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

Percentage Accurate: 89.2% → 96.9%

Time: 17.3s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{\frac{x}{z - t}}{z - y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- z t)) (- z y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (z - t)) / (z - y);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / (z - t)) / (z - y)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (x / (z - t)) / (z - y);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (z - t)) / (z - y)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(z - t)) / Float64(z - y))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (z - t)) / (z - y);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.0%

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

   1. associate-/l/ 96.4%

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

3. Simplified 96.4%

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

5. Final simplification 96.4%

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

Alternative 2: 80.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ t_2 := \frac{\frac{x}{t - z}}{y}\\ \mathbf{if}\;t \leq -4.45 \cdot 10^{-187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- z y)))) (t_2 (/ (/ x (- t z)) y)))
   (if (<= t -4.45e-187)
     t_2
     (if (<= t 5.8e-181)
       t_1
       (if (<= t 8.6e-141)
         t_2
         (if (<= t 5e-27)
           t_1
           (if (<= t 1.85e+157) (/ x (* t (- y z))) (/ (/ x t) (- y z)))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double t_2 = (x / (t - z)) / y;
	double tmp;
	if (t <= -4.45e-187) {
		tmp = t_2;
	} else if (t <= 5.8e-181) {
		tmp = t_1;
	} else if (t <= 8.6e-141) {
		tmp = t_2;
	} else if (t <= 5e-27) {
		tmp = t_1;
	} else if (t <= 1.85e+157) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 / (z * (z - y))
    t_2 = (x / (t - z)) / y
    if (t <= (-4.45d-187)) then
        tmp = t_2
    else if (t <= 5.8d-181) then
        tmp = t_1
    else if (t <= 8.6d-141) then
        tmp = t_2
    else if (t <= 5d-27) then
        tmp = t_1
    else if (t <= 1.85d+157) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * (z - y));
	double t_2 = (x / (t - z)) / y;
	double tmp;
	if (t <= -4.45e-187) {
		tmp = t_2;
	} else if (t <= 5.8e-181) {
		tmp = t_1;
	} else if (t <= 8.6e-141) {
		tmp = t_2;
	} else if (t <= 5e-27) {
		tmp = t_1;
	} else if (t <= 1.85e+157) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * (z - y))
	t_2 = (x / (t - z)) / y
	tmp = 0
	if t <= -4.45e-187:
		tmp = t_2
	elif t <= 5.8e-181:
		tmp = t_1
	elif t <= 8.6e-141:
		tmp = t_2
	elif t <= 5e-27:
		tmp = t_1
	elif t <= 1.85e+157:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(z - y)))
	t_2 = Float64(Float64(x / Float64(t - z)) / y)
	tmp = 0.0
	if (t <= -4.45e-187)
		tmp = t_2;
	elseif (t <= 5.8e-181)
		tmp = t_1;
	elseif (t <= 8.6e-141)
		tmp = t_2;
	elseif (t <= 5e-27)
		tmp = t_1;
	elseif (t <= 1.85e+157)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * (z - y));
	t_2 = (x / (t - z)) / y;
	tmp = 0.0;
	if (t <= -4.45e-187)
		tmp = t_2;
	elseif (t <= 5.8e-181)
		tmp = t_1;
	elseif (t <= 8.6e-141)
		tmp = t_2;
	elseif (t <= 5e-27)
		tmp = t_1;
	elseif (t <= 1.85e+157)
		tmp = x / (t * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -4.45e-187], t$95$2, If[LessEqual[t, 5.8e-181], t$95$1, If[LessEqual[t, 8.6e-141], t$95$2, If[LessEqual[t, 5e-27], t$95$1, If[LessEqual[t, 1.85e+157], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.4500000000000002e-187 or 5.7999999999999996e-181 < t < 8.59999999999999948e-141

