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

Percentage Accurate: 90.4% → 98.0%

Time: 44.3s

Alternatives: 14

Speedup: 0.8×

• could not determine a ground truth

  1. x = 4.312007031122999e+211
  2. y = -3.1038085232112574e+202
  3. z = 1.6232272807680903e-211
  4. t = 1.8284323194583427e-162

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: 90.4% 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: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-20} \lor \neg \left(z \leq 5.1 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-20) (not (<= z 5.1e-23)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-20) || !(z <= 5.1e-23)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.95d-20)) .or. (.not. (z <= 5.1d-23))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-20) || !(z <= 5.1e-23)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-20) or not (z <= 5.1e-23):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e-20) || !(z <= 5.1e-23))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e-20) || ~((z <= 5.1e-23)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e-20], N[Not[LessEqual[z, 5.1e-23]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000004e-20 or 5.10000000000000011e-23 < z

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around inf 83.7%

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

      1. associate-/l* 91.7%

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

   6. Simplified 91.7%

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

   7. Taylor expanded in t around 0 97.6%

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

      1. mul-1-neg 97.6%

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

      2. unsub-neg 97.6%

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

   9. Simplified 97.6%

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

   if -1.95000000000000004e-20 < z < 5.10000000000000011e-23

   1. Initial program 99.7%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-20} \lor \neg \left(z \leq 5.1 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 2: 68.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-269}:\\ \;\;\;\;\frac{y}{t + x \cdot \left(t + \frac{-1}{z}\right)}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-143}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-45}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -8.4e+49)
     t_1
     (if (<= z -2.4e-269)
       (/ y (+ t (* x (+ t (/ -1.0 z)))))
       (if (<= z 1.35e-143)
         1.0
         (if (<= z 5.6e-78)
           t_1
           (if (<= z 5.8e-78)
             1.0
             (if (<= z 1.12e-45) (/ (- x (/ y (/ x z))) (+ x 1.0)) t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -8.4e+49) {
		tmp = t_1;
	} else if (z <= -2.4e-269) {
		tmp = y / (t + (x * (t + (-1.0 / z))));
	} else if (z <= 1.35e-143) {
		tmp = 1.0;
	} else if (z <= 5.6e-78) {
		tmp = t_1;
	} else if (z <= 5.8e-78) {
		tmp = 1.0;
	} else if (z <= 1.12e-45) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (z <= (-8.4d+49)) then
        tmp = t_1
    else if (z <= (-2.4d-269)) then
        tmp = y / (t + (x * (t + ((-1.0d0) / z))))
    else if (z <= 1.35d-143) then
        tmp = 1.0d0
    else if (z <= 5.6d-78) then
        tmp = t_1
    else if (z <= 5.8d-78) then
        tmp = 1.0d0
    else if (z <= 1.12d-45) then
        tmp = (x - (y / (x / z))) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -8.4e+49) {
		tmp = t_1;
	} else if (z <= -2.4e-269) {
		tmp = y / (t + (x * (t + (-1.0 / z))));
	} else if (z <= 1.35e-143) {
		tmp = 1.0;
	} else if (z <= 5.6e-78) {
		tmp = t_1;
	} else if (z <= 5.8e-78) {
		tmp = 1.0;
	} else if (z <= 1.12e-45) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if z <= -8.4e+49:
		tmp = t_1
	elif z <= -2.4e-269:
		tmp = y / (t + (x * (t + (-1.0 / z))))
	elif z <= 1.35e-143:
		tmp = 1.0
	elif z <= 5.6e-78:
		tmp = t_1
	elif z <= 5.8e-78:
		tmp = 1.0
	elif z <= 1.12e-45:
		tmp = (x - (y / (x / z))) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -8.4e+49)
		tmp = t_1;
	elseif (z <= -2.4e-269)
		tmp = Float64(y / Float64(t + Float64(x * Float64(t + Float64(-1.0 / z)))));
	elseif (z <= 1.35e-143)
		tmp = 1.0;
	elseif (z <= 5.6e-78)
		tmp = t_1;
	elseif (z <= 5.8e-78)
		tmp = 1.0;
	elseif (z <= 1.12e-45)
		tmp = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (z <= -8.4e+49)
		tmp = t_1;
	elseif (z <= -2.4e-269)
		tmp = y / (t + (x * (t + (-1.0 / z))));
	elseif (z <= 1.35e-143)
		tmp = 1.0;
	elseif (z <= 5.6e-78)
		tmp = t_1;
	elseif (z <= 5.8e-78)
		tmp = 1.0;
	elseif (z <= 1.12e-45)
		tmp = (x - (y / (x / z))) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.4e+49], t$95$1, If[LessEqual[z, -2.4e-269], N[(y / N[(t + N[(x * N[(t + N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-143], 1.0, If[LessEqual[z, 5.6e-78], t$95$1, If[LessEqual[z, 5.8e-78], 1.0, If[LessEqual[z, 1.12e-45], N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.40000000000000043e49 or 1.35000000000000005e-143 < z < 5.60000000000000047e-78 or 1.1199999999999999e-45 < z

