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

Percentage Accurate: 88.5% → 97.1%

Time: 16.3s

Alternatives: 15

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: 88.5% 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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y 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 88.9%

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

   1. associate-/l/ 97.3%

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

   2. sub-neg 97.3%

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

   3. +-commutative 97.3%

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

   4. neg-sub0 97.3%

      \[\leadsto \frac{\frac{x}{t - z}}{\color{blue}{\left(0 - z\right)} + y} \]

   5. associate-+l- 97.3%

      \[\leadsto \frac{\frac{x}{t - z}}{\color{blue}{0 - \left(z - y\right)}} \]

   6. sub0-neg 97.3%

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

   7. mul-1-neg 97.3%

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

   8. associate-/r* 97.3%

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

   9. associate-/l/ 97.3%

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

   10. mul-1-neg 97.3%

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

   11. sub-neg 97.3%

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

   12. distribute-neg-out 97.3%

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

   13. remove-double-neg 97.3%

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

   14. +-commutative 97.3%

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

   15. sub-neg 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ t_2 := \frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+80}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y (- t z)))) (t_2 (/ x (* t (- y z)))))
   (if (<= z -2.35e+80)
     (/ 1.0 (* z (/ z x)))
     (if (<= z -2.8e-31)
       t_1
       (if (<= z 6.8e-178)
         t_2
         (if (<= z 1.6e-97)
           t_1
           (if (<= z 4.8e+66) t_2 (* (/ x z) (/ 1.0 z)))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double t_2 = x / (t * (y - z));
	double tmp;
	if (z <= -2.35e+80) {
		tmp = 1.0 / (z * (z / x));
	} else if (z <= -2.8e-31) {
		tmp = t_1;
	} else if (z <= 6.8e-178) {
		tmp = t_2;
	} else if (z <= 1.6e-97) {
		tmp = t_1;
	} else if (z <= 4.8e+66) {
		tmp = t_2;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: y 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 / (y * (t - z))
    t_2 = x / (t * (y - z))
    if (z <= (-2.35d+80)) then
        tmp = 1.0d0 / (z * (z / x))
    else if (z <= (-2.8d-31)) then
        tmp = t_1
    else if (z <= 6.8d-178) then
        tmp = t_2
    else if (z <= 1.6d-97) then
        tmp = t_1
    else if (z <= 4.8d+66) then
        tmp = t_2
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double t_2 = x / (t * (y - z));
	double tmp;
	if (z <= -2.35e+80) {
		tmp = 1.0 / (z * (z / x));
	} else if (z <= -2.8e-31) {
		tmp = t_1;
	} else if (z <= 6.8e-178) {
		tmp = t_2;
	} else if (z <= 1.6e-97) {
		tmp = t_1;
	} else if (z <= 4.8e+66) {
		tmp = t_2;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (y * (t - z))
	t_2 = x / (t * (y - z))
	tmp = 0
	if z <= -2.35e+80:
		tmp = 1.0 / (z * (z / x))
	elif z <= -2.8e-31:
		tmp = t_1
	elif z <= 6.8e-178:
		tmp = t_2
	elif z <= 1.6e-97:
		tmp = t_1
	elif z <= 4.8e+66:
		tmp = t_2
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * Float64(t - z)))
	t_2 = Float64(x / Float64(t * Float64(y - z)))
	tmp = 0.0
	if (z <= -2.35e+80)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	elseif (z <= -2.8e-31)
		tmp = t_1;
	elseif (z <= 6.8e-178)
		tmp = t_2;
	elseif (z <= 1.6e-97)
		tmp = t_1;
	elseif (z <= 4.8e+66)
		tmp = t_2;
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * (t - z));
	t_2 = x / (t * (y - z));
	tmp = 0.0;
	if (z <= -2.35e+80)
		tmp = 1.0 / (z * (z / x));
	elseif (z <= -2.8e-31)
		tmp = t_1;
	elseif (z <= 6.8e-178)
		tmp = t_2;
	elseif (z <= 1.6e-97)
		tmp = t_1;
	elseif (z <= 4.8e+66)
		tmp = t_2;
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e+80], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.8e-31], t$95$1, If[LessEqual[z, 6.8e-178], t$95$2, If[LessEqual[z, 1.6e-97], t$95$1, If[LessEqual[z, 4.8e+66], t$95$2, N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.35000000000000005e80

   1. Initial program 83.9%

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

      1. remove-double-neg 83.9%

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

      2. sub0-neg 83.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 83.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 83.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 83.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in t around 0 83.9%

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

      1. clear-num 83.8%

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

      2. inv-pow 83.8%

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

      3. metadata-eval 83.8%

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

      4. sqr-pow 71.0%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

      5. associate-/l* 70.2%

         \[\leadsto {\color{blue}{\left(\frac{z}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      6. div-inv 70.2%

         \[\leadsto {\color{blue}{\left(z \cdot \frac{1}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      7. clear-num 70.2%

         \[\leadsto {\left(z \cdot \color{blue}{\frac{z - y}{x}}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      8. metadata-eval 70.2%

         \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 70.2%

         \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. associate-/l* 76.9%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\frac{z}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \]

      11. div-inv 76.9%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(z \cdot \frac{1}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \]

      12. clear-num 76.9%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \color{blue}{\frac{z - y}{x}}\right)}^{\left(\frac{-1}{2}\right)} \]

      13. metadata-eval 76.9%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \]

      14. metadata-eval 76.9%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{\color{blue}{-0.5}} \]

   6. Applied egg-rr 76.9%

      \[\leadsto \color{blue}{{\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5}} \]
   7. Step-by-step derivation

      1. pow-sqr 97.5%

         \[\leadsto \color{blue}{{\left(z \cdot \frac{z - y}{x}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 97.5%

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

      3. unpow-1 97.5%

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

   8. Simplified 97.5%

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

   9. Taylor expanded in z around inf 94.8%

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

   if -2.35000000000000005e80 < z < -2.7999999999999999e-31 or 6.79999999999999945e-178 < z < 1.5999999999999999e-97

   1. Initial program 88.1%

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

      1. remove-double-neg 88.1%

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

      2. sub0-neg 88.1%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 85.5%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 88.1%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 88.1%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 98.1%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 98.1%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 98.1%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 98.1%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 98.1%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 98.1%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 98.1%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 98.1%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 98.1%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 98.1%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 98.1%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 98.1%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 98.1%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 98.1%

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

      20. distribute-frac-neg 98.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in y around inf 60.2%

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

      1. associate-*r* 60.2%

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

      2. mul-1-neg 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in z around 0 57.7%

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

      1. *-commutative 57.7%

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

      2. mul-1-neg 57.7%

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

      3. distribute-lft-neg-out 57.7%

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

      4. distribute-rgt-out 60.2%

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

      5. +-commutative 60.2%

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

      6. sub-neg 60.2%

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

   9. Simplified 60.2%

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

   if -2.7999999999999999e-31 < z < 6.79999999999999945e-178 or 1.5999999999999999e-97 < z < 4.8000000000000003e66