   1. Initial program 89.3%

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

      1. associate-/l/ 96.2%

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

      2. clear-num 96.0%

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

      3. inv-pow 96.0%

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

      4. div-inv 95.1%

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

      5. clear-num 95.2%

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

   4. Applied egg-rr 95.2%

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

      1. unpow-1 95.2%

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

      2. associate-/r* 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in y around inf 59.2%

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

      1. *-rgt-identity 59.2%

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

      2. times-frac 60.7%

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

      3. associate-*l/ 63.6%

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

      4. associate-*r/ 63.7%

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

      5. *-rgt-identity 63.7%

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

   9. Simplified 63.7%

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

   if -4.4500000000000002e-187 < t < 5.7999999999999996e-181 or 8.59999999999999948e-141 < t < 5.0000000000000002e-27

   1. Initial program 91.1%

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

   3. Taylor expanded in t around 0 82.2%

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

      1. associate-*r/ 82.2%

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

      2. neg-mul-1 82.2%

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

   5. Simplified 82.2%

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

   if 5.0000000000000002e-27 < t < 1.8499999999999999e157

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf 77.0%

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

   if 1.8499999999999999e157 < t

   1. Initial program 68.7%

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

      1. associate-/l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around inf 94.2%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.45 \cdot 10^{-187}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t z) (- y z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- t z)) y)
     (if (<= t_1 5e+299) (/ x t_1) (/ (/ x z) (- z y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+299) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (t - z)) / y;
	} else if (t_1 <= 5e+299) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x / (t - z)) / y
	elif t_1 <= 5e+299:
		tmp = x / t_1
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t_1 <= 5e+299)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (t - z)) / y;
	elseif (t_1 <= 5e+299)
		tmp = x / t_1;
	else
		tmp = (x / z) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t$95$1, 5e+299], N[(x / t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 63.2%

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

      1. associate-/l/ 99.9%

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

      2. clear-num 99.9%

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

      3. inv-pow 99.9%

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

      4. div-inv 99.9%

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

      5. clear-num 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. unpow-1 99.9%

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

      2. associate-/r* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 60.9%

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

      1. *-rgt-identity 60.9%

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

      2. times-frac 85.1%

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

      3. associate-*l/ 87.4%

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

      4. associate-*r/ 87.4%

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

      5. *-rgt-identity 87.4%

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

   9. Simplified 87.4%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5.0000000000000003e299

   1. Initial program 98.5%

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

   if 5.0000000000000003e299 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 69.0%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -8e-84)
   (/ (/ x (- t z)) y)
   (if (<= t 4.8e-27)
     (/ (/ x z) (- z y))
     (if (<= t 3.6e+157) (/ x (* t (- y z))) (/ (/ x t) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e-84) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 4.8e-27) {
		tmp = (x / z) / (z - y);
	} else if (t <= 3.6e+157) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-8d-84)) then
        tmp = (x / (t - z)) / y
    else if (t <= 4.8d-27) then
        tmp = (x / z) / (z - y)
    else if (t <= 3.6d+157) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e-84) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 4.8e-27) {
		tmp = (x / z) / (z - y);
	} else if (t <= 3.6e+157) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -8e-84:
		tmp = (x / (t - z)) / y
	elif t <= 4.8e-27:
		tmp = (x / z) / (z - y)
	elif t <= 3.6e+157:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8e-84)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 4.8e-27)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (t <= 3.6e+157)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8e-84)
		tmp = (x / (t - z)) / y;
	elseif (t <= 4.8e-27)
		tmp = (x / z) / (z - y);
	elseif (t <= 3.6e+157)
		tmp = x / (t * (y - z));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -8e-84], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.8e-27], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+157], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.0000000000000003e-84

   1. Initial program 90.5%

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

      1. associate-/l/ 97.4%

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

      2. clear-num 97.2%

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

      3. inv-pow 97.2%

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

      4. div-inv 96.1%

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

      5. clear-num 96.2%

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

   4. Applied egg-rr 96.2%

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

      1. unpow-1 96.2%

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

      2. associate-/r* 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around inf 62.7%