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around inf 91.8%

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

   if -8.40000000000000043e49 < z < -2.4000000000000001e-269

   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 65.3%

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

      1. associate-/l* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in y around inf 55.9%

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

      1. associate-/l* 57.6%

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

      2. *-commutative 57.6%

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

      3. +-commutative 57.6%

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

   9. Simplified 57.6%

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

   10. Taylor expanded in x around 0 58.8%

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

   if -2.4000000000000001e-269 < z < 1.35000000000000005e-143 or 5.60000000000000047e-78 < z < 5.8000000000000001e-78

   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 26.4%

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

      1. associate-/l* 26.4%

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

   6. Simplified 26.4%

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

   7. Taylor expanded in t around 0 26.5%

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

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

   9. Simplified 26.5%

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

   10. Taylor expanded in x around inf 66.7%

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

   if 5.8000000000000001e-78 < z < 1.1199999999999999e-45

   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 88.0%

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

      1. associate-/l* 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in t around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. mul-1-neg 88.0%

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

      3. unsub-neg 88.0%

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

      4. associate-/l* 88.2%

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

      5. +-commutative 88.2%

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

   9. Simplified 88.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+49}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-269}:\\ \;\;\;\;\frac{y}{t + x \cdot \left(t + \frac{-1}{z}\right)}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-143}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-78}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-45}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 83.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ t_2 := \frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{if}\;z \leq -3 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-267}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))
        (t_2 (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))))
   (if (<= z -3e-195)
     t_2
     (if (<= z -2.15e-239)
       t_1
       (if (<= z -2.75e-266)
         t_2
         (if (<= z 7.2e-267)
           (/ (+ x (- 1.0 (/ y (/ x z)))) (+ x 1.0))
           (if (<= z 1.38e-142) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / (t - (x / z)))) / (x + 1.0);
	double tmp;
	if (z <= -3e-195) {
		tmp = t_2;
	} else if (z <= -2.15e-239) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = t_2;
	} else if (z <= 7.2e-267) {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	} else if (z <= 1.38e-142) {
		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 - (x / ((z * t) - x))) / (x + 1.0d0)
    t_2 = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    if (z <= (-3d-195)) then
        tmp = t_2
    else if (z <= (-2.15d-239)) then
        tmp = t_1
    else if (z <= (-2.75d-266)) then
        tmp = t_2
    else if (z <= 7.2d-267) then
        tmp = (x + (1.0d0 - (y / (x / z)))) / (x + 1.0d0)
    else if (z <= 1.38d-142) 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 - (x / ((z * t) - x))) / (x + 1.0);
	double t_2 = (x + (y / (t - (x / z)))) / (x + 1.0);
	double tmp;
	if (z <= -3e-195) {
		tmp = t_2;
	} else if (z <= -2.15e-239) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = t_2;
	} else if (z <= 7.2e-267) {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	} else if (z <= 1.38e-142) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0)
	t_2 = (x + (y / (t - (x / z)))) / (x + 1.0)
	tmp = 0
	if z <= -3e-195:
		tmp = t_2
	elif z <= -2.15e-239:
		tmp = t_1
	elif z <= -2.75e-266:
		tmp = t_2
	elif z <= 7.2e-267:
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0)
	elif z <= 1.38e-142:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	t_2 = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0))
	tmp = 0.0
	if (z <= -3e-195)
		tmp = t_2;
	elseif (z <= -2.15e-239)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = t_2;
	elseif (z <= 7.2e-267)
		tmp = Float64(Float64(x + Float64(1.0 - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	elseif (z <= 1.38e-142)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (x / ((z * t) - x))) / (x + 1.0);
	t_2 = (x + (y / (t - (x / z)))) / (x + 1.0);
	tmp = 0.0;
	if (z <= -3e-195)
		tmp = t_2;
	elseif (z <= -2.15e-239)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = t_2;
	elseif (z <= 7.2e-267)
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	elseif (z <= 1.38e-142)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-195], t$95$2, If[LessEqual[z, -2.15e-239], t$95$1, If[LessEqual[z, -2.75e-266], t$95$2, If[LessEqual[z, 7.2e-267], N[(N[(x + N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e-142], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e-195 or -2.15e-239 < z < -2.75000000000000013e-266 or 1.37999999999999998e-142 < z

