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

Percentage Accurate: 88.7% → 97.8%

Time: 16.0s

Alternatives: 11

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-36} \lor \neg \left(z \leq 6.2 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.9e-36) (not (<= z 6.2e-53)))
   (/ (+ 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 <= -2.9e-36) || !(z <= 6.2e-53)) {
		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 <= (-2.9d-36)) .or. (.not. (z <= 6.2d-53))) 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 <= -2.9e-36) || !(z <= 6.2e-53)) {
		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 <= -2.9e-36) or not (z <= 6.2e-53):
		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 <= -2.9e-36) || !(z <= 6.2e-53))
		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 <= -2.9e-36) || ~((z <= 6.2e-53)))
		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, -2.9e-36], N[Not[LessEqual[z, 6.2e-53]], $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 < -2.90000000000000013e-36 or 6.20000000000000031e-53 < z

   1. Initial program 78.7%

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

      1. *-commutative 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in y around inf 78.7%

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

      1. associate-/l* 93.0%

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

      2. *-commutative 93.0%

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

      3. *-commutative 93.0%

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

      4. fma-neg 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in t around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. unsub-neg 99.3%

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

   10. Simplified 99.3%

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

   if -2.90000000000000013e-36 < z < 6.20000000000000031e-53

   1. Initial program 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-36} \lor \neg \left(z \leq 6.2 \cdot 10^{-53}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-32}:\\ \;\;\;\;1 - z \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.6e-17)
   (/ x (+ x 1.0))
   (if (<= x 4.5e-90)
     (/ y t)
     (if (<= x 2e-32)
       (- 1.0 (* z (/ y x)))
       (if (<= x 5.2e-20) (/ y t) (/ 1.0 (+ 1.0 (/ 1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.6e-17) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.5e-90) {
		tmp = y / t;
	} else if (x <= 2e-32) {
		tmp = 1.0 - (z * (y / x));
	} else if (x <= 5.2e-20) {
		tmp = y / t;
	} else {
		tmp = 1.0 / (1.0 + (1.0 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.6d-17)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 4.5d-90) then
        tmp = y / t
    else if (x <= 2d-32) then
        tmp = 1.0d0 - (z * (y / x))
    else if (x <= 5.2d-20) then
        tmp = y / t
    else
        tmp = 1.0d0 / (1.0d0 + (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.6e-17) {
		tmp = x / (x + 1.0);
	} else if (x <= 4.5e-90) {
		tmp = y / t;
	} else if (x <= 2e-32) {
		tmp = 1.0 - (z * (y / x));
	} else if (x <= 5.2e-20) {
		tmp = y / t;
	} else {
		tmp = 1.0 / (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.6e-17:
		tmp = x / (x + 1.0)
	elif x <= 4.5e-90:
		tmp = y / t
	elif x <= 2e-32:
		tmp = 1.0 - (z * (y / x))
	elif x <= 5.2e-20:
		tmp = y / t
	else:
		tmp = 1.0 / (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.6e-17)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 4.5e-90)
		tmp = Float64(y / t);
	elseif (x <= 2e-32)
		tmp = Float64(1.0 - Float64(z * Float64(y / x)));
	elseif (x <= 5.2e-20)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 / Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.6e-17)
		tmp = x / (x + 1.0);
	elseif (x <= 4.5e-90)
		tmp = y / t;
	elseif (x <= 2e-32)
		tmp = 1.0 - (z * (y / x));
	elseif (x <= 5.2e-20)
		tmp = y / t;
	else
		tmp = 1.0 / (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.6e-17], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e-90], N[(y / t), $MachinePrecision], If[LessEqual[x, 2e-32], N[(1.0 - N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-20], N[(y / t), $MachinePrecision], N[(1.0 / N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.60000000000000001e-17

   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. Add Preprocessing

   5. Taylor expanded in t around inf 85.5%

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

      1. +-commutative 85.5%

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

   7. Simplified 85.5%

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

   if -6.60000000000000001e-17 < x < 4.50000000000000009e-90 or 2.00000000000000011e-32 < x < 5.1999999999999999e-20

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around inf 53.0%

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

   6. Taylor expanded in x around 0 41.1%

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

      1. times-frac 52.0%

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

      2. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{\color{blue}{{z}^{1}}}{z} \]

      3. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{{z}^{1}}{\color{blue}{{z}^{1}}} \]

