Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A

Percentage Accurate: 99.2% → 99.2%

Time: 12.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - (x / ((y - z) * (y - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Add Preprocessing

3. Final simplification 98.6%

   \[\leadsto 1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
4. Add Preprocessing

Alternative 2: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-184} \lor \neg \left(z \leq 1.7 \cdot 10^{-103}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e-184) (not (<= z 1.7e-103)))
   (+ 1.0 (/ (/ x z) (- y t)))
   (+ 1.0 (/ (/ x t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-184) || !(z <= 1.7e-103)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / y);
	}
	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 <= (-3.2d-184)) .or. (.not. (z <= 1.7d-103))) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 + ((x / t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-184) || !(z <= 1.7e-103)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 + ((x / t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e-184) or not (z <= 1.7e-103):
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 + ((x / t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e-184) || !(z <= 1.7e-103))
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e-184) || ~((z <= 1.7e-103)))
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 + ((x / t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e-184], N[Not[LessEqual[z, 1.7e-103]], $MachinePrecision]], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2e-184 or 1.70000000000000001e-103 < z

   1. Initial program 99.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 99.0%

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

      2. neg-mul-1 99.0%

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

      3. *-commutative 99.0%

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

      4. *-commutative 99.0%

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

      5. associate-/r* 98.5%

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

      6. associate-*r/ 98.5%

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

      7. metadata-eval 98.5%

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

      8. times-frac 98.5%

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

      9. *-lft-identity 98.5%

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

      10. neg-mul-1 98.5%

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

      11. sub-neg 98.5%

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

      12. +-commutative 98.5%

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

      13. distribute-neg-out 98.5%

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

      14. remove-double-neg 98.5%

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

      15. sub-neg 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 91.6%

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

      1. associate-/r* 92.0%

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

   7. Simplified 92.0%

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

   if -3.2e-184 < z < 1.70000000000000001e-103

   1. Initial program 97.5%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.4%

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

      1. associate-*r/ 83.4%

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

      2. neg-mul-1 83.4%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in y around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-/r* 74.9%

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

      3. distribute-neg-frac 74.9%

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

   8. Simplified 74.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-184} \lor \neg \left(z \leq 1.7 \cdot 10^{-103}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-78} \lor \neg \left(z \leq 4.8 \cdot 10^{-102}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e-78) (not (<= z 4.8e-102)))
   (+ 1.0 (/ (/ x z) (- y t)))
   (- 1.0 (/ x (* y (- y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-78) || !(z <= 4.8e-102)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - (x / (y * (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 ((z <= (-1.7d-78)) .or. (.not. (z <= 4.8d-102))) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 - (x / (y * (y - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e-78) || !(z <= 4.8e-102)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - (x / (y * (y - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e-78) or not (z <= 4.8e-102):
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 - (x / (y * (y - t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e-78) || !(z <= 4.8e-102))
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e-78) || ~((z <= 4.8e-102)))
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 - (x / (y * (y - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e-78], N[Not[LessEqual[z, 4.8e-102]], $MachinePrecision]], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(y * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000006e-78 or 4.8e-102 < z

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 96.6%

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

      1. associate-/r* 96.6%

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

   7. Simplified 96.6%

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

   if -1.70000000000000006e-78 < z < 4.8e-102

   1. Initial program 95.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.6%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-78} \lor \neg \left(z \leq 4.8 \cdot 10^{-102}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-78} \lor \neg \left(z \leq 6.4 \cdot 10^{-103}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e-78) (not (<= z 6.4e-103)))
   (+ 1.0 (/ (/ x z) (- y t)))
   (- 1.0 (/ (/ x y) (- y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e-78) || !(z <= 6.4e-103)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / y) / (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 ((z <= (-2.2d-78)) .or. (.not. (z <= 6.4d-103))) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else
        tmp = 1.0d0 - ((x / y) / (y - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e-78) || !(z <= 6.4e-103)) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else {
		tmp = 1.0 - ((x / y) / (y - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e-78) or not (z <= 6.4e-103):
		tmp = 1.0 + ((x / z) / (y - t))
	else:
		tmp = 1.0 - ((x / y) / (y - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e-78) || !(z <= 6.4e-103))
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	else
		tmp = Float64(1.0 - Float64(Float64(x / y) / Float64(y - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e-78) || ~((z <= 6.4e-103)))
		tmp = 1.0 + ((x / z) / (y - t));
	else
		tmp = 1.0 - ((x / y) / (y - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e-78], N[Not[LessEqual[z, 6.4e-103]], $MachinePrecision]], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(x / y), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1999999999999999e-78 or 6.39999999999999953e-103 < z