   1. Initial program 90.5%

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

      1. *-commutative 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around inf 80.5%

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

      1. associate-/l* 85.9%

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

   6. Simplified 85.9%

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

   7. Taylor expanded in t around 0 89.9%

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

      1. mul-1-neg 89.9%

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

      2. unsub-neg 89.9%

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

   9. Simplified 89.9%

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

   if -3e-195 < z < -2.15e-239 or 7.2000000000000002e-267 < z < 1.37999999999999998e-142

   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 77.7%

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

      1. +-commutative 77.7%

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

   6. Simplified 77.7%

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

   if -2.75000000000000013e-266 < z < 7.2000000000000002e-267

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 87.9%

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

      1. +-commutative 87.9%

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

      2. +-commutative 87.9%

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

      3. associate-+l+ 87.9%

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

      4. +-commutative 87.9%

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

      5. mul-1-neg 87.9%

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

      6. unsub-neg 87.9%

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

      7. associate-/l* 87.9%

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

      8. +-commutative 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-195}:\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-239}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-267}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{-142}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \end{array} \]

Alternative 4: 55.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= y -1.7e-170)
     t_1
     (if (<= y 1.02e-141)
       (/ x (+ x 1.0))
       (if (<= y 6.6e-59)
         (/ y (* t (+ x 1.0)))
         (if (<= y 3.2e-14) 1.0 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (y <= -1.7e-170) {
		tmp = t_1;
	} else if (y <= 1.02e-141) {
		tmp = x / (x + 1.0);
	} else if (y <= 6.6e-59) {
		tmp = y / (t * (x + 1.0));
	} else if (y <= 3.2e-14) {
		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 = y * (z / ((z * t) - x))
    if (y <= (-1.7d-170)) then
        tmp = t_1
    else if (y <= 1.02d-141) then
        tmp = x / (x + 1.0d0)
    else if (y <= 6.6d-59) then
        tmp = y / (t * (x + 1.0d0))
    else if (y <= 3.2d-14) 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 = y * (z / ((z * t) - x));
	double tmp;
	if (y <= -1.7e-170) {
		tmp = t_1;
	} else if (y <= 1.02e-141) {
		tmp = x / (x + 1.0);
	} else if (y <= 6.6e-59) {
		tmp = y / (t * (x + 1.0));
	} else if (y <= 3.2e-14) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if y <= -1.7e-170:
		tmp = t_1
	elif y <= 1.02e-141:
		tmp = x / (x + 1.0)
	elif y <= 6.6e-59:
		tmp = y / (t * (x + 1.0))
	elif y <= 3.2e-14:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (y <= -1.7e-170)
		tmp = t_1;
	elseif (y <= 1.02e-141)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (y <= 6.6e-59)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	elseif (y <= 3.2e-14)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (y <= -1.7e-170)
		tmp = t_1;
	elseif (y <= 1.02e-141)
		tmp = x / (x + 1.0);
	elseif (y <= 6.6e-59)
		tmp = y / (t * (x + 1.0));
	elseif (y <= 3.2e-14)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-170], t$95$1, If[LessEqual[y, 1.02e-141], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-59], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-14], 1.0, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.70000000000000006e-170 or 3.2000000000000002e-14 < y

   1. Initial program 88.2%

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

      1. *-commutative 88.2%

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

   3. Simplified 88.2%

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

   4. Taylor expanded in y around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. *-commutative 61.7%

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

      3. times-frac 68.0%

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

      4. +-commutative 68.0%

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

      5. *-commutative 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in x around 0 65.1%

