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

Percentage Accurate: 99.1% → 99.1%

Time: 7.1s

Alternatives: 10

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: 99.1% 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: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 89.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{x}{\left(t - y\right) \cdot z}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ x (* (- t y) z))))
        (t_2 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_2 -100.0) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((t - y) * z));
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -100.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 - (x / ((t - y) * z))
    t_2 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_2 <= (-100.0d0)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - (x / ((t - y) * z));
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -100.0) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - (x / ((t - y) * z))
	t_2 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_2 <= -100.0:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_2 <= -100.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - (x / ((t - y) * z));
	t_2 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_2 <= -100.0)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -100.0], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -100 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 57.3

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

   5. Applied rewrites 57.3%

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

   if -100 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -100:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \mathbf{if}\;t\_1 \leq -5000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0004:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* (- t y) (- y z)))))
   (if (<= t_1 -5000.0) t_2 (if (<= t_1 0.0004) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / ((t - y) * (y - z));
	double tmp;
	if (t_1 <= -5000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    t_2 = x / ((t - y) * (y - z))
    if (t_1 <= (-5000.0d0)) then
        tmp = t_2
    else if (t_1 <= 0.0004d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / ((t - y) * (y - z));
	double tmp;
	if (t_1 <= -5000.0) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / ((t - y) * (y - z))
	tmp = 0
	if t_1 <= -5000.0:
		tmp = t_2
	elif t_1 <= 0.0004:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(Float64(t - y) * Float64(y - z)))
	tmp = 0.0
	if (t_1 <= -5000.0)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / ((t - y) * (y - z));
	tmp = 0.0;
	if (t_1 <= -5000.0)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5000.0], t$95$2, If[LessEqual[t$95$1, 0.0004], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5e3 or 4.00000000000000019e-4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 94.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 95.0

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

   4. Applied rewrites 95.0%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 91.2

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

   7. Applied rewrites 91.2%

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

   if -5e3 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.00000000000000019e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 99.2%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -5000:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.0004:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - y\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t \cdot y}\\ t_2 := 1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_2 \leq -1000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+228}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* t y))) (t_2 (- 1.0 (/ x (* (- t y) (- z y))))))
   (if (<= t_2 -1000000.0) t_1 (if (<= t_2 5e+228) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (t * y);
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -1000000.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+228) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (t * y)
    t_2 = 1.0d0 - (x / ((t - y) * (z - y)))
    if (t_2 <= (-1000000.0d0)) then
        tmp = t_1
    else if (t_2 <= 5d+228) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (t * y);
	double t_2 = 1.0 - (x / ((t - y) * (z - y)));
	double tmp;
	if (t_2 <= -1000000.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+228) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (t * y)
	t_2 = 1.0 - (x / ((t - y) * (z - y)))
	tmp = 0
	if t_2 <= -1000000.0:
		tmp = t_1
	elif t_2 <= 5e+228:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * y))
	t_2 = Float64(1.0 - Float64(x / Float64(Float64(t - y) * Float64(z - y))))
	tmp = 0.0
	if (t_2 <= -1000000.0)
		tmp = t_1;
	elseif (t_2 <= 5e+228)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (t * y);
	t_2 = 1.0 - (x / ((t - y) * (z - y)));
	tmp = 0.0;
	if (t_2 <= -1000000.0)
		tmp = t_1;
	elseif (t_2 <= 5e+228)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1000000.0], t$95$1, If[LessEqual[t$95$2, 5e+228], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -1e6 or 5e228 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 92.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 95.4

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

   4. Applied rewrites 95.4%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 90.7

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

   7. Applied rewrites 90.7%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 47.4%

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

   11. Taylor expanded in y around inf

       \[\leadsto \frac{x}{t \cdot y} \]
   12. Step-by-step derivation

   13. Applied rewrites 19.6%

       \[\leadsto \frac{x}{t \cdot y} \]