      4. pow-div 52.0%

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

      5. metadata-eval 52.0%

         \[\leadsto \frac{y}{t} \cdot {z}^{\color{blue}{0}} \]

      6. metadata-eval 52.0%

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

   8. Applied egg-rr 52.0%

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

   if 4.50000000000000009e-90 < x < 2.00000000000000011e-32

   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. Add Preprocessing

   5. Taylor expanded in z around 0 71.8%

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

   6. Taylor expanded in y around inf 68.9%

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

      1. associate-*r/ 68.9%

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

      2. mul-1-neg 68.9%

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

      3. +-commutative 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in x around 0 68.9%

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

       1. associate-*r/ 68.9%

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

       2. neg-mul-1 68.9%

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

   11. Simplified 68.9%

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

   if 5.1999999999999999e-20 < x

   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. Add Preprocessing

   5. Taylor expanded in t around inf 85.6%

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

      1. +-commutative 85.6%

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

   7. Simplified 85.6%

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

      1. clear-num 85.6%

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

      2. +-commutative 85.6%

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

      3. inv-pow 85.6%

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

      4. +-commutative 85.6%

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

   9. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{{\left(\frac{x + 1}{x}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 85.6%

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

   11. Simplified 85.6%

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

   12. Taylor expanded in x around 0 85.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-32}:\\ \;\;\;\;1 - z \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-37}:\\ \;\;\;\;1 + z \cdot \frac{t - y}{x}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.14e-14)
   (/ x (+ x 1.0))
   (if (<= x 1.15e-88)
     (/ y t)
     (if (<= x 1.35e-37)
       (+ 1.0 (* z (/ (- t y) x)))
       (if (<= x 3.4e-20) (/ y t) (/ 1.0 (+ 1.0 (/ 1.0 x))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.14e-14) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.15e-88) {
		tmp = y / t;
	} else if (x <= 1.35e-37) {
		tmp = 1.0 + (z * ((t - y) / x));
	} else if (x <= 3.4e-20) {
		tmp = y / t;
	} else {
		tmp = 1.0 / (1.0 + (1.0 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.14d-14)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.15d-88) then
        tmp = y / t
    else if (x <= 1.35d-37) then
        tmp = 1.0d0 + (z * ((t - y) / x))
    else if (x <= 3.4d-20) then
        tmp = y / t
    else
        tmp = 1.0d0 / (1.0d0 + (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.14e-14) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.15e-88) {
		tmp = y / t;
	} else if (x <= 1.35e-37) {
		tmp = 1.0 + (z * ((t - y) / x));
	} else if (x <= 3.4e-20) {
		tmp = y / t;
	} else {
		tmp = 1.0 / (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.14e-14:
		tmp = x / (x + 1.0)
	elif x <= 1.15e-88:
		tmp = y / t
	elif x <= 1.35e-37:
		tmp = 1.0 + (z * ((t - y) / x))
	elif x <= 3.4e-20:
		tmp = y / t
	else:
		tmp = 1.0 / (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.14e-14)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.15e-88)
		tmp = Float64(y / t);
	elseif (x <= 1.35e-37)
		tmp = Float64(1.0 + Float64(z * Float64(Float64(t - y) / x)));
	elseif (x <= 3.4e-20)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 / Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.14e-14)
		tmp = x / (x + 1.0);
	elseif (x <= 1.15e-88)
		tmp = y / t;
	elseif (x <= 1.35e-37)
		tmp = 1.0 + (z * ((t - y) / x));
	elseif (x <= 3.4e-20)
		tmp = y / t;
	else
		tmp = 1.0 / (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.14e-14], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-88], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.35e-37], N[(1.0 + N[(z * N[(N[(t - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.4e-20], N[(y / t), $MachinePrecision], N[(1.0 / N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.1400000000000001e-14

   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. Add Preprocessing

   5. Taylor expanded in t around inf 85.5%

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

      1. +-commutative 85.5%

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

   7. Simplified 85.5%

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

   if -1.1400000000000001e-14 < x < 1.14999999999999993e-88 or 1.35000000000000008e-37 < x < 3.3999999999999997e-20

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in y around inf 53.0%

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

   6. Taylor expanded in x around 0 41.1%

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

      1. times-frac 52.0%

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

      2. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{\color{blue}{{z}^{1}}}{z} \]

      3. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{{z}^{1}}{\color{blue}{{z}^{1}}} \]

      4. pow-div 52.0%

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

      5. metadata-eval 52.0%

         \[\leadsto \frac{y}{t} \cdot {z}^{\color{blue}{0}} \]