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

      1. *-rgt-identity 62.7%

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

      2. times-frac 61.1%

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

      3. associate-*l/ 66.3%

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

      4. associate-*r/ 66.3%

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

      5. *-rgt-identity 66.3%

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

   9. Simplified 66.3%

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

   if -8.0000000000000003e-84 < t < 4.80000000000000004e-27

   1. Initial program 89.5%

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

      1. associate-/l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in t around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. neg-mul-1 82.8%

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

   7. Simplified 82.8%

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

   if 4.80000000000000004e-27 < t < 3.60000000000000024e157

   1. Initial program 89.0%

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

   3. Taylor expanded in t around inf 77.0%

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

   if 3.60000000000000024e157 < t

   1. Initial program 68.7%

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

      1. associate-/l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around inf 94.2%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-173}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-65)
   (/ (/ x (- t z)) y)
   (if (<= y 2.2e-173) (/ -1.0 (* z (/ (- t z) x))) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-65) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 2.2e-173) {
		tmp = -1.0 / (z * ((t - z) / x));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.05d-65)) then
        tmp = (x / (t - z)) / y
    else if (y <= 2.2d-173) then
        tmp = (-1.0d0) / (z * ((t - z) / x))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-65) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 2.2e-173) {
		tmp = -1.0 / (z * ((t - z) / x));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-65:
		tmp = (x / (t - z)) / y
	elif y <= 2.2e-173:
		tmp = -1.0 / (z * ((t - z) / x))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-65)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 2.2e-173)
		tmp = Float64(-1.0 / Float64(z * Float64(Float64(t - z) / x)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e-65)
		tmp = (x / (t - z)) / y;
	elseif (y <= 2.2e-173)
		tmp = -1.0 / (z * ((t - z) / x));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-65], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 2.2e-173], N[(-1.0 / N[(z * N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000001e-65

   1. Initial program 77.3%

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

      1. associate-/l/ 96.9%

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

      2. clear-num 96.3%

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

      3. inv-pow 96.3%

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

      4. div-inv 96.2%

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

      5. clear-num 96.4%

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

   4. Applied egg-rr 96.4%

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

      1. unpow-1 96.4%

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

      2. associate-/r* 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in y around inf 75.8%

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

      1. *-rgt-identity 75.8%

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

      2. times-frac 86.0%

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

      3. associate-*l/ 86.7%

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

      4. associate-*r/ 86.8%

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

      5. *-rgt-identity 86.8%

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

   9. Simplified 86.8%

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

   if -1.05000000000000001e-65 < y < 2.1999999999999999e-173

   1. Initial program 93.7%

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

      1. associate-/l/ 97.7%

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

      2. clear-num 97.6%

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

      3. inv-pow 97.6%

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

      4. div-inv 96.5%

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

      5. clear-num 96.6%

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

   4. Applied egg-rr 96.6%

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

      1. unpow-1 96.6%

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

      2. associate-/r* 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around 0 87.0%

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

      1. associate-/l/ 87.0%

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

      2. div-inv 87.0%

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

      3. *-commutative 87.0%

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

   9. Applied egg-rr 87.0%

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

       1. associate-*r/ 83.7%

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

       2. associate-*r/ 83.7%

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

       3. metadata-eval 83.7%

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

       4. associate-*r/ 87.0%

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

   11. Simplified 87.0%

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

   if 2.1999999999999999e-173 < y

   1. Initial program 87.4%

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

      1. associate-/l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around inf 63.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-173}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t - z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+98} \lor \neg \left(z \leq 3.3 \cdot 10^{+125}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e+98) (not (<= z 3.3e+125)))
   (/ x (* z (- y z)))
   (/ x (* t (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+98) || !(z <= 3.3e+125)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-4.8d+98)) .or. (.not. (z <= 3.3d+125))) then
        tmp = x / (z * (y - z))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e+98) || !(z <= 3.3e+125)) {
		tmp = x / (z * (y - z));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e+98) or not (z <= 3.3e+125):
		tmp = x / (z * (y - z))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.8e+98) || !(z <= 3.3e+125))
		tmp = Float64(x / Float64(z * Float64(y - z)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.8e+98) || ~((z <= 3.3e+125)))
		tmp = x / (z * (y - z));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.8e+98], N[Not[LessEqual[z, 3.3e+125]], $MachinePrecision]], N[(x / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7999999999999997e98 or 3.30000000000000005e125 < z