   if -1e6 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 5e228

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 91.7%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -1000000:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;1 - \frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 5 \cdot 10^{+228}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 200:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ x (* t (- y z)))))
   (if (<= t_1 -1e+31) t_2 (if (<= t_1 200.0) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / (t * (y - z));
	double tmp;
	if (t_1 <= -1e+31) {
		tmp = t_2;
	} else if (t_1 <= 200.0) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    t_2 = x / (t * (y - z))
    if (t_1 <= (-1d+31)) then
        tmp = t_2
    else if (t_1 <= 200.0d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = x / (t * (y - z));
	double tmp;
	if (t_1 <= -1e+31) {
		tmp = t_2;
	} else if (t_1 <= 200.0) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = x / (t * (y - z))
	tmp = 0
	if t_1 <= -1e+31:
		tmp = t_2
	elif t_1 <= 200.0:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(x / Float64(t * Float64(y - z)))
	tmp = 0.0
	if (t_1 <= -1e+31)
		tmp = t_2;
	elseif (t_1 <= 200.0)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = x / (t * (y - z));
	tmp = 0.0;
	if (t_1 <= -1e+31)
		tmp = t_2;
	elseif (t_1 <= 200.0)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+31], t$95$2, If[LessEqual[t$95$1, 200.0], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.9999999999999996e30 or 200 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 94.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 94.9

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

   4. Applied rewrites 94.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 93.1

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

   7. Applied rewrites 93.1%

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

   8. Taylor expanded in t around inf

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

   10. Applied rewrites 50.2%

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

   if -9.9999999999999996e30 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 200

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.3%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 200:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq 0.0004:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))))
   (if (<= t_1 -1e+31)
     (/ (- x) (* t z))
     (if (<= t_1 0.0004) 1.0 (/ (- x) (* y y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -1e+31) {
		tmp = -x / (t * z);
	} else if (t_1 <= 0.0004) {
		tmp = 1.0;
	} else {
		tmp = -x / (y * 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    if (t_1 <= (-1d+31)) then
        tmp = -x / (t * z)
    else if (t_1 <= 0.0004d0) then
        tmp = 1.0d0
    else
        tmp = -x / (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double tmp;
	if (t_1 <= -1e+31) {
		tmp = -x / (t * z);
	} else if (t_1 <= 0.0004) {
		tmp = 1.0;
	} else {
		tmp = -x / (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	tmp = 0
	if t_1 <= -1e+31:
		tmp = -x / (t * z)
	elif t_1 <= 0.0004:
		tmp = 1.0
	else:
		tmp = -x / (y * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -1e+31)
		tmp = Float64(Float64(-x) / Float64(t * z));
	elseif (t_1 <= 0.0004)
		tmp = 1.0;
	else
		tmp = Float64(Float64(-x) / Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	tmp = 0.0;
	if (t_1 <= -1e+31)
		tmp = -x / (t * z);
	elseif (t_1 <= 0.0004)
		tmp = 1.0;
	else
		tmp = -x / (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+31], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0004], 1.0, N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.9999999999999996e30

   1. Initial program 93.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 96.7

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

   4. Applied rewrites 96.7%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 93.5

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

   7. Applied rewrites 93.5%

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

   8. Taylor expanded in y around 0

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

   10. Applied rewrites 48.3%

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

   12. Applied rewrites 48.3%

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

   if -9.9999999999999996e30 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.00000000000000019e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.7%

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

   if 4.00000000000000019e-4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 90.5

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

   7. Applied rewrites 90.5%

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

   8. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{{y}^{2}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 32.2%

       \[\leadsto \frac{\frac{-x}{y}}{\color{blue}{y}} \]
   11. Step-by-step derivation

   12. Applied rewrites 32.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -1 \cdot 10^{+31}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.0004:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(t - y\right) \cdot \left(z - y\right)}\\ t_2 := \frac{-x}{y \cdot y}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0004:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- t y) (- z y)))) (t_2 (/ (- x) (* y y))))
   (if (<= t_1 -2e+65) t_2 (if (<= t_1 0.0004) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = -x / (y * y);
	double tmp;
	if (t_1 <= -2e+65) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((t - y) * (z - y))
    t_2 = -x / (y * y)
    if (t_1 <= (-2d+65)) then
        tmp = t_2
    else if (t_1 <= 0.0004d0) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((t - y) * (z - y));
	double t_2 = -x / (y * y);
	double tmp;
	if (t_1 <= -2e+65) {
		tmp = t_2;
	} else if (t_1 <= 0.0004) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((t - y) * (z - y))
	t_2 = -x / (y * y)
	tmp = 0
	if t_1 <= -2e+65:
		tmp = t_2
	elif t_1 <= 0.0004:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(t - y) * Float64(z - y)))
	t_2 = Float64(Float64(-x) / Float64(y * y))
	tmp = 0.0
	if (t_1 <= -2e+65)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((t - y) * (z - y));
	t_2 = -x / (y * y);
	tmp = 0.0;
	if (t_1 <= -2e+65)
		tmp = t_2;
	elseif (t_1 <= 0.0004)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(t - y), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+65], t$95$2, If[LessEqual[t$95$1, 0.0004], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -2e65 or 4.00000000000000019e-4 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 94.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 94.9