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

   if -1.70000000000000006e-170 < y < 1.02e-141

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around inf 49.6%

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

      1. +-commutative 49.6%

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

   6. Simplified 49.6%

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

   if 1.02e-141 < y < 6.59999999999999964e-59

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. times-frac 57.4%

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

      4. +-commutative 57.4%

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

      5. *-commutative 57.4%

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

   6. Simplified 57.4%

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

   7. Taylor expanded in z around inf 63.0%

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

   if 6.59999999999999964e-59 < y < 3.2000000000000002e-14

   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 35.4%

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

      1. associate-/l* 35.4%

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

   6. Simplified 35.4%

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

   7. Taylor expanded in t around 0 35.4%

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

      1. mul-1-neg 35.4%

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

      2. unsub-neg 35.4%

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

   9. Simplified 35.4%

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

   10. Taylor expanded in x around inf 61.6%

       \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \end{array} \]

Alternative 5: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-144} \lor \neg \left(z \leq 2.15 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.1e-144) (not (<= z 2.15e-54)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (- 1.0 (/ y (/ x z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e-144) || !(z <= 2.15e-54)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.1d-144)) .or. (.not. (z <= 2.15d-54))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (1.0d0 - (y / (x / z)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.1e-144) || !(z <= 2.15e-54)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.1e-144) or not (z <= 2.15e-54):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.1e-144) || !(z <= 2.15e-54))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(1.0 - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.1e-144) || ~((z <= 2.15e-54)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.1e-144], N[Not[LessEqual[z, 2.15e-54]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1000000000000001e-144 or 2.15e-54 < z

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

   3. Simplified 88.5%

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

   4. Taylor expanded in z around inf 85.6%

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

   if -2.1000000000000001e-144 < z < 2.15e-54

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 65.7%

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

      1. +-commutative 65.7%

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

      2. +-commutative 65.7%

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

      3. associate-+l+ 65.7%

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

      4. +-commutative 65.7%

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

      5. mul-1-neg 65.7%

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

      6. unsub-neg 65.7%

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

      7. associate-/l* 65.8%

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

      8. +-commutative 65.8%

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

   6. Simplified 65.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-144} \lor \neg \left(z \leq 2.15 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

Alternative 6: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-266} \lor \neg \left(z \leq 4.5 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.75e-266) (not (<= z 4.5e-150)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (+ x (- 1.0 (/ y (/ x z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.75e-266) || !(z <= 4.5e-150)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.75d-266)) .or. (.not. (z <= 4.5d-150))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x + (1.0d0 - (y / (x / z)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.75e-266) || !(z <= 4.5e-150)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.75e-266) or not (z <= 4.5e-150):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.75e-266) || !(z <= 4.5e-150))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(1.0 - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.75e-266) || ~((z <= 4.5e-150)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.75e-266], N[Not[LessEqual[z, 4.5e-150]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75000000000000013e-266 or 4.5000000000000002e-150 < z

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around inf 77.7%

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

      1. associate-/l* 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in t around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. unsub-neg 86.7%

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

   9. Simplified 86.7%

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

   if -2.75000000000000013e-266 < z < 4.5000000000000002e-150

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 76.9%

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

      1. +-commutative 76.9%

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

      2. +-commutative 76.9%

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

      3. associate-+l+ 76.9%

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

      4. +-commutative 76.9%

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

      5. mul-1-neg 76.9%

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

      6. unsub-neg 76.9%

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

      7. associate-/l* 76.9%

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

      8. +-commutative 76.9%

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

   6. Simplified 76.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-266} \lor \neg \left(z \leq 4.5 \cdot 10^{-150}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

Alternative 7: 70.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -3.85 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;z \leq 10^{-150}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -3.85e-59)
     t_1
     (if (<= z -2.75e-266)
       (* y (/ z (- (* z t) x)))
       (if (<= z 1e-150) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -3.85e-59) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = y * (z / ((z * t) - x));
	} else if (z <= 1e-150) {
		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 (z <= (-3.85d-59)) then
        tmp = t_1
    else if (z <= (-2.75d-266)) then
        tmp = y * (z / ((z * t) - x))
    else if (z <= 1d-150) 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 (z <= -3.85e-59) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = y * (z / ((z * t) - x));
	} else if (z <= 1e-150) {
		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 z <= -3.85e-59:
		tmp = t_1
	elif z <= -2.75e-266:
		tmp = y * (z / ((z * t) - x))
	elif z <= 1e-150:
		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 (z <= -3.85e-59)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	elseif (z <= 1e-150)
		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 (z <= -3.85e-59)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = y * (z / ((z * t) - x));
	elseif (z <= 1e-150)
		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[z, -3.85e-59], t$95$1, If[LessEqual[z, -2.75e-266], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-150], 1.0, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.85e-59 or 1.00000000000000001e-150 < z