   1. Initial program 78.3%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 91.2%

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

      1. associate-*r/ 91.2%

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

      2. neg-mul-1 91.2%

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

   7. Simplified 91.2%

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

      1. *-un-lft-identity 91.2%

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

      2. associate-/l/ 75.2%

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

      3. add-sqr-sqrt 37.3%

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

      4. sqrt-unprod 65.4%

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

      5. sqr-neg 65.4%

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

      6. sqrt-unprod 32.7%

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

      7. add-sqr-sqrt 66.7%

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

      8. *-commutative 66.7%

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

   9. Applied egg-rr 66.7%

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

       1. *-lft-identity 66.7%

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

   11. Simplified 66.7%

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

   if -4.7999999999999997e98 < z < 3.30000000000000005e125

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf 63.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+98} \lor \neg \left(z \leq 3.3 \cdot 10^{+125}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-187}:\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.2e-89)
   (/ (/ x t) y)
   (if (<= t 4e-187) (- (/ x (* z y))) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e-89) {
		tmp = (x / t) / y;
	} else if (t <= 4e-187) {
		tmp = -(x / (z * y));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-5.2d-89)) then
        tmp = (x / t) / y
    else if (t <= 4d-187) then
        tmp = -(x / (z * y))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e-89) {
		tmp = (x / t) / y;
	} else if (t <= 4e-187) {
		tmp = -(x / (z * y));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -5.2e-89:
		tmp = (x / t) / y
	elif t <= 4e-187:
		tmp = -(x / (z * y))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.2e-89)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 4e-187)
		tmp = Float64(-Float64(x / Float64(z * y)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.2e-89)
		tmp = (x / t) / y;
	elseif (t <= 4e-187)
		tmp = -(x / (z * y));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -5.2e-89], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4e-187], (-N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1999999999999997e-89

   1. Initial program 90.6%

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

      1. associate-/l/ 97.4%

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

      2. clear-num 97.3%

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

      3. inv-pow 97.3%

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

      4. div-inv 96.1%

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

      5. clear-num 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in z around 0 47.0%