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 96.6%

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

      1. associate-/r* 96.6%

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

   7. Simplified 96.6%

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

   if -2.1999999999999999e-78 < z < 6.39999999999999953e-103

   1. Initial program 95.7%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. clear-num 95.7%

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

      2. inv-pow 95.7%

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

      3. *-commutative 95.7%

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

      4. associate-/l* 88.5%

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

   4. Applied egg-rr 88.5%

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

      1. unpow-1 88.5%

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

      2. associate-/r/ 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 81.6%

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

      1. associate-/r* 77.8%

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

   9. Simplified 77.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-78} \lor \neg \left(z \leq 6.4 \cdot 10^{-103}\right):\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{x}{y}}{y - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-206}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-143}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.5e-206)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 1.3e-143)
     (- 1.0 (/ x (* y (- y z))))
     (+ 1.0 (/ x (* (- y z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-206) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.3e-143) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + (x / ((y - z) * 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 (t <= (-2.5d-206)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 1.3d-143) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else
        tmp = 1.0d0 + (x / ((y - z) * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.5e-206) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 1.3e-143) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + (x / ((y - z) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.5e-206:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 1.3e-143:
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 + (x / ((y - z) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.5e-206)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 1.3e-143)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	else
		tmp = Float64(1.0 + Float64(x / Float64(Float64(y - z) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.5e-206)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 1.3e-143)
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 + (x / ((y - z) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.5e-206], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-143], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e-206

   1. Initial program 97.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 97.9%

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

      2. neg-mul-1 97.9%

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

      3. *-commutative 97.9%

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

      4. *-commutative 97.9%

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

      5. associate-/r* 95.2%

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

      6. associate-*r/ 95.2%

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

      7. metadata-eval 95.2%

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

      8. times-frac 95.2%

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

      9. *-lft-identity 95.2%

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

      10. neg-mul-1 95.2%

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

      11. sub-neg 95.2%

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

      12. +-commutative 95.2%

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

      13. distribute-neg-out 95.2%

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

      14. remove-double-neg 95.2%

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

      15. sub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 74.7%

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

      1. associate-/r* 76.5%

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

   7. Simplified 76.5%

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

   if -2.5e-206 < t < 1.29999999999999994e-143

   1. Initial program 97.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.6%

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

   if 1.29999999999999994e-143 < t

   1. Initial program 99.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 95.1%

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

      1. associate-*r/ 95.1%

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

      2. neg-mul-1 95.1%

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

   5. Simplified 95.1%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-206}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-143}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-205}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e-205)
   (+ 1.0 (/ (/ x z) (- y t)))
   (if (<= t 2.55e-61)
     (- 1.0 (/ x (* y (- y z))))
     (+ 1.0 (/ (/ x t) (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e-205) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 2.55e-61) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.7d-205)) then
        tmp = 1.0d0 + ((x / z) / (y - t))
    else if (t <= 2.55d-61) then
        tmp = 1.0d0 - (x / (y * (y - z)))
    else
        tmp = 1.0d0 + ((x / t) / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e-205) {
		tmp = 1.0 + ((x / z) / (y - t));
	} else if (t <= 2.55e-61) {
		tmp = 1.0 - (x / (y * (y - z)));
	} else {
		tmp = 1.0 + ((x / t) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.7e-205:
		tmp = 1.0 + ((x / z) / (y - t))
	elif t <= 2.55e-61:
		tmp = 1.0 - (x / (y * (y - z)))
	else:
		tmp = 1.0 + ((x / t) / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.7e-205)
		tmp = Float64(1.0 + Float64(Float64(x / z) / Float64(y - t)));
	elseif (t <= 2.55e-61)
		tmp = Float64(1.0 - Float64(x / Float64(y * Float64(y - z))));
	else
		tmp = Float64(1.0 + Float64(Float64(x / t) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.7e-205)
		tmp = 1.0 + ((x / z) / (y - t));
	elseif (t <= 2.55e-61)
		tmp = 1.0 - (x / (y * (y - z)));
	else
		tmp = 1.0 + ((x / t) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.7e-205], N[(1.0 + N[(N[(x / z), $MachinePrecision] / N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e-61], N[(1.0 - N[(x / N[(y * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000001e-205