   1. Initial program 92.0%

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

      1. remove-double-neg 92.0%

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

      2. sub0-neg 92.0%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 89.3%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 92.0%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 92.0%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 94.5%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 94.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 94.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 94.5%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 94.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 94.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 94.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 94.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 94.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 94.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 94.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 94.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 94.5%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 94.5%

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

      20. distribute-frac-neg 94.5%

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

   3. Simplified 92.0%

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

      1. associate-/l/ 95.3%

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

      2. div-inv 95.2%

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

   5. Applied egg-rr 95.2%

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

   6. Taylor expanded in t around inf 70.3%

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

      1. associate-*r/ 70.3%

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

      2. neg-mul-1 70.3%

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

   8. Simplified 70.3%

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

      1. distribute-frac-neg 70.3%

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

      2. neg-sub0 70.3%

         \[\leadsto \color{blue}{0 - \frac{x}{t \cdot \left(z - y\right)}} \]

      3. sub-neg 70.3%

         \[\leadsto \color{blue}{0 + \left(-\frac{x}{t \cdot \left(z - y\right)}\right)} \]

      4. frac-2neg 70.3%

         \[\leadsto 0 + \left(-\color{blue}{\frac{-x}{-t \cdot \left(z - y\right)}}\right) \]

      5. distribute-frac-neg 70.3%

         \[\leadsto 0 + \color{blue}{\frac{-\left(-x\right)}{-t \cdot \left(z - y\right)}} \]

      6. remove-double-neg 70.3%

         \[\leadsto 0 + \frac{\color{blue}{x}}{-t \cdot \left(z - y\right)} \]

      7. distribute-rgt-neg-in 70.3%

         \[\leadsto 0 + \frac{x}{\color{blue}{t \cdot \left(-\left(z - y\right)\right)}} \]

      8. associate-/r* 73.2%

         \[\leadsto 0 + \color{blue}{\frac{\frac{x}{t}}{-\left(z - y\right)}} \]

      9. neg-sub0 73.2%

         \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{0 - \left(z - y\right)}} \]

      10. sub-neg 73.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \]

      11. +-commutative 73.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \]

      12. associate--r+ 73.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \]

      13. neg-sub0 73.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{\left(-\left(-y\right)\right)} - z} \]

      14. remove-double-neg 73.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{y} - z} \]

   10. Applied egg-rr 73.2%

       \[\leadsto \color{blue}{0 + \frac{\frac{x}{t}}{y - z}} \]
   11. Step-by-step derivation

       1. +-lft-identity 73.2%

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

       2. associate-/l/ 70.3%

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

       3. *-commutative 70.3%

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

   12. Simplified 70.3%

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

   if 4.8000000000000003e66 < z

   1. Initial program 86.4%

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

      1. remove-double-neg 86.4%

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

      2. sub0-neg 86.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 86.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 86.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 86.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 86.4%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 83.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 83.6%

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

   8. Simplified 83.6%

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

      1. associate-/r* 93.8%

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

      2. div-inv 93.8%

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

   10. Applied egg-rr 93.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+80}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 3: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))))
   (if (<= z -8.6e+33)
     t_1
     (if (<= z 5.2e-42)
       (/ (/ x t) y)
       (if (<= z 7.2e+57) (/ (- x) (* z t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -8.6e+33) {
		tmp = t_1;
	} else if (z <= 5.2e-42) {
		tmp = (x / t) / y;
	} else if (z <= 7.2e+57) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y 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) :: tmp
    t_1 = (x / z) * (1.0d0 / z)
    if (z <= (-8.6d+33)) then
        tmp = t_1
    else if (z <= 5.2d-42) then
        tmp = (x / t) / y
    else if (z <= 7.2d+57) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (z <= -8.6e+33) {
		tmp = t_1;
	} else if (z <= 5.2e-42) {
		tmp = (x / t) / y;
	} else if (z <= 7.2e+57) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if z <= -8.6e+33:
		tmp = t_1
	elif z <= 5.2e-42:
		tmp = (x / t) / y
	elif z <= 7.2e+57:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (z <= -8.6e+33)
		tmp = t_1;
	elseif (z <= 5.2e-42)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 7.2e+57)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (1.0 / z);
	tmp = 0.0;
	if (z <= -8.6e+33)
		tmp = t_1;
	elseif (z <= 5.2e-42)
		tmp = (x / t) / y;
	elseif (z <= 7.2e+57)
		tmp = -x / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+33], t$95$1, If[LessEqual[z, 5.2e-42], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 7.2e+57], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.60000000000000057e33 or 7.2000000000000005e57 < z

   1. Initial program 85.3%

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

      1. remove-double-neg 85.3%

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

      2. sub0-neg 85.3%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 85.3%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 85.3%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 85.3%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 85.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 79.0%

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

   8. Simplified 79.0%

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

      1. associate-/r* 89.9%

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

      2. div-inv 89.9%

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

   10. Applied egg-rr 89.9%

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

   if -8.60000000000000057e33 < z < 5.2e-42

   1. Initial program 89.5%

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

      1. remove-double-neg 89.5%

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

      2. sub0-neg 89.5%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 86.2%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.5%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.5%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 95.0%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 95.0%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 95.0%

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

      20. distribute-frac-neg 95.0%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around 0 58.4%

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

      1. associate-/l/ 65.1%

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

      2. div-inv 65.0%

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

   6. Applied egg-rr 65.0%

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

      1. associate-*l/ 64.2%

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

      2. un-div-inv 64.4%

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

   8. Applied egg-rr 64.4%

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

   if 5.2e-42 < z < 7.2000000000000005e57

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 99.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 99.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 99.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.3%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.3%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.3%

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

      20. distribute-frac-neg 96.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 60.8%

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

   5. Taylor expanded in z around 0 42.2%

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

      1. *-commutative 42.2%

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

      2. associate-*r/ 42.2%

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

      3. neg-mul-1 42.2%

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

   7. Simplified 42.2%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 4: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.7e+33)
   (/ 1.0 (* z (/ z x)))
   (if (<= z 5.5e-47)
     (/ (/ x t) y)
     (if (<= z 9.4e+62) (/ (- x) (* z t)) (* (/ x z) (/ 1.0 z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+33) {
		tmp = 1.0 / (z * (z / x));
	} else if (z <= 5.5e-47) {
		tmp = (x / t) / y;
	} else if (z <= 9.4e+62) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-3.7d+33)) then
        tmp = 1.0d0 / (z * (z / x))
    else if (z <= 5.5d-47) then
        tmp = (x / t) / y
    else if (z <= 9.4d+62) then
        tmp = -x / (z * t)
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.7e+33) {
		tmp = 1.0 / (z * (z / x));
	} else if (z <= 5.5e-47) {
		tmp = (x / t) / y;
	} else if (z <= 9.4e+62) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.7e+33:
		tmp = 1.0 / (z * (z / x))
	elif z <= 5.5e-47:
		tmp = (x / t) / y
	elif z <= 9.4e+62:
		tmp = -x / (z * t)
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.7e+33)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	elseif (z <= 5.5e-47)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 9.4e+62)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.7e+33)
		tmp = 1.0 / (z * (z / x));
	elseif (z <= 5.5e-47)
		tmp = (x / t) / y;
	elseif (z <= 9.4e+62)
		tmp = -x / (z * t);
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.7e+33], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-47], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 9.4e+62], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.6999999999999999e33