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

      1. associate-/r* 51.7%

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

   7. Simplified 51.7%

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

   if -5.1999999999999997e-89 < t < 4.0000000000000001e-187

   1. Initial program 91.9%

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

      1. associate-/l/ 92.0%

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

      2. clear-num 91.3%

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

      3. inv-pow 91.3%

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

      4. div-inv 91.3%

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

      5. clear-num 91.4%

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

   4. Applied egg-rr 91.4%

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

   5. Taylor expanded in y around inf 52.0%

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

      1. associate-/r* 53.2%

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

   7. Simplified 53.2%

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

   8. Taylor expanded in t around 0 40.7%

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

      1. mul-1-neg 40.7%

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

      2. distribute-neg-frac2 40.7%

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

      3. distribute-lft-neg-out 40.7%

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

      4. neg-mul-1 40.7%

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

      5. *-commutative 40.7%

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

      6. associate-*l* 40.7%

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

      7. neg-mul-1 40.7%

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

   10. Simplified 40.7%

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

   if 4.0000000000000001e-187 < t

   1. Initial program 82.0%

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

   3. Taylor expanded in t around inf 61.4%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-89}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-187}:\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+31} \lor \neg \left(z \leq 1.7 \cdot 10^{+34}\right):\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e+31) (not (<= z 1.7e+34)))
   (- (/ x (* z y)))
   (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+31) || !(z <= 1.7e+34)) {
		tmp = -(x / (z * y));
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-3.9d+31)) .or. (.not. (z <= 1.7d+34))) then
        tmp = -(x / (z * y))
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+31) || !(z <= 1.7e+34)) {
		tmp = -(x / (z * y));
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e+31) or not (z <= 1.7e+34):
		tmp = -(x / (z * y))
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e+31) || !(z <= 1.7e+34))
		tmp = Float64(-Float64(x / Float64(z * y)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.9e+31) || ~((z <= 1.7e+34)))
		tmp = -(x / (z * y));
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e+31], N[Not[LessEqual[z, 1.7e+34]], $MachinePrecision]], (-N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.89999999999999999e31 or 1.7e34 < z

   1. Initial program 81.5%

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

      1. associate-/l/ 99.8%

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

      2. clear-num 99.7%

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

      3. inv-pow 99.7%

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

      4. div-inv 99.6%

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

      5. clear-num 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf 42.9%

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

      1. associate-/r* 46.6%

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

   7. Simplified 46.6%

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

   8. Taylor expanded in t around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. distribute-neg-frac2 39.4%

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

      3. distribute-lft-neg-out 39.4%

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

      4. neg-mul-1 39.4%

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

      5. *-commutative 39.4%

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

      6. associate-*l* 39.4%

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

      7. neg-mul-1 39.4%

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

   10. Simplified 39.4%

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

   if -3.89999999999999999e31 < z < 1.7e34

   1. Initial program 92.0%

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

      1. associate-/l/ 93.4%

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

      2. clear-num 93.1%

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

      3. inv-pow 93.1%

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

      4. div-inv 92.4%

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

      5. clear-num 92.4%

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

   4. Applied egg-rr 92.4%

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

   5. Taylor expanded in z around 0 56.5%

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

      1. associate-/r* 61.4%

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

   7. Simplified 61.4%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+31} \lor \neg \left(z \leq 1.7 \cdot 10^{+34}\right):\\ \;\;\;\;-\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 71.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e-34) (/ x (* (- t z) y)) (/ x (* t (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-34) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-4d-34)) then
        tmp = x / ((t - z) * y)
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-34) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4e-34:
		tmp = x / ((t - z) * y)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e-34)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e-34)
		tmp = x / ((t - z) * y);
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4e-34], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999971e-34

   1. Initial program 76.6%

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

   3. Taylor expanded in y around inf 75.1%

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

      1. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -3.99999999999999971e-34 < y

   1. Initial program 90.5%

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

   3. Taylor expanded in t around inf 61.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-64) (/ x (* (- t z) y)) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-64) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.05d-64)) then
        tmp = x / ((t - z) * y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-64) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-64:
		tmp = x / ((t - z) * y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-64)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e-64)
		tmp = x / ((t - z) * y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-64], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05000000000000006e-64

   1. Initial program 77.3%

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

   3. Taylor expanded in y around inf 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   if -1.05000000000000006e-64 < y

   1. Initial program 90.4%

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

      1. associate-/l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 62.6%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.25e-46) (/ (/ x y) (- t z)) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-46) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.25d-46)) then
        tmp = (x / y) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.25e-46) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.25e-46:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.25e-46)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.25e-46)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.25e-46], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25e-46

   1. Initial program 77.0%

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

      1. associate-/l/ 96.9%

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

      2. clear-num 96.3%

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

      3. inv-pow 96.3%

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

      4. div-inv 96.2%

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

      5. clear-num 96.3%

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

   4. Applied egg-rr 96.3%

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

   5. Taylor expanded in y around inf 75.4%

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

      1. associate-/r* 85.9%

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

   7. Simplified 85.9%

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

   if -2.25e-46 < y

   1. Initial program 90.5%

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

      1. associate-/l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 62.8%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-46}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e-35) (/ (/ x (- t z)) y) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-35) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.7d-35)) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e-35) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e-35:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e-35)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e-35)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e-35], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e-35

   1. Initial program 76.6%

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

      1. associate-/l/ 96.8%

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

      2. clear-num 96.2%

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

      3. inv-pow 96.2%

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

      4. div-inv 96.1%

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

      5. clear-num 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. unpow-1 96.3%