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around inf 85.8%

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

   if -3.85e-59 < z < -2.75000000000000013e-266

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. *-commutative 55.8%

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

      3. times-frac 55.8%

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

      4. +-commutative 55.8%

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

      5. *-commutative 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in x around 0 53.8%

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

   if -2.75000000000000013e-266 < z < 1.00000000000000001e-150

   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 26.8%

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

      1. associate-/l* 26.8%

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

   6. Simplified 26.8%

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

   7. Taylor expanded in t around 0 26.8%

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

      1. mul-1-neg 26.8%

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

      2. unsub-neg 26.8%

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

   9. Simplified 26.8%

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

   10. Taylor expanded in x around inf 66.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.85 \cdot 10^{-59}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;z \leq 10^{-150}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 8: 69.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;\frac{y}{t + x \cdot \left(t + \frac{-1}{z}\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -1.32e+47)
     t_1
     (if (<= z -2.75e-266)
       (/ y (+ t (* x (+ t (/ -1.0 z)))))
       (if (<= z 1.5e-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 (z <= -1.32e+47) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = y / (t + (x * (t + (-1.0 / z))));
	} else if (z <= 1.5e-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 (z <= (-1.32d+47)) then
        tmp = t_1
    else if (z <= (-2.75d-266)) then
        tmp = y / (t + (x * (t + ((-1.0d0) / z))))
    else if (z <= 1.5d-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 (z <= -1.32e+47) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = y / (t + (x * (t + (-1.0 / z))));
	} else if (z <= 1.5e-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 z <= -1.32e+47:
		tmp = t_1
	elif z <= -2.75e-266:
		tmp = y / (t + (x * (t + (-1.0 / z))))
	elif z <= 1.5e-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 (z <= -1.32e+47)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = Float64(y / Float64(t + Float64(x * Float64(t + Float64(-1.0 / z)))));
	elseif (z <= 1.5e-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 (z <= -1.32e+47)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = y / (t + (x * (t + (-1.0 / z))));
	elseif (z <= 1.5e-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[z, -1.32e+47], t$95$1, If[LessEqual[z, -2.75e-266], N[(y / N[(t + N[(x * N[(t + N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-151], 1.0, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.31999999999999992e47 or 1.5e-151 < z

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 88.1%

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

   if -1.31999999999999992e47 < z < -2.75000000000000013e-266

   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 65.3%

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

      1. associate-/l* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in y around inf 55.9%

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

      1. associate-/l* 57.6%

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

      2. *-commutative 57.6%

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

      3. +-commutative 57.6%

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

   9. Simplified 57.6%

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

   10. Taylor expanded in x around 0 58.8%

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

   if -2.75000000000000013e-266 < z < 1.5e-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 26.8%

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

      1. associate-/l* 26.8%

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

   6. Simplified 26.8%

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

   7. Taylor expanded in t around 0 26.8%

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

      1. mul-1-neg 26.8%

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

      2. unsub-neg 26.8%

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

   9. Simplified 26.8%

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

   10. Taylor expanded in x around inf 66.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+47}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;\frac{y}{t + x \cdot \left(t + \frac{-1}{z}\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 9: 69.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;z \leq -1.32 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;\frac{\frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-146}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= z -1.32e+47)
     t_1
     (if (<= z -2.75e-266)
       (/ (/ y (- t (/ x z))) (+ x 1.0))
       (if (<= z 1.25e-146) 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (z <= -1.32e+47) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = (y / (t - (x / z))) / (x + 1.0);
	} else if (z <= 1.25e-146) {
		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 (z <= (-1.32d+47)) then
        tmp = t_1
    else if (z <= (-2.75d-266)) then
        tmp = (y / (t - (x / z))) / (x + 1.0d0)
    else if (z <= 1.25d-146) 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 (z <= -1.32e+47) {
		tmp = t_1;
	} else if (z <= -2.75e-266) {
		tmp = (y / (t - (x / z))) / (x + 1.0);
	} else if (z <= 1.25e-146) {
		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 z <= -1.32e+47:
		tmp = t_1
	elif z <= -2.75e-266:
		tmp = (y / (t - (x / z))) / (x + 1.0)
	elif z <= 1.25e-146:
		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 (z <= -1.32e+47)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = Float64(Float64(y / Float64(t - Float64(x / z))) / Float64(x + 1.0));
	elseif (z <= 1.25e-146)
		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 (z <= -1.32e+47)
		tmp = t_1;
	elseif (z <= -2.75e-266)
		tmp = (y / (t - (x / z))) / (x + 1.0);
	elseif (z <= 1.25e-146)
		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[z, -1.32e+47], t$95$1, If[LessEqual[z, -2.75e-266], N[(N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-146], 1.0, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.31999999999999992e47 or 1.24999999999999989e-146 < z