   1. Initial program 83.9%

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

      1. remove-double-neg 83.9%

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

      2. sub0-neg 83.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 83.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 83.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 83.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in t around 0 77.7%

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

      1. clear-num 77.7%

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

      2. inv-pow 77.7%

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

      3. metadata-eval 77.7%

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

      4. sqr-pow 64.2%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

      5. associate-/l* 63.5%

         \[\leadsto {\color{blue}{\left(\frac{z}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      6. div-inv 63.5%

         \[\leadsto {\color{blue}{\left(z \cdot \frac{1}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      7. clear-num 63.5%

         \[\leadsto {\left(z \cdot \color{blue}{\frac{z - y}{x}}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      8. metadata-eval 63.5%

         \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 63.5%

         \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. associate-/l* 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\frac{z}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \]

      11. div-inv 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(z \cdot \frac{1}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \]

      12. clear-num 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \color{blue}{\frac{z - y}{x}}\right)}^{\left(\frac{-1}{2}\right)} \]

      13. metadata-eval 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \]

      14. metadata-eval 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{\color{blue}{-0.5}} \]

   6. Applied egg-rr 69.3%

      \[\leadsto \color{blue}{{\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5}} \]
   7. Step-by-step derivation

      1. pow-sqr 89.5%

         \[\leadsto \color{blue}{{\left(z \cdot \frac{z - y}{x}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 89.5%

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

      3. unpow-1 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in z around inf 85.1%

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

   if -3.6999999999999999e33 < z < 5.5000000000000002e-47

   1. Initial program 89.5%

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

      1. remove-double-neg 89.5%

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

      2. sub0-neg 89.5%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 86.2%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.5%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.5%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 95.0%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 95.0%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 95.0%

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

      20. distribute-frac-neg 95.0%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around 0 58.4%

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

      1. associate-/l/ 65.1%

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

      2. div-inv 65.0%

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

   6. Applied egg-rr 65.0%

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

      1. associate-*l/ 64.2%

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

      2. un-div-inv 64.4%

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

   8. Applied egg-rr 64.4%

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

   if 5.5000000000000002e-47 < z < 9.4000000000000006e62

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 99.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 99.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 99.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.3%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.3%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.3%

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

      20. distribute-frac-neg 96.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 60.8%

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

   5. Taylor expanded in z around 0 42.2%

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

      1. *-commutative 42.2%

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

      2. associate-*r/ 42.2%

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

      3. neg-mul-1 42.2%

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

   7. Simplified 42.2%

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

   if 9.4000000000000006e62 < z

   1. Initial program 86.4%

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

      1. remove-double-neg 86.4%

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

      2. sub0-neg 86.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 86.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 86.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 86.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 86.4%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 83.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 83.6%

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

   8. Simplified 83.6%

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

      1. associate-/r* 93.8%

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

      2. div-inv 93.8%

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

   10. Applied egg-rr 93.8%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+62}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 5: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+161)
   (/ (/ x z) (- z y))
   (if (<= z 4.2e+102) (/ x (* (- y z) (- t z))) (/ (/ x z) (- z t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+161) {
		tmp = (x / z) / (z - y);
	} else if (z <= 4.2e+102) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-6.8d+161)) then
        tmp = (x / z) / (z - y)
    else if (z <= 4.2d+102) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / (z - t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+161) {
		tmp = (x / z) / (z - y);
	} else if (z <= 4.2e+102) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e+161:
		tmp = (x / z) / (z - y)
	elif z <= 4.2e+102:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+161)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (z <= 4.2e+102)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.8e+161)
		tmp = (x / z) / (z - y);
	elseif (z <= 4.2e+102)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+161], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+102], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999986e161

   1. Initial program 71.4%

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

      1. remove-double-neg 71.4%

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

      2. sub0-neg 71.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 71.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 71.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 71.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 71.4%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in t around 0 71.4%

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

      1. associate-/r* 95.6%

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

   8. Simplified 95.6%

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

   if -6.79999999999999986e161 < z < 4.20000000000000003e102

   1. Initial program 92.3%

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

   if 4.20000000000000003e102 < z

   1. Initial program 83.5%

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

      1. remove-double-neg 83.5%

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

      2. sub0-neg 83.5%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 83.5%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 83.5%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 83.5%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in y around 0 82.5%

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

      1. frac-2neg 82.5%

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

      2. distribute-frac-neg 82.5%

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

      3. neg-sub0 82.5%

         \[\leadsto \color{blue}{0 - \frac{x}{-z \cdot \left(z - t\right)}} \]

      4. sub-neg 82.5%

         \[\leadsto \color{blue}{0 + \left(-\frac{x}{-z \cdot \left(z - t\right)}\right)} \]

      5. distribute-frac-neg 82.5%

         \[\leadsto 0 + \color{blue}{\frac{-x}{-z \cdot \left(z - t\right)}} \]

      6. frac-2neg 82.5%

         \[\leadsto 0 + \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]

      7. associate-/r* 94.8%

         \[\leadsto 0 + \color{blue}{\frac{\frac{x}{z}}{z - t}} \]

   6. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{0 + \frac{\frac{x}{z}}{z - t}} \]
   7. Step-by-step derivation

      1. +-lft-identity 94.8%

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

   8. Simplified 94.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 6: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y 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))))
   (if (<= z -1.1e+34)
     t_1
     (if (<= z 5e-42)
       (/ (/ x t) y)
       (if (<= z 6.5e+58) (/ (- x) (* z t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -1.1e+34) {
		tmp = t_1;
	} else if (z <= 5e-42) {
		tmp = (x / t) / y;
	} else if (z <= 6.5e+58) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y 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) :: tmp
    t_1 = x / (z * z)
    if (z <= (-1.1d+34)) then
        tmp = t_1
    else if (z <= 5d-42) then
        tmp = (x / t) / y
    else if (z <= 6.5d+58) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -1.1e+34) {
		tmp = t_1;
	} else if (z <= 5e-42) {
		tmp = (x / t) / y;
	} else if (z <= 6.5e+58) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -1.1e+34:
		tmp = t_1
	elif z <= 5e-42:
		tmp = (x / t) / y
	elif z <= 6.5e+58:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -1.1e+34)
		tmp = t_1;
	elseif (z <= 5e-42)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 6.5e+58)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -1.1e+34)
		tmp = t_1;
	elseif (z <= 5e-42)
		tmp = (x / t) / y;
	elseif (z <= 6.5e+58)
		tmp = -x / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y 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 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+34], t$95$1, If[LessEqual[z, 5e-42], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 6.5e+58], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e34 or 6.49999999999999998e58 < z