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

      2. associate-/r* 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around inf 75.1%

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

      1. *-rgt-identity 75.1%

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

      2. times-frac 85.6%

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

      3. associate-*l/ 86.4%

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

      4. associate-*r/ 86.4%

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

      5. *-rgt-identity 86.4%

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

   9. Simplified 86.4%

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

   if -1.7000000000000001e-35 < y

   1. Initial program 90.5%

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

      1. associate-/l/ 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in t around inf 63.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.16e-59) (/ (/ x (- t z)) y) (/ (/ x (- y z)) t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.16e-59) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.16d-59)) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.16e-59) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.16e-59:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.16e-59)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.16e-59)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.16e-59], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.16e-59

   1. Initial program 77.3%

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

      1. associate-/l/ 96.9%

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

      2. clear-num 96.3%

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

      3. inv-pow 96.3%

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

      4. div-inv 96.2%

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

      5. clear-num 96.4%

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

   4. Applied egg-rr 96.4%

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

      1. unpow-1 96.4%

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

      2. associate-/r* 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in y around inf 75.8%

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

      1. *-rgt-identity 75.8%

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

      2. times-frac 86.0%

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

      3. associate-*l/ 86.7%

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

      4. associate-*r/ 86.8%

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

      5. *-rgt-identity 86.8%

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

   9. Simplified 86.8%

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

   if -1.16e-59 < y

   1. Initial program 90.4%

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

      1. associate-/l/ 96.3%

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

      2. clear-num 96.2%

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

      3. inv-pow 96.2%

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

      4. div-inv 95.7%

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

      5. clear-num 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in t around inf 61.0%

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

      1. *-commutative 61.0%

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

      2. associate-/r* 67.6%

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

   7. Simplified 67.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-59}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-47) (/ (/ x y) t) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-47) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-5d-47)) then
        tmp = (x / y) / t
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-47) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5e-47:
		tmp = (x / y) / t
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-47)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-47)
		tmp = (x / y) / t;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5e-47], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000011e-47

   1. Initial program 77.0%

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

   3. Taylor expanded in z around 0 47.9%

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

      1. div-inv 47.9%

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

      2. associate-/r* 47.8%

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

   5. Applied egg-rr 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*l/ 50.5%

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

      3. associate-*r/ 51.7%

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

      4. associate-*l/ 51.7%

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

      5. *-lft-identity 51.7%

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

   7. Simplified 51.7%

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

   if -5.00000000000000011e-47 < y

   1. Initial program 90.5%

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

      1. associate-/l/ 96.3%

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

      2. clear-num 96.2%

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

      3. inv-pow 96.2%

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

      4. div-inv 95.7%

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

      5. clear-num 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in z around 0 35.1%

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

      1. associate-/r* 39.4%

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

   7. Simplified 39.4%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{t \cdot y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* t y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (t * y)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (t * y)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(t * y))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (t * y);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.0%

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

3. Taylor expanded in z around 0 38.4%

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

4. Final simplification 38.4%

   \[\leadsto \frac{x}{t \cdot y} \]
5. Add Preprocessing

Alternative 16: 43.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{\frac{x}{t}}{y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x t) y))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / t) / y;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / t) / y
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (x / t) / y;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / t) / y

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / t) / y)
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / t) / y;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 87.0%

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

   1. associate-/l/ 96.4%

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

   2. clear-num 96.2%

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

   3. inv-pow 96.2%

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

   4. div-inv 95.8%

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

   5. clear-num 95.9%

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

4. Applied egg-rr 95.9%

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

5. Taylor expanded in z around 0 38.4%

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

   1. associate-/r* 42.2%

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

7. Simplified 42.2%

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

8. Final simplification 42.2%

   \[\leadsto \frac{\frac{x}{t}}{y} \]
9. Add Preprocessing

Developer target: 88.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024076 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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