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in z around inf 88.1%

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

   if -1.31999999999999992e47 < z < -2.75000000000000013e-266

   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 65.3%

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

      1. associate-/l* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in t around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. unsub-neg 69.7%

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

   9. Simplified 69.7%

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

   10. Taylor expanded in y around inf 60.4%

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

   if -2.75000000000000013e-266 < z < 1.24999999999999989e-146

   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 26.8%

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

      1. associate-/l* 26.8%

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

   6. Simplified 26.8%

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

   7. Taylor expanded in t around 0 26.8%

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

      1. mul-1-neg 26.8%

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

      2. unsub-neg 26.8%

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

   9. Simplified 26.8%

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

   10. Taylor expanded in x around inf 66.0%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{+47}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;\frac{\frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-146}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 10: 50.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-144} \lor \neg \left(z \leq 5.3 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4e-144) (not (<= z 5.3e-34))) (/ y (* t (+ x 1.0))) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-144) || !(z <= 5.3e-34)) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4d-144)) .or. (.not. (z <= 5.3d-34))) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4e-144) || !(z <= 5.3e-34)) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4e-144) or not (z <= 5.3e-34):
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4e-144) || !(z <= 5.3e-34))
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4e-144) || ~((z <= 5.3e-34)))
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4e-144], N[Not[LessEqual[z, 5.3e-34]], $MachinePrecision]], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999998e-144 or 5.2999999999999997e-34 < z

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in y around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

      3. times-frac 59.0%

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

      4. +-commutative 59.0%

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

      5. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in z around inf 56.8%

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

   if -3.9999999999999998e-144 < z < 5.2999999999999997e-34

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 45.8%

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

      1. associate-/l* 45.8%

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

   6. Simplified 45.8%

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

   7. Taylor expanded in t around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. unsub-neg 45.9%

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

   9. Simplified 45.9%

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

   10. Taylor expanded in x around inf 48.0%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-144} \lor \neg \left(z \leq 5.3 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 31.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-53} \lor \neg \left(z \leq 2.85 \cdot 10^{-33}\right):\\ \;\;\;\;x + x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.2e-53) (not (<= z 2.85e-33))) (+ x (* x x)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.2e-53) || !(z <= 2.85e-33)) {
		tmp = x + (x * 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 ((z <= (-8.2d-53)) .or. (.not. (z <= 2.85d-33))) then
        tmp = x + (x * 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 ((z <= -8.2e-53) || !(z <= 2.85e-33)) {
		tmp = x + (x * x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.2e-53) or not (z <= 2.85e-33):
		tmp = x + (x * x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.2e-53) || !(z <= 2.85e-33))
		tmp = Float64(x + Float64(x * x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.2e-53) || ~((z <= 2.85e-33)))
		tmp = x + (x * x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.2e-53], N[Not[LessEqual[z, 2.85e-33]], $MachinePrecision]], N[(x + N[(x * x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -8.2000000000000001e-53 or 2.85000000000000013e-33 < z

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in t around inf 34.1%

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

      1. +-commutative 34.1%

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

   6. Simplified 34.1%

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

   7. Taylor expanded in x around 0 32.4%

      \[\leadsto \color{blue}{-1 \cdot {x}^{2} + x} \]
   8. Step-by-step derivation

      1. +-commutative 32.4%

         \[\leadsto \color{blue}{x + -1 \cdot {x}^{2}} \]

      2. mul-1-neg 32.4%

         \[\leadsto x + \color{blue}{\left(-{x}^{2}\right)} \]

      3. unsub-neg 32.4%

         \[\leadsto \color{blue}{x - {x}^{2}} \]

      4. unpow2 32.4%

         \[\leadsto x - \color{blue}{x \cdot x} \]