   1. Initial program 85.3%

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

      1. remove-double-neg 85.3%

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

      2. sub0-neg 85.3%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 85.3%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 85.3%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 85.3%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 85.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 79.0%

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

   8. Simplified 79.0%

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

   if -1.1000000000000001e34 < z < 5.00000000000000003e-42

   1. Initial program 89.5%

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

      1. remove-double-neg 89.5%

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

      2. sub0-neg 89.5%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 86.2%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.5%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.5%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 95.0%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 95.0%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 95.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 95.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 95.0%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 95.0%

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

      20. distribute-frac-neg 95.0%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around 0 58.4%

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

      1. associate-/l/ 65.1%

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

      2. div-inv 65.0%

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

   6. Applied egg-rr 65.0%

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

      1. associate-*l/ 64.2%

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

      2. un-div-inv 64.4%

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

   8. Applied egg-rr 64.4%

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

   if 5.00000000000000003e-42 < z < 6.49999999999999998e58

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. sub0-neg 99.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 99.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 99.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 99.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.3%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.3%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.3%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.3%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.3%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.3%

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

      20. distribute-frac-neg 96.3%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 60.8%

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

   5. Taylor expanded in z around 0 42.2%

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

      1. *-commutative 42.2%

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

      2. associate-*r/ 42.2%

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

      3. neg-mul-1 42.2%

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

   7. Simplified 42.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 7: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.6e+33)
   (/ 1.0 (* z (/ z x)))
   (if (<= z 3.8e+58) (/ x (* t (- y z))) (* (/ x z) (/ 1.0 z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+33) {
		tmp = 1.0 / (z * (z / x));
	} else if (z <= 3.8e+58) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-3.6d+33)) then
        tmp = 1.0d0 / (z * (z / x))
    else if (z <= 3.8d+58) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.6e+33) {
		tmp = 1.0 / (z * (z / x));
	} else if (z <= 3.8e+58) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.6e+33:
		tmp = 1.0 / (z * (z / x))
	elif z <= 3.8e+58:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.6e+33)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	elseif (z <= 3.8e+58)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.6e+33)
		tmp = 1.0 / (z * (z / x));
	elseif (z <= 3.8e+58)
		tmp = x / (t * (y - z));
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.6e+33], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+58], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6000000000000003e33

   1. Initial program 83.9%

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

      1. remove-double-neg 83.9%

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

      2. sub0-neg 83.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 83.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 83.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 83.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in t around 0 77.7%

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

      1. clear-num 77.7%

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

      2. inv-pow 77.7%

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

      3. metadata-eval 77.7%

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

      4. sqr-pow 64.2%

         \[\leadsto \color{blue}{{\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)}} \]

      5. associate-/l* 63.5%

         \[\leadsto {\color{blue}{\left(\frac{z}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      6. div-inv 63.5%

         \[\leadsto {\color{blue}{\left(z \cdot \frac{1}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      7. clear-num 63.5%

         \[\leadsto {\left(z \cdot \color{blue}{\frac{z - y}{x}}\right)}^{\left(\frac{-1}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      8. metadata-eval 63.5%

         \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      9. metadata-eval 63.5%

         \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{\color{blue}{-0.5}} \cdot {\left(\frac{z \cdot \left(z - y\right)}{x}\right)}^{\left(\frac{-1}{2}\right)} \]

      10. associate-/l* 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(\frac{z}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \]

      11. div-inv 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\color{blue}{\left(z \cdot \frac{1}{\frac{x}{z - y}}\right)}}^{\left(\frac{-1}{2}\right)} \]

      12. clear-num 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \color{blue}{\frac{z - y}{x}}\right)}^{\left(\frac{-1}{2}\right)} \]

      13. metadata-eval 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{\left(\frac{\color{blue}{-1}}{2}\right)} \]

      14. metadata-eval 69.3%

          \[\leadsto {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{\color{blue}{-0.5}} \]

   6. Applied egg-rr 69.3%

      \[\leadsto \color{blue}{{\left(z \cdot \frac{z - y}{x}\right)}^{-0.5} \cdot {\left(z \cdot \frac{z - y}{x}\right)}^{-0.5}} \]
   7. Step-by-step derivation

      1. pow-sqr 89.5%

         \[\leadsto \color{blue}{{\left(z \cdot \frac{z - y}{x}\right)}^{\left(2 \cdot -0.5\right)}} \]

      2. metadata-eval 89.5%

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

      3. unpow-1 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in z around inf 85.1%

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

   if -3.6000000000000003e33 < z < 3.7999999999999999e58

   1. Initial program 91.3%

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

      1. remove-double-neg 91.3%

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

      2. sub0-neg 91.3%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 88.6%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 91.3%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 91.3%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 95.2%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 95.2%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 95.2%

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

      20. distribute-frac-neg 95.2%

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

   3. Simplified 91.3%

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

      1. associate-/l/ 95.6%

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

      2. div-inv 95.6%

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

   5. Applied egg-rr 95.6%

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

   6. Taylor expanded in t around inf 66.8%

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

      1. associate-*r/ 66.8%

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

      2. neg-mul-1 66.8%

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

   8. Simplified 66.8%

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

      1. distribute-frac-neg 66.8%

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

      2. neg-sub0 66.8%

         \[\leadsto \color{blue}{0 - \frac{x}{t \cdot \left(z - y\right)}} \]

      3. sub-neg 66.8%

         \[\leadsto \color{blue}{0 + \left(-\frac{x}{t \cdot \left(z - y\right)}\right)} \]

      4. frac-2neg 66.8%

         \[\leadsto 0 + \left(-\color{blue}{\frac{-x}{-t \cdot \left(z - y\right)}}\right) \]

      5. distribute-frac-neg 66.8%

         \[\leadsto 0 + \color{blue}{\frac{-\left(-x\right)}{-t \cdot \left(z - y\right)}} \]

      6. remove-double-neg 66.8%

         \[\leadsto 0 + \frac{\color{blue}{x}}{-t \cdot \left(z - y\right)} \]

      7. distribute-rgt-neg-in 66.8%

         \[\leadsto 0 + \frac{x}{\color{blue}{t \cdot \left(-\left(z - y\right)\right)}} \]

      8. associate-/r* 70.2%

         \[\leadsto 0 + \color{blue}{\frac{\frac{x}{t}}{-\left(z - y\right)}} \]

      9. neg-sub0 70.2%

         \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{0 - \left(z - y\right)}} \]

      10. sub-neg 70.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \]

      11. +-commutative 70.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \]

      12. associate--r+ 70.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \]

      13. neg-sub0 70.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{\left(-\left(-y\right)\right)} - z} \]

      14. remove-double-neg 70.2%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{y} - z} \]

   10. Applied egg-rr 70.2%

       \[\leadsto \color{blue}{0 + \frac{\frac{x}{t}}{y - z}} \]
   11. Step-by-step derivation

