151 < t

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in z around inf 85.7%

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

   if -1.16000000000000008e-143 < t < -1.1999999999999999e-288

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*l/ 79.2%

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

      3. *-commutative 79.2%

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

      4. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in t around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. distribute-frac-neg 71.8%

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

   9. Simplified 71.8%

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

       1. distribute-frac-neg 71.8%

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

       2. add-sqr-sqrt 41.8%

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

       3. sqrt-unprod 49.9%

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

       4. sqr-neg 49.9%

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

       5. sqrt-unprod 18.8%

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

       6. add-sqr-sqrt 38.2%

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

       7. distribute-rgt-neg-in 38.2%

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

       8. sub-neg 38.2%

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

       9. clear-num 38.2%

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

       10. clear-num 38.2%

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

       11. add-sqr-sqrt 18.8%

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

       12. sqrt-unprod 49.9%

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

       13. sqr-neg 49.9%

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

       14. sqrt-unprod 41.8%

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

       15. add-sqr-sqrt 71.8%

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

   11. Applied egg-rr 71.8%

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

   if -1.1999999999999999e-288 < t < 5.59999999999999982e-285 or 1.50000000000000001e-201 < t < 5.40000000000000014e-151

   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 inf 57.0%

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

      1. *-commutative 57.0%

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

      2. associate-*l/ 57.0%

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

      3. *-commutative 57.0%

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

      4. *-commutative 57.0%

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

   6. Simplified 57.0%

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

   7. Taylor expanded in x around inf 88.3%

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

   if 5.59999999999999982e-285 < t < 1.50000000000000001e-201

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

   3. Simplified 90.1%

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

   4. Taylor expanded in y around inf 56.4%

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

      1. times-frac 65.6%

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

      2. +-commutative 65.6%

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

   6. Simplified 65.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-143}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-288}:\\ \;\;\;\;\frac{x - z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-285}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-201}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x + 1\right) - \frac{y \cdot z}{x}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -3 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (+ x 1.0) (/ (* y z) x)) (+ x 1.0)))
        (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -3e-143)
     t_2
     (if (<= t 2.3e-260)
       t_1
       (if (<= t 2.8e-205)
         (* (/ y (+ x 1.0)) (/ z (- (* z t) x)))
         (if (<= t 1.12e-150) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x + 1.0) - ((y * z) / x)) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -3e-143) {
		tmp = t_2;
	} else if (t <= 2.3e-260) {
		tmp = t_1;
	} else if (t <= 2.8e-205) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 1.12e-150) {
		tmp = t_1;
	} 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 + 1.0d0) - ((y * z) / x)) / (x + 1.0d0)
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-3d-143)) then
        tmp = t_2
    else if (t <= 2.3d-260) then
        tmp = t_1
    else if (t <= 2.8d-205) then
        tmp = (y / (x + 1.0d0)) * (z / ((z * t) - x))
    else if (t <= 1.12d-150) then
        tmp = t_1
    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 + 1.0) - ((y * z) / x)) / (x + 1.0);
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -3e-143) {
		tmp = t_2;
	} else if (t <= 2.3e-260) {
		tmp = t_1;
	} else if (t <= 2.8e-205) {
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	} else if (t <= 1.12e-150) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x + 1.0) - ((y * z) / x)) / (x + 1.0)
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -3e-143:
		tmp = t_2
	elif t <= 2.3e-260:
		tmp = t_1
	elif t <= 2.8e-205:
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x))
	elif t <= 1.12e-150:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x + 1.0) - Float64(Float64(y * z) / x)) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -3e-143)
		tmp = t_2;
	elseif (t <= 2.3e-260)
		tmp = t_1;
	elseif (t <= 2.8e-205)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / Float64(Float64(z * t) - x)));
	elseif (t <= 1.12e-150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x + 1.0) - ((y * z) / x)) / (x + 1.0);
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -3e-143)
		tmp = t_2;
	elseif (t <= 2.3e-260)
		tmp = t_1;
	elseif (t <= 2.8e-205)
		tmp = (y / (x + 1.0)) * (z / ((z * t) - x));
	elseif (t <= 1.12e-150)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x + 1.0), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / x), $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[t, -3e-143], t$95$2, If[LessEqual[t, 2.3e-260], t$95$1, If[LessEqual[t, 2.8e-205], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e-150], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.99999999999999985e-143 or 1.12e-150 < t