   9. Simplified 32.4%

      \[\leadsto \color{blue}{x - x \cdot x} \]
   10. Step-by-step derivation

       1. cancel-sign-sub-inv 32.4%

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

       2. add-sqr-sqrt 13.3%

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

       3. sqrt-unprod 32.4%

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

       4. sqr-neg 32.4%

          \[\leadsto x + \sqrt{\color{blue}{x \cdot x}} \cdot x \]

       5. sqrt-prod 19.1%

          \[\leadsto x + \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot x \]

       6. add-sqr-sqrt 32.4%

          \[\leadsto x + \color{blue}{x} \cdot x \]

   11. Applied egg-rr 32.4%

       \[\leadsto \color{blue}{x + x \cdot x} \]

   if -8.2000000000000001e-53 < z < 2.85000000000000013e-33

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 50.4%

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

      1. associate-/l* 50.6%

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

   6. Simplified 50.6%

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

   7. Taylor expanded in t around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   9. Simplified 50.6%

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

   10. Taylor expanded in x around inf 42.2%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-53} \lor \neg \left(z \leq 2.85 \cdot 10^{-33}\right):\\ \;\;\;\;x + x \cdot x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 32.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-51} \lor \neg \left(z \leq 2.25 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e-51) (not (<= z 2.25e-53))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-51) || !(z <= 2.25e-53)) {
		tmp = x / (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 <= (-3.6d-51)) .or. (.not. (z <= 2.25d-53))) then
        tmp = x / (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 <= -3.6e-51) || !(z <= 2.25e-53)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.6e-51) or not (z <= 2.25e-53):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e-51) || !(z <= 2.25e-53))
		tmp = Float64(x / 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 <= -3.6e-51) || ~((z <= 2.25e-53)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.6e-51], N[Not[LessEqual[z, 2.25e-53]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e-51 or 2.24999999999999992e-53 < z

   1. Initial program 86.5%

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

      1. *-commutative 86.5%

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

   3. Simplified 86.5%

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

   4. Taylor expanded in t around inf 34.8%

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

      1. +-commutative 34.8%

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

   6. Simplified 34.8%

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

   if -3.6e-51 < z < 2.24999999999999992e-53

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 50.0%

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

      1. associate-/l* 50.1%

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

   6. Simplified 50.1%

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

   7. Taylor expanded in t around 0 50.2%

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

      1. mul-1-neg 50.2%

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

      2. unsub-neg 50.2%

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

   9. Simplified 50.2%

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

   10. Taylor expanded in x around inf 41.7%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-51} \lor \neg \left(z \leq 2.25 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 31.0% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.2e-52) x (if (<= z 1.15e-26) 1.0 x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e-52) {
		tmp = x;
	} else if (z <= 1.15e-26) {
		tmp = 1.0;
	} else {
		tmp = 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 <= (-6.2d-52)) then
        tmp = x
    else if (z <= 1.15d-26) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.2e-52) {
		tmp = x;
	} else if (z <= 1.15e-26) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.2e-52:
		tmp = x
	elif z <= 1.15e-26:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.2e-52)
		tmp = x;
	elseif (z <= 1.15e-26)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.2e-52)
		tmp = x;
	elseif (z <= 1.15e-26)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.2e-52], x, If[LessEqual[z, 1.15e-26], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999998e-52 or 1.15000000000000004e-26 < z

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in t around inf 34.1%

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

      1. +-commutative 34.1%

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

   6. Simplified 34.1%

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

   7. Taylor expanded in x around 0 32.4%

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

   if -6.1999999999999998e-52 < z < 1.15000000000000004e-26

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 50.4%

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

      1. associate-/l* 50.6%

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

   6. Simplified 50.6%

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

   7. Taylor expanded in t around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. unsub-neg 50.6%

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

   9. Simplified 50.6%

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

   10. Taylor expanded in x around inf 42.2%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 19.7% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.6%

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

   1. *-commutative 92.6%

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

3. Simplified 92.6%

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

4. Taylor expanded in y around inf 68.0%

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

   1. associate-/l* 72.2%

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

6. Simplified 72.2%

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

7. Taylor expanded in t around 0 75.2%

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

   1. mul-1-neg 75.2%

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

   2. unsub-neg 75.2%

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

9. Simplified 75.2%

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

10. Taylor expanded in x around inf 22.7%

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

11. Final simplification 22.7%

    \[\leadsto 1 \]

Developer target: 99.9% 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 2023278 
(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)))