       1. +-lft-identity 70.2%

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

       2. associate-/l/ 66.8%

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

       3. *-commutative 66.8%

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

   12. Simplified 66.8%

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

   if 3.7999999999999999e58 < z

   1. Initial program 86.4%

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

      1. remove-double-neg 86.4%

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

      2. sub0-neg 86.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 86.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 86.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 86.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 86.4%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 83.6%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 83.6%

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

   8. Simplified 83.6%

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

      1. associate-/r* 93.8%

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

      2. div-inv 93.8%

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

   10. Applied egg-rr 93.8%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 8: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.8e-21)
   (/ x (* y (- t z)))
   (if (<= y 3.5e-108) (/ x (* z (- z t))) (/ x (* t (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e-21) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.5e-108) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-7.8d-21)) then
        tmp = x / (y * (t - z))
    else if (y <= 3.5d-108) then
        tmp = x / (z * (z - t))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e-21) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.5e-108) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -7.8e-21:
		tmp = x / (y * (t - z))
	elif y <= 3.5e-108:
		tmp = x / (z * (z - t))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.8e-21)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 3.5e-108)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.8e-21)
		tmp = x / (y * (t - z));
	elseif (y <= 3.5e-108)
		tmp = x / (z * (z - t));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -7.8e-21], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-108], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8000000000000001e-21

   1. Initial program 89.4%

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

      1. remove-double-neg 89.4%

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

      2. sub0-neg 89.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 89.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 97.5%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 97.5%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 97.5%

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

      20. distribute-frac-neg 97.5%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. associate-*r* 82.9%

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

      2. mul-1-neg 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in z around 0 78.6%

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

      1. *-commutative 78.6%

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

      2. mul-1-neg 78.6%

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

      3. distribute-lft-neg-out 78.6%

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

      4. distribute-rgt-out 82.9%

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

      5. +-commutative 82.9%

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

      6. sub-neg 82.9%

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

   9. Simplified 82.9%

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

   if -7.8000000000000001e-21 < y < 3.4999999999999999e-108

   1. Initial program 86.9%

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

      1. remove-double-neg 86.9%

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

      2. sub0-neg 86.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 82.6%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 86.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 86.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in y around 0 75.2%

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

   if 3.4999999999999999e-108 < y

   1. Initial program 91.0%

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

      1. remove-double-neg 91.0%

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

      2. sub0-neg 91.0%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 91.0%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 91.0%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 91.0%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 91.0%

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

      1. associate-/l/ 97.4%

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

      2. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in t around inf 61.9%

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

      1. associate-*r/ 61.9%

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

      2. neg-mul-1 61.9%

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

   8. Simplified 61.9%

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

      1. distribute-frac-neg 61.9%

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

      2. neg-sub0 61.9%

         \[\leadsto \color{blue}{0 - \frac{x}{t \cdot \left(z - y\right)}} \]

      3. sub-neg 61.9%

         \[\leadsto \color{blue}{0 + \left(-\frac{x}{t \cdot \left(z - y\right)}\right)} \]

      4. frac-2neg 61.9%

         \[\leadsto 0 + \left(-\color{blue}{\frac{-x}{-t \cdot \left(z - y\right)}}\right) \]

      5. distribute-frac-neg 61.9%

         \[\leadsto 0 + \color{blue}{\frac{-\left(-x\right)}{-t \cdot \left(z - y\right)}} \]

      6. remove-double-neg 61.9%

         \[\leadsto 0 + \frac{\color{blue}{x}}{-t \cdot \left(z - y\right)} \]

      7. distribute-rgt-neg-in 61.9%

         \[\leadsto 0 + \frac{x}{\color{blue}{t \cdot \left(-\left(z - y\right)\right)}} \]

      8. associate-/r* 65.5%

         \[\leadsto 0 + \color{blue}{\frac{\frac{x}{t}}{-\left(z - y\right)}} \]

      9. neg-sub0 65.5%

         \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{0 - \left(z - y\right)}} \]

      10. sub-neg 65.5%

          \[\leadsto 0 + \frac{\frac{x}{t}}{0 - \color{blue}{\left(z + \left(-y\right)\right)}} \]

      11. +-commutative 65.5%

          \[\leadsto 0 + \frac{\frac{x}{t}}{0 - \color{blue}{\left(\left(-y\right) + z\right)}} \]

      12. associate--r+ 65.5%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{\left(0 - \left(-y\right)\right) - z}} \]

      13. neg-sub0 65.5%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{\left(-\left(-y\right)\right)} - z} \]

      14. remove-double-neg 65.5%

          \[\leadsto 0 + \frac{\frac{x}{t}}{\color{blue}{y} - z} \]

   10. Applied egg-rr 65.5%

       \[\leadsto \color{blue}{0 + \frac{\frac{x}{t}}{y - z}} \]
   11. Step-by-step derivation

       1. +-lft-identity 65.5%

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

       2. associate-/l/ 61.9%

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

       3. *-commutative 61.9%

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

   12. Simplified 61.9%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 9: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-27)
   (/ x (* y (- t z)))
   (if (<= y 2.7e-104) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-27) {
		tmp = x / (y * (t - z));
	} else if (y <= 2.7e-104) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-5.8d-27)) then
        tmp = x / (y * (t - z))
    else if (y <= 2.7d-104) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-27) {
		tmp = x / (y * (t - z));
	} else if (y <= 2.7e-104) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-27:
		tmp = x / (y * (t - z))
	elif y <= 2.7e-104:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-27)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 2.7e-104)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e-27)
		tmp = x / (y * (t - z));
	elseif (y <= 2.7e-104)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-27], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-104], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.80000000000000008e-27

   1. Initial program 89.4%

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

      1. remove-double-neg 89.4%

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

      2. sub0-neg 89.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 89.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 97.5%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 97.5%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 97.5%

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

      20. distribute-frac-neg 97.5%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. associate-*r* 82.9%

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

      2. mul-1-neg 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in z around 0 78.6%

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

      1. *-commutative 78.6%

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

      2. mul-1-neg 78.6%

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

      3. distribute-lft-neg-out 78.6%

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

      4. distribute-rgt-out 82.9%

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

      5. +-commutative 82.9%

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

      6. sub-neg 82.9%

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

   9. Simplified 82.9%

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

   if -5.80000000000000008e-27 < y < 2.6999999999999998e-104

   1. Initial program 87.0%

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

      1. remove-double-neg 87.0%

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

      2. sub0-neg 87.0%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 82.8%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 87.0%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 87.0%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in y around 0 75.4%

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

   if 2.6999999999999998e-104 < y

   1. Initial program 90.9%

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

      1. remove-double-neg 90.9%

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

      2. sub0-neg 90.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 90.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 90.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 90.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 90.9%