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

   4. Applied rewrites 94.9%

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

   5. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower--.f64 91.9

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

   7. Applied rewrites 91.9%

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

   8. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{\frac{x}{{y}^{2}}} \]
   9. Step-by-step derivation

   10. Applied rewrites 37.9%

       \[\leadsto \frac{\frac{-x}{y}}{\color{blue}{y}} \]
   11. Step-by-step derivation

   12. Applied rewrites 36.1%

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

   if -2e65 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 4.00000000000000019e-4

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.3%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq -2 \cdot 10^{+65}:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \mathbf{elif}\;\frac{x}{\left(t - y\right) \cdot \left(z - y\right)} \leq 0.0004:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{elif}\;z \leq 10^{-142}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(z - y\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e-86)
   (- 1.0 (/ x (* (- t y) z)))
   (if (<= z 1e-142) (- 1.0 (/ x (* (- y t) y))) (- 1.0 (/ x (* (- z y) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e-86) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 1e-142) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = 1.0 - (x / ((z - 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 <= (-5.5d-86)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else if (z <= 1d-142) then
        tmp = 1.0d0 - (x / ((y - t) * y))
    else
        tmp = 1.0d0 - (x / ((z - 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 <= -5.5e-86) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else if (z <= 1e-142) {
		tmp = 1.0 - (x / ((y - t) * y));
	} else {
		tmp = 1.0 - (x / ((z - y) * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e-86:
		tmp = 1.0 - (x / ((t - y) * z))
	elif z <= 1e-142:
		tmp = 1.0 - (x / ((y - t) * y))
	else:
		tmp = 1.0 - (x / ((z - y) * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e-86)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	elseif (z <= 1e-142)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(z - y) * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e-86)
		tmp = 1.0 - (x / ((t - y) * z));
	elseif (z <= 1e-142)
		tmp = 1.0 - (x / ((y - t) * y));
	else
		tmp = 1.0 - (x / ((z - y) * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e-86], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-142], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(z - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5e-86

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 92.9

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

   5. Applied rewrites 92.9%

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

   if -5.5e-86 < z < 1e-142

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 94.3

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

   5. Applied rewrites 94.3%

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

   if 1e-142 < z

   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

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 80.5

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

   5. Applied rewrites 80.5%

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

Alternative 9: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-86}:\\ \;\;\;\;1 - \frac{x}{\left(t - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{\left(y - t\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e-86) (- 1.0 (/ x (* (- t y) z))) (- 1.0 (/ x (* (- y t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e-86) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else {
		tmp = 1.0 - (x / ((y - 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 <= (-5.5d-86)) then
        tmp = 1.0d0 - (x / ((t - y) * z))
    else
        tmp = 1.0d0 - (x / ((y - 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 <= -5.5e-86) {
		tmp = 1.0 - (x / ((t - y) * z));
	} else {
		tmp = 1.0 - (x / ((y - t) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e-86:
		tmp = 1.0 - (x / ((t - y) * z))
	else:
		tmp = 1.0 - (x / ((y - t) * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e-86)
		tmp = Float64(1.0 - Float64(x / Float64(Float64(t - y) * z)));
	else
		tmp = Float64(1.0 - Float64(x / Float64(Float64(y - t) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e-86)
		tmp = 1.0 - (x / ((t - y) * z));
	else
		tmp = 1.0 - (x / ((y - t) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e-86], N[(1.0 - N[(x / N[(N[(t - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / N[(N[(y - t), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e-86

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. mul-1-neg N/A

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

      7. +-commutative N/A

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

      8. distribute-neg-in N/A

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

      9. unsub-neg N/A

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

      10. mul-1-neg N/A

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

      11. remove-double-neg N/A

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

      12. lower--.f64 92.9

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

   5. Applied rewrites 92.9%

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

   if -5.5e-86 < z

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 80.9

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

   5. Applied rewrites 80.9%

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

Alternative 10: 75.8% accurate, 26.0× 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 98.7%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 77.0%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024285 
(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)))))