   1. Initial program 97.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 97.9%

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

      2. neg-mul-1 97.9%

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

      3. *-commutative 97.9%

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

      4. *-commutative 97.9%

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

      5. associate-/r* 95.2%

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

      6. associate-*r/ 95.2%

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

      7. metadata-eval 95.2%

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

      8. times-frac 95.2%

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

      9. *-lft-identity 95.2%

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

      10. neg-mul-1 95.2%

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

      11. sub-neg 95.2%

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

      12. +-commutative 95.2%

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

      13. distribute-neg-out 95.2%

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

      14. remove-double-neg 95.2%

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

      15. sub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around inf 74.7%

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

      1. associate-/r* 76.5%

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

   7. Simplified 76.5%

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

   if -3.7000000000000001e-205 < t < 2.54999999999999984e-61

   1. Initial program 98.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 94.5%

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

   if 2.54999999999999984e-61 < t

   1. Initial program 99.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 96.7%

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

      1. associate-*r/ 96.7%

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

      2. neg-mul-1 96.7%

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

   5. Simplified 96.7%

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

   6. Taylor expanded in x around 0 96.7%

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

      1. mul-1-neg 96.7%

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

      2. associate-/r* 96.8%

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

      3. distribute-neg-frac 96.8%

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

   8. Simplified 96.8%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-205}:\\ \;\;\;\;1 + \frac{\frac{x}{z}}{y - t}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-61}:\\ \;\;\;\;1 - \frac{x}{y \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-129}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-221}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.8e-129) 1.0 (if (<= t 4.1e-221) (+ 1.0 (/ x (* y z))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.8e-129) {
		tmp = 1.0;
	} else if (t <= 4.1e-221) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-9.8d-129)) then
        tmp = 1.0d0
    else if (t <= 4.1d-221) then
        tmp = 1.0d0 + (x / (y * z))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.8e-129) {
		tmp = 1.0;
	} else if (t <= 4.1e-221) {
		tmp = 1.0 + (x / (y * z));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.8e-129:
		tmp = 1.0
	elif t <= 4.1e-221:
		tmp = 1.0 + (x / (y * z))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.8e-129)
		tmp = 1.0;
	elseif (t <= 4.1e-221)
		tmp = Float64(1.0 + Float64(x / Float64(y * z)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.8e-129)
		tmp = 1.0;
	elseif (t <= 4.1e-221)
		tmp = 1.0 + (x / (y * z));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.8e-129], 1.0, If[LessEqual[t, 4.1e-221], N[(1.0 + N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -9.80000000000000004e-129 or 4.09999999999999981e-221 < t

   1. Initial program 99.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 68.8%

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

   4. Taylor expanded in x around 0 76.9%

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

   if -9.80000000000000004e-129 < t < 4.09999999999999981e-221

   1. Initial program 95.9%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Step-by-step derivation

      1. sub-neg 95.9%

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

      2. neg-mul-1 95.9%

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

      3. *-commutative 95.9%

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

      4. *-commutative 95.9%

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

      5. associate-/r* 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. times-frac 99.9%

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

      9. *-lft-identity 99.9%

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

      10. neg-mul-1 99.9%

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

      11. sub-neg 99.9%

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

      12. +-commutative 99.9%

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

      13. distribute-neg-out 99.9%

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

      14. remove-double-neg 99.9%

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

      15. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 82.0%

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

      1. associate-/r* 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

   10. Simplified 77.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{-129}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-221}:\\ \;\;\;\;1 + \frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-170}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-109}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.35e-170) 1.0 (if (<= z 3.05e-109) (+ 1.0 (/ x (* y t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.35e-170) {
		tmp = 1.0;
	} else if (z <= 3.05e-109) {
		tmp = 1.0 + (x / (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 (z <= (-1.35d-170)) then
        tmp = 1.0d0
    else if (z <= 3.05d-109) then
        tmp = 1.0d0 + (x / (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 (z <= -1.35e-170) {
		tmp = 1.0;
	} else if (z <= 3.05e-109) {
		tmp = 1.0 + (x / (y * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.35e-170:
		tmp = 1.0
	elif z <= 3.05e-109:
		tmp = 1.0 + (x / (y * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.35e-170)
		tmp = 1.0;
	elseif (z <= 3.05e-109)
		tmp = Float64(1.0 + Float64(x / Float64(y * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.35e-170)
		tmp = 1.0;
	elseif (z <= 3.05e-109)
		tmp = 1.0 + (x / (y * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.35e-170], 1.0, If[LessEqual[z, 3.05e-109], N[(1.0 + N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e-170 or 3.0499999999999998e-109 < z