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in z around inf 85.7%

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

   if -2.99999999999999985e-143 < t < 2.3e-260 or 2.79999999999999991e-205 < t < 1.12e-150

   1. Initial program 96.6%

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

      1. *-commutative 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around 0 91.6%

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

      1. associate-+r+ 91.6%

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

      2. +-commutative 91.6%

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

      3. associate-*r/ 91.6%

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

      4. mul-1-neg 91.6%

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

      5. *-commutative 91.6%

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

      6. +-commutative 91.6%

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

   6. Simplified 91.6%

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

   if 2.3e-260 < t < 2.79999999999999991e-205

   1. Initial program 83.8%

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

      1. *-commutative 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in y around inf 59.5%

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

      1. times-frac 74.8%

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

      2. +-commutative 74.8%

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

   6. Simplified 74.8%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-143}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-260}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y \cdot z}{x}}{x + 1}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-205}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-150}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y \cdot z}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 79.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-28}:\\ \;\;\;\;\frac{x - \frac{x}{t_1}}{x + 1}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t_1}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{x - z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -3.1e-50)
     t_2
     (if (<= z 3.3e-28)
       (/ (- x (/ x t_1)) (+ x 1.0))
       (if (<= z 5.5e-18)
         (* (/ y (+ x 1.0)) (/ z t_1))
         (if (<= z 2.2e+66) (/ (- x (* z (/ y x))) (+ x 1.0)) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -3.1e-50) {
		tmp = t_2;
	} else if (z <= 3.3e-28) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (z <= 5.5e-18) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (z <= 2.2e+66) {
		tmp = (x - (z * (y / 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 = (z * t) - x
    t_2 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-3.1d-50)) then
        tmp = t_2
    else if (z <= 3.3d-28) then
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    else if (z <= 5.5d-18) then
        tmp = (y / (x + 1.0d0)) * (z / t_1)
    else if (z <= 2.2d+66) then
        tmp = (x - (z * (y / 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 = (z * t) - x;
	double t_2 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -3.1e-50) {
		tmp = t_2;
	} else if (z <= 3.3e-28) {
		tmp = (x - (x / t_1)) / (x + 1.0);
	} else if (z <= 5.5e-18) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (z <= 2.2e+66) {
		tmp = (x - (z * (y / x))) / (x + 1.0);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -3.1e-50:
		tmp = t_2
	elif z <= 3.3e-28:
		tmp = (x - (x / t_1)) / (x + 1.0)
	elif z <= 5.5e-18:
		tmp = (y / (x + 1.0)) * (z / t_1)
	elif z <= 2.2e+66:
		tmp = (x - (z * (y / x))) / (x + 1.0)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -3.1e-50)
		tmp = t_2;
	elseif (z <= 3.3e-28)
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	elseif (z <= 5.5e-18)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / t_1));
	elseif (z <= 2.2e+66)
		tmp = Float64(Float64(x - Float64(z * Float64(y / x))) / Float64(x + 1.0));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -3.1e-50)
		tmp = t_2;
	elseif (z <= 3.3e-28)
		tmp = (x - (x / t_1)) / (x + 1.0);
	elseif (z <= 5.5e-18)
		tmp = (y / (x + 1.0)) * (z / t_1);
	elseif (z <= 2.2e+66)
		tmp = (x - (z * (y / 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[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-50], t$95$2, If[LessEqual[z, 3.3e-28], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-18], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+66], N[(N[(x - N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1000000000000002e-50 or 2.1999999999999998e66 < z