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

      1. associate-/l/ 97.4%

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

      2. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in t around inf 61.5%

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

      1. associate-*r/ 61.5%

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

      2. neg-mul-1 61.5%

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

   8. Simplified 61.5%

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

      1. frac-2neg 61.5%

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

      2. remove-double-neg 61.5%

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

      3. *-rgt-identity 61.5%

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

      4. *-commutative 61.5%

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

      5. distribute-rgt-neg-in 61.5%

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

      6. times-frac 67.6%

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

      7. metadata-eval 67.6%

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

      8. metadata-eval 67.6%

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

      9. frac-2neg 67.6%

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

      10. metadata-eval 67.6%

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

   10. Applied egg-rr 67.6%

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

       1. *-commutative 67.6%

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

       2. frac-times 61.5%

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

       3. neg-mul-1 61.5%

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

       4. remove-double-neg 61.5%

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

       5. neg-sub0 61.5%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(0 - \left(z - y\right)\right)}\right)} \]

       6. associate-+l- 61.5%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(\left(0 - z\right) + y\right)}\right)} \]

       7. neg-sub0 61.5%

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

       8. +-commutative 61.5%

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

       9. sub-neg 61.5%

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

       10. distribute-rgt-neg-in 61.5%

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

       11. frac-2neg 61.5%

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

   12. Applied egg-rr 61.5%

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

       1. associate-/r* 65.1%

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

   14. Simplified 65.1%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 10: 79.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e-22)
   (/ (/ x y) (- t z))
   (if (<= y 5.2e-105) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-22) {
		tmp = (x / y) / (t - z);
	} else if (y <= 5.2e-105) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-2.7d-22)) then
        tmp = (x / y) / (t - z)
    else if (y <= 5.2d-105) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-22) {
		tmp = (x / y) / (t - z);
	} else if (y <= 5.2e-105) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e-22:
		tmp = (x / y) / (t - z)
	elif y <= 5.2e-105:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e-22)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 5.2e-105)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e-22)
		tmp = (x / y) / (t - z);
	elseif (y <= 5.2e-105)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e-22], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-105], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7000000000000002e-22

   1. Initial program 89.4%

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

      1. remove-double-neg 89.4%

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

      2. sub0-neg 89.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 89.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 97.5%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 97.5%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 97.5%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 97.5%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 97.5%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 97.5%

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

      20. distribute-frac-neg 97.5%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. associate-*r* 82.9%

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

      2. mul-1-neg 82.9%

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

   6. Simplified 82.9%

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

      1. div-inv 82.8%

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

      2. distribute-lft-neg-out 82.8%

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

      3. distribute-rgt-neg-in 82.8%

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

      4. associate-/r* 84.4%

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

      5. neg-sub0 84.4%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. sub-neg 84.4%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} \]

      7. +-commutative 84.4%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} \]

      8. associate--r+ 84.4%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      9. neg-sub0 84.4%

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

      10. remove-double-neg 84.4%

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

   8. Applied egg-rr 84.4%

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

      1. associate-*r/ 85.7%

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

      2. associate-*r/ 85.7%

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

      3. *-rgt-identity 85.7%

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

   10. Simplified 85.7%

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

   if -2.7000000000000002e-22 < y < 5.1999999999999997e-105

   1. Initial program 87.0%

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

      1. remove-double-neg 87.0%

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

      2. sub0-neg 87.0%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 82.8%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 87.0%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 87.0%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in y around 0 75.4%

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

   if 5.1999999999999997e-105 < y

   1. Initial program 90.9%

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

      1. remove-double-neg 90.9%

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

      2. sub0-neg 90.9%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 90.9%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 90.9%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 90.9%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 90.9%

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

      1. associate-/l/ 97.4%

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

      2. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in t around inf 61.5%

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

      1. associate-*r/ 61.5%

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

      2. neg-mul-1 61.5%

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

   8. Simplified 61.5%

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

      1. frac-2neg 61.5%

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

      2. remove-double-neg 61.5%

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

      3. *-rgt-identity 61.5%

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

      4. *-commutative 61.5%

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

      5. distribute-rgt-neg-in 61.5%

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

      6. times-frac 67.6%

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

      7. metadata-eval 67.6%

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

      8. metadata-eval 67.6%

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

      9. frac-2neg 67.6%

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

      10. metadata-eval 67.6%

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

   10. Applied egg-rr 67.6%

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

       1. *-commutative 67.6%

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

       2. frac-times 61.5%

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

       3. neg-mul-1 61.5%

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

       4. remove-double-neg 61.5%

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

       5. neg-sub0 61.5%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(0 - \left(z - y\right)\right)}\right)} \]

       6. associate-+l- 61.5%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(\left(0 - z\right) + y\right)}\right)} \]

       7. neg-sub0 61.5%

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

       8. +-commutative 61.5%

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

       9. sub-neg 61.5%

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

       10. distribute-rgt-neg-in 61.5%

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

       11. frac-2neg 61.5%

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

   12. Applied egg-rr 61.5%

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

       1. associate-/r* 65.1%

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

   14. Simplified 65.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e+33)
   (/ (/ x y) (- t z))
   (if (<= y 6.8e-107) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+33) {
		tmp = (x / y) / (t - z);
	} else if (y <= 6.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-4.2d+33)) then
        tmp = (x / y) / (t - z)
    else if (y <= 6.8d-107) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+33) {
		tmp = (x / y) / (t - z);
	} else if (y <= 6.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e+33:
		tmp = (x / y) / (t - z)
	elif y <= 6.8e-107:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e+33)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 6.8e-107)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e+33)
		tmp = (x / y) / (t - z);
	elseif (y <= 6.8e-107)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e+33], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-107], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000001e33

   1. Initial program 89.1%

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

      1. remove-double-neg 89.1%

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

      2. sub0-neg 89.1%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 89.1%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.1%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.1%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 97.0%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 97.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 97.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 97.0%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 97.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 97.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 97.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 97.0%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 97.0%

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

      20. distribute-frac-neg 97.0%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. associate-*r* 87.5%

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

      2. mul-1-neg 87.5%

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

   6. Simplified 87.5%

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

      1. div-inv 87.5%

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

      2. distribute-lft-neg-out 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

      4. associate-/r* 89.5%

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

      5. neg-sub0 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. sub-neg 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} \]

      7. +-commutative 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} \]

      8. associate--r+ 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      9. neg-sub0 89.5%

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

      10. remove-double-neg 89.5%

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

   8. Applied egg-rr 89.5%

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

      1. associate-*r/ 90.8%

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

      2. associate-*r/ 90.8%

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

      3. *-rgt-identity 90.8%

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

   10. Simplified 90.8%

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

   if -4.2000000000000001e33 < y < 6.79999999999999989e-107

   1. Initial program 87.3%

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

      1. remove-double-neg 87.3%

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

      2. sub0-neg 87.3%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 83.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 87.3%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 87.3%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 97.2%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 97.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 97.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 97.2%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 97.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 97.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 97.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 97.2%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 97.2%

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

      20. distribute-frac-neg 97.2%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in y around 0 72.4%

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

      1. frac-2neg 72.4%

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

      2. distribute-frac-neg 72.4%

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

      3. neg-sub0 72.4%

         \[\leadsto \color{blue}{0 - \frac{x}{-z \cdot \left(z - t\right)}} \]