   1. Initial program 99.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 62.4%

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

   4. Taylor expanded in x around 0 79.5%

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

   if -1.3499999999999999e-170 < z < 3.0499999999999998e-109

   1. Initial program 96.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.6%

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

   4. Taylor expanded in t around inf 71.8%

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

      1. +-commutative 71.8%

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

   6. Simplified 71.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-170}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-109}:\\ \;\;\;\;1 + \frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.76e-99) 1.0 (if (<= y 3.9e-56) (- 1.0 (/ x (* z t))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.76e-99) {
		tmp = 1.0;
	} else if (y <= 3.9e-56) {
		tmp = 1.0 - (x / (z * 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 (y <= (-1.76d-99)) then
        tmp = 1.0d0
    else if (y <= 3.9d-56) then
        tmp = 1.0d0 - (x / (z * 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 (y <= -1.76e-99) {
		tmp = 1.0;
	} else if (y <= 3.9e-56) {
		tmp = 1.0 - (x / (z * t));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.76e-99:
		tmp = 1.0
	elif y <= 3.9e-56:
		tmp = 1.0 - (x / (z * t))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.76e-99)
		tmp = 1.0;
	elseif (y <= 3.9e-56)
		tmp = Float64(1.0 - Float64(x / Float64(z * t)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.76e-99)
		tmp = 1.0;
	elseif (y <= 3.9e-56)
		tmp = 1.0 - (x / (z * t));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.76e-99], 1.0, If[LessEqual[y, 3.9e-56], N[(1.0 - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75999999999999991e-99 or 3.9e-56 < y

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.8%

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

   4. Taylor expanded in x around 0 89.5%

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

   if -1.75999999999999991e-99 < y < 3.9e-56

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.76 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-56}:\\ \;\;\;\;1 - \frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-57}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.5e-99) 1.0 (if (<= y 4.7e-57) (- 1.0 (/ (/ x t) z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.5e-99) {
		tmp = 1.0;
	} else if (y <= 4.7e-57) {
		tmp = 1.0 - ((x / t) / z);
	} 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 (y <= (-4.5d-99)) then
        tmp = 1.0d0
    else if (y <= 4.7d-57) then
        tmp = 1.0d0 - ((x / t) / z)
    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 (y <= -4.5e-99) {
		tmp = 1.0;
	} else if (y <= 4.7e-57) {
		tmp = 1.0 - ((x / t) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.5e-99:
		tmp = 1.0
	elif y <= 4.7e-57:
		tmp = 1.0 - ((x / t) / z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.5e-99)
		tmp = 1.0;
	elseif (y <= 4.7e-57)
		tmp = Float64(1.0 - Float64(Float64(x / t) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.5e-99)
		tmp = 1.0;
	elseif (y <= 4.7e-57)
		tmp = 1.0 - ((x / t) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.5e-99], 1.0, If[LessEqual[y, 4.7e-57], N[(1.0 - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000003e-99 or 4.6999999999999998e-57 < y

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.8%

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

   4. Taylor expanded in x around 0 89.5%

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

   if -4.5000000000000003e-99 < y < 4.6999999999999998e-57

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

   5. Simplified 83.7%

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

   6. Taylor expanded in y around 0 74.3%

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

      1. associate-/r* 75.8%

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

   8. Simplified 75.8%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-57}:\\ \;\;\;\;1 - \frac{\frac{x}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((x / (z - y)) / (y - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.6%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Step-by-step derivation

   1. sub-neg 98.6%

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

   2. neg-mul-1 98.6%

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

   3. *-commutative 98.6%

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

   4. *-commutative 98.6%

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

   5. associate-/r* 96.3%

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

   6. associate-*r/ 96.3%

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

   7. metadata-eval 96.3%

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

   8. times-frac 96.3%

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

   9. *-lft-identity 96.3%

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

   10. neg-mul-1 96.3%

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

   11. sub-neg 96.3%

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

   12. +-commutative 96.3%

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

   13. distribute-neg-out 96.3%

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

   14. remove-double-neg 96.3%

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

   15. sub-neg 96.3%

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

3. Simplified 96.3%

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

5. Final simplification 96.3%

   \[\leadsto 1 + \frac{\frac{x}{z - y}}{y - t} \]
6. Add Preprocessing

Alternative 12: 76.2% accurate, 11.0× 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 98.6%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 68.5%

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

4. Taylor expanded in x around 0 74.4%

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

5. Final simplification 74.4%

   \[\leadsto 1 \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))