   1. Initial program 74.4%

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

      1. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in z around inf 85.4%

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

   if -3.1000000000000002e-50 < z < 3.3000000000000002e-28

   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 81.2%

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

      1. +-commutative 81.2%

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

   6. Simplified 81.2%

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

   if 3.3000000000000002e-28 < z < 5.5e-18

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 94.2%

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

      1. times-frac 94.2%

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

      2. +-commutative 94.2%

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

   6. Simplified 94.2%

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

   if 5.5e-18 < z < 2.1999999999999998e66

   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 inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*l/ 75.7%

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

      3. *-commutative 75.7%

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

      4. *-commutative 75.7%

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

   6. Simplified 75.7%

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

   7. Taylor expanded in t around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. distribute-frac-neg 69.3%

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

   9. Simplified 69.3%

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

       1. distribute-frac-neg 69.3%

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

       2. add-sqr-sqrt 34.7%

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

       3. sqrt-unprod 42.8%

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

       4. sqr-neg 42.8%

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

       5. sqrt-unprod 27.8%

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

       6. add-sqr-sqrt 41.9%

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

       7. distribute-rgt-neg-in 41.9%

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

       8. sub-neg 41.9%

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

       9. clear-num 41.9%

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

       10. clear-num 41.9%

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

       11. add-sqr-sqrt 27.8%

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

       12. sqrt-unprod 42.8%

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

       13. sqr-neg 42.8%

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

       14. sqrt-unprod 34.7%

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

       15. add-sqr-sqrt 69.3%

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

   11. Applied egg-rr 69.3%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-28}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{x - z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 5: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-207} \lor \neg \left(z \leq 1.4 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t_1}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{t_1}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (or (<= z -6.5e-207) (not (<= z 1.4e-131)))
     (/ (+ x (* z (/ y t_1))) (+ x 1.0))
     (/ (- x (/ x t_1)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if ((z <= -6.5e-207) || !(z <= 1.4e-131)) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) - x
    if ((z <= (-6.5d-207)) .or. (.not. (z <= 1.4d-131))) then
        tmp = (x + (z * (y / t_1))) / (x + 1.0d0)
    else
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if ((z <= -6.5e-207) || !(z <= 1.4e-131)) {
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if (z <= -6.5e-207) or not (z <= 1.4e-131):
		tmp = (x + (z * (y / t_1))) / (x + 1.0)
	else:
		tmp = (x - (x / t_1)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if ((z <= -6.5e-207) || !(z <= 1.4e-131))
		tmp = Float64(Float64(x + Float64(z * Float64(y / t_1))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if ((z <= -6.5e-207) || ~((z <= 1.4e-131)))
		tmp = (x + (z * (y / t_1))) / (x + 1.0);
	else
		tmp = (x - (x / t_1)) / (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]}, If[Or[LessEqual[z, -6.5e-207], N[Not[LessEqual[z, 1.4e-131]], $MachinePrecision]], N[(N[(x + N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000001e-207 or 1.4e-131 < z