      6. metadata-eval 52.0%

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

   8. Applied egg-rr 52.0%

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

   if 1.14999999999999993e-88 < x < 1.35000000000000008e-37

   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. Add Preprocessing

   5. Taylor expanded in z around 0 71.8%

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

   6. Taylor expanded in x around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. sub-neg 71.8%

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

   8. Simplified 71.8%

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

   if 3.3999999999999997e-20 < x

   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. Add Preprocessing

   5. Taylor expanded in t around inf 85.6%

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

      1. +-commutative 85.6%

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

   7. Simplified 85.6%

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

      1. clear-num 85.6%

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

      2. +-commutative 85.6%

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

      3. inv-pow 85.6%

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

      4. +-commutative 85.6%

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

   9. Applied egg-rr 85.6%

      \[\leadsto \color{blue}{{\left(\frac{x + 1}{x}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 85.6%

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

   11. Simplified 85.6%

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

   12. Taylor expanded in x around 0 85.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.14 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-37}:\\ \;\;\;\;1 + z \cdot \frac{t - y}{x}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-153} \lor \neg \left(z \leq 4.4 \cdot 10^{-217}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot \left(t - y\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e-153) (not (<= z 4.4e-217)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (+ 1.0 (/ (* z (- t y)) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-153) || !(z <= 4.4e-217)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = 1.0 + ((z * (t - y)) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.8d-153)) .or. (.not. (z <= 4.4d-217))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = 1.0d0 + ((z * (t - y)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e-153) || !(z <= 4.4e-217)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = 1.0 + ((z * (t - y)) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e-153) or not (z <= 4.4e-217):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = 1.0 + ((z * (t - y)) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e-153) || !(z <= 4.4e-217))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(Float64(z * Float64(t - y)) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e-153) || ~((z <= 4.4e-217)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = 1.0 + ((z * (t - y)) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e-153], N[Not[LessEqual[z, 4.4e-217]], $MachinePrecision]], N[(N[(x + N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(z * N[(t - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e-153 or 4.39999999999999964e-217 < z

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

   3. Simplified 84.4%

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

   5. Taylor expanded in y around inf 79.5%

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

      1. associate-/l* 90.0%

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

      2. *-commutative 90.0%

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

      3. *-commutative 90.0%

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

      4. fma-neg 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in t around 0 94.7%

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

      1. mul-1-neg 94.7%

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

      2. unsub-neg 94.7%

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

   10. Simplified 94.7%

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

   if -1.7999999999999999e-153 < z < 4.39999999999999964e-217

   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. Add Preprocessing

   5. Taylor expanded in z around 0 83.3%

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

   6. Taylor expanded in x around 0 87.4%

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

      1. associate-/l* 83.3%

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

      2. mul-1-neg 83.3%

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

      3. sub-neg 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in z around 0 87.4%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-153} \lor \neg \left(z \leq 4.4 \cdot 10^{-217}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{z \cdot \left(t - y\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-83} \lor \neg \left(z \leq 9.5 \cdot 10^{-220}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-83) (not (<= z 9.5e-220)))
   (/ (+ x (/ y (- t (/ x z)))) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-83) || !(z <= 9.5e-220)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (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 <= (-7.2d-83)) .or. (.not. (z <= 9.5d-220))) then
        tmp = (x + (y / (t - (x / z)))) / (x + 1.0d0)
    else
        tmp = (x - (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 <= -7.2e-83) || !(z <= 9.5e-220)) {
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-83) or not (z <= 9.5e-220):
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-83) || !(z <= 9.5e-220))
		tmp = Float64(Float64(x + Float64(y / Float64(t - Float64(x / z)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(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 <= -7.2e-83) || ~((z <= 9.5e-220)))
		tmp = (x + (y / (t - (x / z)))) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-83], N[Not[LessEqual[z, 9.5e-220]], $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[(x / 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 < -7.20000000000000025e-83 or 9.50000000000000062e-220 < z

   1. Initial program 83.4%

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

      1. *-commutative 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in y around inf 79.9%