      4. sub-neg 72.4%

         \[\leadsto \color{blue}{0 + \left(-\frac{x}{-z \cdot \left(z - t\right)}\right)} \]

      5. distribute-frac-neg 72.4%

         \[\leadsto 0 + \color{blue}{\frac{-x}{-z \cdot \left(z - t\right)}} \]

      6. frac-2neg 72.4%

         \[\leadsto 0 + \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]

      7. associate-/r* 81.6%

         \[\leadsto 0 + \color{blue}{\frac{\frac{x}{z}}{z - t}} \]

   6. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{0 + \frac{\frac{x}{z}}{z - t}} \]
   7. Step-by-step derivation

      1. +-lft-identity 81.6%

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

   8. Simplified 81.6%

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

   if 6.79999999999999989e-107 < y

   1. Initial program 91.0%

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

      1. remove-double-neg 91.0%

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

      2. sub0-neg 91.0%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 91.0%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 91.0%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 91.0%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 91.0%

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

      1. associate-/l/ 97.4%

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

      2. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in t around inf 61.9%

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

      1. associate-*r/ 61.9%

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

      2. neg-mul-1 61.9%

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

   8. Simplified 61.9%

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

      1. frac-2neg 61.9%

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

      2. remove-double-neg 61.9%

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

      3. *-rgt-identity 61.9%

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

      4. *-commutative 61.9%

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

      5. distribute-rgt-neg-in 61.9%

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

      6. times-frac 68.0%

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

      7. metadata-eval 68.0%

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

      8. metadata-eval 68.0%

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

      9. frac-2neg 68.0%

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

      10. metadata-eval 68.0%

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

   10. Applied egg-rr 68.0%

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

       1. *-commutative 68.0%

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

       2. frac-times 61.9%

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

       3. neg-mul-1 61.9%

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

       4. remove-double-neg 61.9%

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

       5. neg-sub0 61.9%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(0 - \left(z - y\right)\right)}\right)} \]

       6. associate-+l- 61.9%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(\left(0 - z\right) + y\right)}\right)} \]

       7. neg-sub0 61.9%

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

       8. +-commutative 61.9%

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

       9. sub-neg 61.9%

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

       10. distribute-rgt-neg-in 61.9%

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

       11. frac-2neg 61.9%

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

   12. Applied egg-rr 61.9%

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

       1. associate-/r* 65.5%

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

   14. Simplified 65.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.06e+33)
   (/ (/ x (- t z)) y)
   (if (<= y 9.8e-107) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e+33) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 9.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-2.06d+33)) then
        tmp = (x / (t - z)) / y
    else if (y <= 9.8d-107) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e+33) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 9.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.06e+33:
		tmp = (x / (t - z)) / y
	elif y <= 9.8e-107:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.06e+33)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 9.8e-107)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.06e+33)
		tmp = (x / (t - z)) / y;
	elseif (y <= 9.8e-107)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.06e+33], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 9.8e-107], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05999999999999993e33

   1. Initial program 89.1%

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

      1. remove-double-neg 89.1%

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

      2. sub0-neg 89.1%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 89.1%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 89.1%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 89.1%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 97.0%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 97.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 97.0%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 97.0%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 97.0%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 97.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 97.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 97.0%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 97.0%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 97.0%

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

      20. distribute-frac-neg 97.0%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in y around inf 87.5%

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

      1. associate-*r* 87.5%

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

      2. mul-1-neg 87.5%

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

   6. Simplified 87.5%

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

      1. div-inv 87.5%

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

      2. distribute-lft-neg-out 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

      4. associate-/r* 89.5%

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

      5. neg-sub0 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{0 - \left(z - t\right)}} \]

      6. sub-neg 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} \]

      7. +-commutative 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} \]

      8. associate--r+ 89.5%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      9. neg-sub0 89.5%

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

      10. remove-double-neg 89.5%

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

   8. Applied egg-rr 89.5%

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

      1. associate-*r/ 90.8%

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

      2. associate-*r/ 90.8%

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

      3. *-rgt-identity 90.8%

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

   10. Simplified 90.8%

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

       1. div-inv 90.8%

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

       2. div-inv 90.8%

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

       3. associate-*l* 89.4%

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

       4. un-div-inv 89.5%

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

   12. Applied egg-rr 89.5%

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

       1. associate-*r/ 90.8%

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

       2. associate-*l/ 92.1%

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

       3. associate-*r/ 92.1%

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

       4. *-rgt-identity 92.1%

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

   14. Simplified 92.1%

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

   if -2.05999999999999993e33 < y < 9.79999999999999959e-107

   1. Initial program 87.3%

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

      1. remove-double-neg 87.3%

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

      2. sub0-neg 87.3%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 83.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 87.3%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 87.3%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 97.2%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 97.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 97.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 97.2%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 97.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 97.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 97.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 97.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 97.2%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 97.2%

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

      20. distribute-frac-neg 97.2%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in y around 0 72.4%

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

      1. frac-2neg 72.4%

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

      2. distribute-frac-neg 72.4%

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

      3. neg-sub0 72.4%

         \[\leadsto \color{blue}{0 - \frac{x}{-z \cdot \left(z - t\right)}} \]

      4. sub-neg 72.4%

         \[\leadsto \color{blue}{0 + \left(-\frac{x}{-z \cdot \left(z - t\right)}\right)} \]

      5. distribute-frac-neg 72.4%

         \[\leadsto 0 + \color{blue}{\frac{-x}{-z \cdot \left(z - t\right)}} \]

      6. frac-2neg 72.4%

         \[\leadsto 0 + \color{blue}{\frac{x}{z \cdot \left(z - t\right)}} \]

      7. associate-/r* 81.6%

         \[\leadsto 0 + \color{blue}{\frac{\frac{x}{z}}{z - t}} \]

   6. Applied egg-rr 81.6%

      \[\leadsto \color{blue}{0 + \frac{\frac{x}{z}}{z - t}} \]
   7. Step-by-step derivation

      1. +-lft-identity 81.6%

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

   8. Simplified 81.6%

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

   if 9.79999999999999959e-107 < y

   1. Initial program 91.0%

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

      1. remove-double-neg 91.0%

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

      2. sub0-neg 91.0%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 91.0%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 91.0%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 91.0%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 96.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 96.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 96.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 96.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 96.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 96.9%

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

      20. distribute-frac-neg 96.9%

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

   3. Simplified 91.0%

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

      1. associate-/l/ 97.4%

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

      2. div-inv 97.2%

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

   5. Applied egg-rr 97.2%

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

   6. Taylor expanded in t around inf 61.9%

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

      1. associate-*r/ 61.9%

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

      2. neg-mul-1 61.9%

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

   8. Simplified 61.9%

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

      1. frac-2neg 61.9%

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

      2. remove-double-neg 61.9%

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

      3. *-rgt-identity 61.9%

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

      4. *-commutative 61.9%

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

      5. distribute-rgt-neg-in 61.9%

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

      6. times-frac 68.0%

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

      7. metadata-eval 68.0%

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

      8. metadata-eval 68.0%

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

      9. frac-2neg 68.0%

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

      10. metadata-eval 68.0%

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

   10. Applied egg-rr 68.0%

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

       1. *-commutative 68.0%

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

       2. frac-times 61.9%

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

       3. neg-mul-1 61.9%

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

       4. remove-double-neg 61.9%

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

       5. neg-sub0 61.9%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(0 - \left(z - y\right)\right)}\right)} \]