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l/ 88.8%

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

      3. *-commutative 88.8%

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

      4. *-commutative 88.8%

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

   6. Simplified 88.8%

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

   if -6.5000000000000001e-207 < z < 1.4e-131

   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 87.2%

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

      1. +-commutative 87.2%

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

   6. Simplified 87.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-207} \lor \neg \left(z \leq 1.4 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 6: 85.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-205} \lor \neg \left(z \leq 6.5 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{t_1}{y}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{t_1}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (or (<= z -2.5e-205) (not (<= z 6.5e-129)))
     (/ (+ x (/ z (/ t_1 y))) (+ x 1.0))
     (/ (- x (/ x t_1)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if ((z <= -2.5e-205) || !(z <= 6.5e-129)) {
		tmp = (x + (z / (t_1 / y))) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) - x
    if ((z <= (-2.5d-205)) .or. (.not. (z <= 6.5d-129))) then
        tmp = (x + (z / (t_1 / y))) / (x + 1.0d0)
    else
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if ((z <= -2.5e-205) || !(z <= 6.5e-129)) {
		tmp = (x + (z / (t_1 / y))) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if (z <= -2.5e-205) or not (z <= 6.5e-129):
		tmp = (x + (z / (t_1 / y))) / (x + 1.0)
	else:
		tmp = (x - (x / t_1)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if ((z <= -2.5e-205) || !(z <= 6.5e-129))
		tmp = Float64(Float64(x + Float64(z / Float64(t_1 / y))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if ((z <= -2.5e-205) || ~((z <= 6.5e-129)))
		tmp = (x + (z / (t_1 / y))) / (x + 1.0);
	else
		tmp = (x - (x / t_1)) / (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]}, If[Or[LessEqual[z, -2.5e-205], N[Not[LessEqual[z, 6.5e-129]], $MachinePrecision]], N[(N[(x + N[(z / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e-205 or 6.49999999999999952e-129 < z

   1. Initial program 83.2%

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

      1. *-commutative 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in y around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-*l/ 88.8%

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

      3. *-commutative 88.8%

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

      4. *-commutative 88.8%

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

   6. Simplified 88.8%

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

      1. clear-num 88.8%

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

      2. un-div-inv 88.9%

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

      3. *-commutative 88.9%

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

   8. Applied egg-rr 88.9%

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

   if -2.5e-205 < z < 6.49999999999999952e-129

   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 87.2%

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

      1. +-commutative 87.2%

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

   6. Simplified 87.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-205} \lor \neg \left(z \leq 6.5 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{z \cdot t - x}{y}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 7: 75.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x - z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -4.6e-144)
     t_1
     (if (<= t -5.5e-287)
       (/ (- x (* z (/ y x))) (+ x 1.0))
       (if (<= t 5.4e-151) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4.6e-144) {
		tmp = t_1;
	} else if (t <= -5.5e-287) {
		tmp = (x - (z * (y / x))) / (x + 1.0);
	} else if (t <= 5.4e-151) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-4.6d-144)) then
        tmp = t_1
    else if (t <= (-5.5d-287)) then
        tmp = (x - (z * (y / x))) / (x + 1.0d0)
    else if (t <= 5.4d-151) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4.6e-144) {
		tmp = t_1;
	} else if (t <= -5.5e-287) {
		tmp = (x - (z * (y / x))) / (x + 1.0);
	} else if (t <= 5.4e-151) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -4.6e-144:
		tmp = t_1
	elif t <= -5.5e-287:
		tmp = (x - (z * (y / x))) / (x + 1.0)
	elif t <= 5.4e-151:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -4.6e-144)
		tmp = t_1;
	elseif (t <= -5.5e-287)
		tmp = Float64(Float64(x - Float64(z * Float64(y / x))) / Float64(x + 1.0));
	elseif (t <= 5.4e-151)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -4.6e-144)
		tmp = t_1;
	elseif (t <= -5.5e-287)
		tmp = (x - (z * (y / x))) / (x + 1.0);
	elseif (t <= 5.4e-151)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.6e-144], t$95$1, If[LessEqual[t, -5.5e-287], N[(N[(x - N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-151], 1.0, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6e-144 or 5.40000000000000014e-151 < t

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in z around inf 85.7%

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

   if -4.6e-144 < t < -5.4999999999999998e-287

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-*l/ 79.2%

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

      3. *-commutative 79.2%

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

      4. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in t around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. distribute-frac-neg 71.8%