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

      1. associate-/l* 91.0%

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

      2. *-commutative 91.0%

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

      3. *-commutative 91.0%

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

      4. fma-neg 91.0%

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

   7. Simplified 91.0%

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

   8. Taylor expanded in t around 0 96.0%

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

      1. mul-1-neg 96.0%

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

      2. unsub-neg 96.0%

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

   10. Simplified 96.0%

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

   if -7.20000000000000025e-83 < z < 9.50000000000000062e-220

   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. Add Preprocessing

   5. Taylor expanded in y around 0 89.8%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-83} \lor \neg \left(z \leq 9.5 \cdot 10^{-220}\right):\\ \;\;\;\;\frac{x + \frac{y}{t - \frac{x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 300000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.1e+35) 1.0 (if (<= x 300000.0) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.1e+35) {
		tmp = 1.0;
	} else if (x <= 300000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-5.1d+35)) then
        tmp = 1.0d0
    else if (x <= 300000.0d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.1e+35) {
		tmp = 1.0;
	} else if (x <= 300000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.1e+35:
		tmp = 1.0
	elif x <= 300000.0:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.1e+35)
		tmp = 1.0;
	elseif (x <= 300000.0)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.1e+35)
		tmp = 1.0;
	elseif (x <= 300000.0)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.1e+35], 1.0, If[LessEqual[x, 300000.0], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.10000000000000017e35 or 3e5 < x

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in y around inf 87.7%

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

      1. associate-/l* 97.5%

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

      2. *-commutative 97.5%

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

      3. *-commutative 97.5%

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

      4. fma-neg 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around inf 91.6%

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

   if -5.10000000000000017e35 < x < 3e5

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in z around inf 70.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 300000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 270000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.8e+81)
   (/ (- x (/ y (/ x z))) (+ x 1.0))
   (if (<= x 270000.0) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e+81) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 270000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.8d+81)) then
        tmp = (x - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 270000.0d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e+81) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 270000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.8e+81:
		tmp = (x - (y / (x / z))) / (x + 1.0)
	elif x <= 270000.0:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.8e+81)
		tmp = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 270000.0)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.8e+81)
		tmp = (x - (y / (x / z))) / (x + 1.0);
	elseif (x <= 270000.0)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.8e+81], N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 270000.0], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -2.79999999999999995e81

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in y around inf 91.0%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 91.0%

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

      1. mul-1-neg 91.0%

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

      2. unsub-neg 91.0%

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

      3. associate-/l* 97.8%

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

      4. +-commutative 97.8%

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

   10. Simplified 97.8%

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

   if -2.79999999999999995e81 < x < 2.7e5

   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. Add Preprocessing

   5. Taylor expanded in z around inf 71.2%

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

   if 2.7e5 < x

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in y around inf 83.9%

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

      1. associate-/l* 95.6%

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

      2. *-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. fma-neg 95.6%

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

   7. Simplified 95.6%

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

   8. Taylor expanded in x around inf 89.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 270000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.3e-15)
   (/ x (+ x 1.0))
   (if (<= x 8.8e-82) (/ y t) (/ 1.0 (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.3e-15) {
		tmp = x / (x + 1.0);
	} else if (x <= 8.8e-82) {
		tmp = y / t;
	} else {
		tmp = 1.0 / (1.0 + (1.0 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.3d-15)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 8.8d-82) then
        tmp = y / t
    else
        tmp = 1.0d0 / (1.0d0 + (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.3e-15) {
		tmp = x / (x + 1.0);
	} else if (x <= 8.8e-82) {
		tmp = y / t;
	} else {
		tmp = 1.0 / (1.0 + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.3e-15:
		tmp = x / (x + 1.0)
	elif x <= 8.8e-82:
		tmp = y / t
	else:
		tmp = 1.0 / (1.0 + (1.0 / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.3e-15)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 8.8e-82)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 / Float64(1.0 + Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.3e-15)
		tmp = x / (x + 1.0);
	elseif (x <= 8.8e-82)
		tmp = y / t;
	else
		tmp = 1.0 / (1.0 + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.3e-15], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e-82], N[(y / t), $MachinePrecision], N[(1.0 / N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.29999999999999982e-15

   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. Add Preprocessing

   5. Taylor expanded in t around inf 85.5%

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

      1. +-commutative 85.5%

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

   7. Simplified 85.5%

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

   if -6.29999999999999982e-15 < x < 8.79999999999999943e-82

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around inf 53.0%

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

   6. Taylor expanded in x around 0 41.0%

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

      1. times-frac 52.0%

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

      2. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{\color{blue}{{z}^{1}}}{z} \]

      3. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{{z}^{1}}{\color{blue}{{z}^{1}}} \]

      4. pow-div 52.0%

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

      5. metadata-eval 52.0%

         \[\leadsto \frac{y}{t} \cdot {z}^{\color{blue}{0}} \]