       6. associate-+l- 61.9%

          \[\leadsto \frac{-x}{t \cdot \left(-\color{blue}{\left(\left(0 - z\right) + y\right)}\right)} \]

       7. neg-sub0 61.9%

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

       8. +-commutative 61.9%

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

       9. sub-neg 61.9%

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

       10. distribute-rgt-neg-in 61.9%

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

       11. frac-2neg 61.9%

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

   12. Applied egg-rr 61.9%

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

       1. associate-/r* 65.5%

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

   14. Simplified 65.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 13: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+33} \lor \neg \left(z \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7e+33) (not (<= z 6.8e+55))) (/ x (* z z)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e+33) || !(z <= 6.8e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-7d+33)) .or. (.not. (z <= 6.8d+55))) then
        tmp = x / (z * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e+33) || !(z <= 6.8e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -7e+33) or not (z <= 6.8e+55):
		tmp = x / (z * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7e+33) || !(z <= 6.8e+55))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7e+33) || ~((z <= 6.8e+55)))
		tmp = x / (z * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7e+33], N[Not[LessEqual[z, 6.8e+55]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0000000000000002e33 or 6.7999999999999996e55 < z

   1. Initial program 85.4%

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

      1. remove-double-neg 85.4%

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

      2. sub0-neg 85.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 85.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 85.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 85.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 85.4%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 78.3%

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

   8. Simplified 78.3%

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

   if -7.0000000000000002e33 < z < 6.7999999999999996e55

   1. Initial program 91.3%

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

      1. remove-double-neg 91.3%

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

      2. sub0-neg 91.3%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 88.5%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 91.3%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 91.3%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 95.2%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 95.2%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 95.2%

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

      20. distribute-frac-neg 95.2%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in z around 0 53.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+33} \lor \neg \left(z \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 14: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+33} \lor \neg \left(z \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e+33) (not (<= z 6.8e+55))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+33) || !(z <= 6.8e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y 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+33)) .or. (.not. (z <= 6.8d+55))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+33) || !(z <= 6.8e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e+33) or not (z <= 6.8e+55):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e+33) || !(z <= 6.8e+55))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.9e+33) || ~((z <= 6.8e+55)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e+33], N[Not[LessEqual[z, 6.8e+55]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9000000000000002e33 or 6.7999999999999996e55 < z

   1. Initial program 85.4%

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

      1. remove-double-neg 85.4%

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

      2. sub0-neg 85.4%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 85.4%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 85.4%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 85.4%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 99.9%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 99.9%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 99.9%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 99.9%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 99.9%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 99.9%

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

      20. distribute-frac-neg 99.9%

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

   3. Simplified 85.4%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 78.3%

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

   8. Simplified 78.3%

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

   if -3.9000000000000002e33 < z < 6.7999999999999996e55

   1. Initial program 91.3%

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

      1. remove-double-neg 91.3%

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

      2. sub0-neg 91.3%

         \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      3. div-sub 88.5%

         \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

      4. div0 91.3%

         \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      5. div0 91.3%

         \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

      6. associate-/r* 95.2%

         \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

      7. distribute-frac-neg 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

      8. neg-mul-1 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

      9. sub-neg 95.2%

         \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

      10. +-commutative 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

      11. neg-sub0 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

      12. associate-+l- 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

      13. sub0-neg 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

      14. mul-1-neg 95.2%

          \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

      15. times-frac 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

      16. metadata-eval 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

      17. *-lft-identity 95.2%

          \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

      18. div-sub 95.2%

          \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

      19. neg-sub0 95.2%

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

      20. distribute-frac-neg 95.2%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in z around 0 53.3%

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

      1. associate-/l/ 58.9%

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

      2. div-inv 58.8%

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

   6. Applied egg-rr 58.8%

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

      1. associate-*l/ 60.0%

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

      2. un-div-inv 60.1%

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

   8. Applied egg-rr 60.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+33} \lor \neg \left(z \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 38.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y 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 88.9%

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

   1. remove-double-neg 88.9%

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

   2. sub0-neg 88.9%

      \[\leadsto \frac{\color{blue}{0 - \left(-x\right)}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   3. div-sub 87.3%

      \[\leadsto \color{blue}{\frac{0}{\left(y - z\right) \cdot \left(t - z\right)} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)}} \]

   4. div0 88.9%

      \[\leadsto \color{blue}{0} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   5. div0 88.9%

      \[\leadsto \color{blue}{\frac{0}{z - t}} - \frac{-x}{\left(y - z\right) \cdot \left(t - z\right)} \]

   6. associate-/r* 97.1%

      \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{-x}{y - z}}{t - z}} \]

   7. distribute-frac-neg 97.1%

      \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-\frac{x}{y - z}}}{t - z} \]

   8. neg-mul-1 97.1%

      \[\leadsto \frac{0}{z - t} - \frac{\color{blue}{-1 \cdot \frac{x}{y - z}}}{t - z} \]

   9. sub-neg 97.1%

      \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{t + \left(-z\right)}} \]

   10. +-commutative 97.1%

       \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(-z\right) + t}} \]

   11. neg-sub0 97.1%

       \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{\left(0 - z\right)} + t} \]

   12. associate-+l- 97.1%

       \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{0 - \left(z - t\right)}} \]

   13. sub0-neg 97.1%

       \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-\left(z - t\right)}} \]

   14. mul-1-neg 97.1%

       \[\leadsto \frac{0}{z - t} - \frac{-1 \cdot \frac{x}{y - z}}{\color{blue}{-1 \cdot \left(z - t\right)}} \]

   15. times-frac 97.1%

       \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{-1}{-1} \cdot \frac{\frac{x}{y - z}}{z - t}} \]

   16. metadata-eval 97.1%

       \[\leadsto \frac{0}{z - t} - \color{blue}{1} \cdot \frac{\frac{x}{y - z}}{z - t} \]

   17. *-lft-identity 97.1%

       \[\leadsto \frac{0}{z - t} - \color{blue}{\frac{\frac{x}{y - z}}{z - t}} \]

   18. div-sub 97.1%

       \[\leadsto \color{blue}{\frac{0 - \frac{x}{y - z}}{z - t}} \]

   19. neg-sub0 97.1%

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

   20. distribute-frac-neg 97.1%

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

3. Simplified 88.9%

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

4. Taylor expanded in z around 0 40.7%

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

5. Final simplification 40.7%

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

Developer target: 87.2% 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 2023297 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (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))))