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

   9. Simplified 71.8%

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

       1. distribute-frac-neg 71.8%

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

       2. add-sqr-sqrt 41.8%

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

       3. sqrt-unprod 49.9%

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

       4. sqr-neg 49.9%

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

       5. sqrt-unprod 18.8%

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

       6. add-sqr-sqrt 38.2%

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

       7. distribute-rgt-neg-in 38.2%

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

       8. sub-neg 38.2%

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

       9. clear-num 38.2%

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

       10. clear-num 38.2%

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

       11. add-sqr-sqrt 18.8%

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

       12. sqrt-unprod 49.9%

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

       13. sqr-neg 49.9%

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

       14. sqrt-unprod 41.8%

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

       15. add-sqr-sqrt 71.8%

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

   11. Applied egg-rr 71.8%

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

   if -5.4999999999999998e-287 < t < 5.40000000000000014e-151

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   4. Taylor expanded in y around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. associate-*l/ 70.0%

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

      3. *-commutative 70.0%

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

      4. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in x around inf 65.2%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-287}:\\ \;\;\;\;\frac{x - z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 8: 74.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-181} \lor \neg \left(t \leq 8.2 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.1e-181) (not (<= t 8.2e-151)))
   (/ (+ x (/ y t)) (+ x 1.0))
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.1e-181) || !(t <= 8.2e-151)) {
		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 ((t <= (-2.1d-181)) .or. (.not. (t <= 8.2d-151))) 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 ((t <= -2.1e-181) || !(t <= 8.2e-151)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.1e-181) or not (t <= 8.2e-151):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.1e-181) || !(t <= 8.2e-151))
		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 ((t <= -2.1e-181) || ~((t <= 8.2e-151)))
		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[t, -2.1e-181], N[Not[LessEqual[t, 8.2e-151]], $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 t < -2.10000000000000003e-181 or 8.2000000000000002e-151 < t

   1. Initial program 84.3%

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

      1. *-commutative 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in z around inf 84.7%

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

   if -2.10000000000000003e-181 < t < 8.2000000000000002e-151

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in y around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-*l/ 71.1%

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

      3. *-commutative 71.1%

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

      4. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in x around inf 61.3%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-181} \lor \neg \left(t \leq 8.2 \cdot 10^{-151}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 67.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.2e-25) 1.0 (if (<= x 7.8e-99) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e-25) {
		tmp = 1.0;
	} else if (x <= 7.8e-99) {
		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 <= (-3.2d-25)) then
        tmp = 1.0d0
    else if (x <= 7.8d-99) 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 <= -3.2e-25) {
		tmp = 1.0;
	} else if (x <= 7.8e-99) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.2e-25:
		tmp = 1.0
	elif x <= 7.8e-99:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.2e-25)
		tmp = 1.0;
	elseif (x <= 7.8e-99)
		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 <= -3.2e-25)
		tmp = 1.0;
	elseif (x <= 7.8e-99)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.2e-25], 1.0, If[LessEqual[x, 7.8e-99], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2000000000000001e-25 or 7.79999999999999975e-99 < x

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around inf 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-*l/ 92.4%

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

      3. *-commutative 92.4%

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

      4. *-commutative 92.4%

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

   6. Simplified 92.4%

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

   7. Taylor expanded in x around inf 81.1%

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

   if -3.2000000000000001e-25 < x < 7.79999999999999975e-99

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

   3. Simplified 85.8%

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

   4. Taylor expanded in z around inf 68.3%

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

   5. Taylor expanded in y around inf 52.9%

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

      1. +-commutative 52.9%

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

   7. Simplified 52.9%

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

   8. Taylor expanded in x around 0 52.9%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-25}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

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 86.9%

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

   1. *-commutative 86.9%

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

3. Simplified 86.9%

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

4. Taylor expanded in y around inf 74.9%

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

   1. *-commutative 74.9%

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

   2. associate-*l/ 82.3%

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

   3. *-commutative 82.3%

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

   4. *-commutative 82.3%

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

6. Simplified 82.3%

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

7. Taylor expanded in x around inf 57.0%

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

8. Final simplification 57.0%

   \[\leadsto 1 \]

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 2023301 
(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)))