      6. metadata-eval 52.0%

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

   8. Applied egg-rr 52.0%

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

   if 8.79999999999999943e-82 < x

   1. Initial program 85.9%

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

      1. *-commutative 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in t around inf 78.2%

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

      1. +-commutative 78.2%

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

   7. Simplified 78.2%

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

      1. clear-num 78.2%

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

      2. +-commutative 78.2%

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

      3. inv-pow 78.2%

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

      4. +-commutative 78.2%

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

   9. Applied egg-rr 78.2%

      \[\leadsto \color{blue}{{\left(\frac{x + 1}{x}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 78.2%

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

   11. Simplified 78.2%

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

   12. Taylor expanded in x around 0 78.3%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + \frac{1}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-17} \lor \neg \left(x \leq 2.55 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e-17) (not (<= x 2.55e-82))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-17) || !(x <= 2.55e-82)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.2d-17)) .or. (.not. (x <= 2.55d-82))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-17) || !(x <= 2.55e-82)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e-17) or not (x <= 2.55e-82):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e-17) || !(x <= 2.55e-82))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e-17) || ~((x <= 2.55e-82)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e-17], N[Not[LessEqual[x, 2.55e-82]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.1999999999999999e-17 or 2.54999999999999996e-82 < x

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around inf 81.5%

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

      1. +-commutative 81.5%

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

   7. Simplified 81.5%

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

   if -7.1999999999999999e-17 < x < 2.54999999999999996e-82

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around inf 53.0%

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

   6. Taylor expanded in x around 0 41.0%

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

      1. times-frac 52.0%

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

      2. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{\color{blue}{{z}^{1}}}{z} \]

      3. pow1 52.0%

         \[\leadsto \frac{y}{t} \cdot \frac{{z}^{1}}{\color{blue}{{z}^{1}}} \]

      4. pow-div 52.0%

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

      5. metadata-eval 52.0%

         \[\leadsto \frac{y}{t} \cdot {z}^{\color{blue}{0}} \]

      6. metadata-eval 52.0%

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

   8. Applied egg-rr 52.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-17} \lor \neg \left(x \leq 2.55 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.18:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.65e-22) 1.0 (if (<= x 0.18) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e-22) {
		tmp = 1.0;
	} else if (x <= 0.18) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.65d-22)) then
        tmp = 1.0d0
    else if (x <= 0.18d0) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e-22) {
		tmp = 1.0;
	} else if (x <= 0.18) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.65e-22:
		tmp = 1.0
	elif x <= 0.18:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.65e-22)
		tmp = 1.0;
	elseif (x <= 0.18)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.65e-22)
		tmp = 1.0;
	elseif (x <= 0.18)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.65e-22], 1.0, If[LessEqual[x, 0.18], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.65e-22 or 0.17999999999999999 < x

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in y around inf 83.5%

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

      1. associate-/l* 93.3%

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

      2. *-commutative 93.3%

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

      3. *-commutative 93.3%

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

      4. fma-neg 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in x around inf 85.9%

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

   if -1.65e-22 < x < 0.17999999999999999

   1. Initial program 87.8%

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

      1. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in y around inf 52.5%

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

   6. Taylor expanded in x around 0 38.6%

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

      1. times-frac 48.0%

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

      2. pow1 48.0%

         \[\leadsto \frac{y}{t} \cdot \frac{\color{blue}{{z}^{1}}}{z} \]

      3. pow1 48.0%

         \[\leadsto \frac{y}{t} \cdot \frac{{z}^{1}}{\color{blue}{{z}^{1}}} \]

      4. pow-div 48.0%

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

      5. metadata-eval 48.0%

         \[\leadsto \frac{y}{t} \cdot {z}^{\color{blue}{0}} \]

      6. metadata-eval 48.0%

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

   8. Applied egg-rr 48.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.18:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 87.2%

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

   1. *-commutative 87.2%

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

3. Simplified 87.2%

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

5. Taylor expanded in y around inf 77.7%

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

   1. associate-/l* 86.2%

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

   2. *-commutative 86.2%

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

   3. *-commutative 86.2%

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

   4. fma-neg 86.2%

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

7. Simplified 86.2%

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

8. Taylor expanded in x around inf 53.5%

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

9. Final simplification 53.5%

   \[\leadsto 1 \]
10. Add Preprocessing

Developer target: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024011 
(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)))