Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3

Percentage Accurate: 84.4% → 96.2%

Time: 14.1s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

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(Float64(x * 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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 84.4% accurate, 1.0× speedup

Math

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

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(Float64(x * 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[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+81} \lor \neg \left(z \leq 6.4 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.6e+81) (not (<= z 6.4e-90)))
   (/ x (/ (- t z) (- y z)))
   (* (/ x (- z t)) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+81) || !(z <= 6.4e-90)) {
		tmp = x / ((t - z) / (y - z));
	} else {
		tmp = (x / (z - t)) * (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.6d+81)) .or. (.not. (z <= 6.4d-90))) then
        tmp = x / ((t - z) / (y - z))
    else
        tmp = (x / (z - t)) * (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+81) || !(z <= 6.4e-90)) {
		tmp = x / ((t - z) / (y - z));
	} else {
		tmp = (x / (z - t)) * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.6e+81) or not (z <= 6.4e-90):
		tmp = x / ((t - z) / (y - z))
	else:
		tmp = (x / (z - t)) * (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.6e+81) || !(z <= 6.4e-90))
		tmp = Float64(x / Float64(Float64(t - z) / Float64(y - z)));
	else
		tmp = Float64(Float64(x / Float64(z - t)) * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.6e+81) || ~((z <= 6.4e-90)))
		tmp = x / ((t - z) / (y - z));
	else
		tmp = (x / (z - t)) * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.6e+81], N[Not[LessEqual[z, 6.4e-90]], $MachinePrecision]], N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6000000000000003e81 or 6.40000000000000014e-90 < z

   1. Initial program 79.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -8.6000000000000003e81 < z < 6.40000000000000014e-90

   1. Initial program 90.9%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in x around 0 90.9%

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

      1. remove-double-neg 90.9%

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

      2. distribute-neg-frac2 90.9%

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

      3. *-commutative 90.9%

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

      4. associate-/l* 97.4%

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

      5. distribute-lft-neg-out 97.4%

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

      6. neg-sub0 97.4%

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

      7. associate--r- 97.4%

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

      8. neg-sub0 97.4%

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

      9. +-commutative 97.4%

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

      10. sub-neg 97.4%

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

      11. neg-sub0 97.4%

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

      12. associate--r- 97.4%

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

      13. neg-sub0 97.4%

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

      14. +-commutative 97.4%

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

      15. sub-neg 97.4%

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

      16. *-commutative 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+81} \lor \neg \left(z \leq 6.4 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{x}{\frac{t - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-180}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+148} \lor \neg \left(z \leq 2.2 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x t))))
   (if (<= z -1.05e-106)
     (* x (/ (- z y) z))
     (if (<= z -9.5e-172)
       t_1
       (if (<= z -3e-180)
         (/ (* x (- y)) z)
         (if (<= z 5.4e+14)
           t_1
           (if (<= z 1.3e+97)
             (* (- z y) (/ x z))
             (if (<= z 1.55e+97)
               (* z (/ x (- t)))
               (if (or (<= z 2.15e+148) (not (<= z 2.2e+148)))
                 (* x (- 1.0 (/ y z)))
                 (* x (/ (- z) t)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 5.4e+14) {
		tmp = t_1;
	} else if (z <= 1.3e+97) {
		tmp = (z - y) * (x / z);
	} else if (z <= 1.55e+97) {
		tmp = z * (x / -t);
	} else if ((z <= 2.15e+148) || !(z <= 2.2e+148)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (x / t)
    if (z <= (-1.05d-106)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-9.5d-172)) then
        tmp = t_1
    else if (z <= (-3d-180)) then
        tmp = (x * -y) / z
    else if (z <= 5.4d+14) then
        tmp = t_1
    else if (z <= 1.3d+97) then
        tmp = (z - y) * (x / z)
    else if (z <= 1.55d+97) then
        tmp = z * (x / -t)
    else if ((z <= 2.15d+148) .or. (.not. (z <= 2.2d+148))) then
        tmp = x * (1.0d0 - (y / z))
    else
        tmp = x * (-z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 5.4e+14) {
		tmp = t_1;
	} else if (z <= 1.3e+97) {
		tmp = (z - y) * (x / z);
	} else if (z <= 1.55e+97) {
		tmp = z * (x / -t);
	} else if ((z <= 2.15e+148) || !(z <= 2.2e+148)) {
		tmp = x * (1.0 - (y / z));
	} else {
		tmp = x * (-z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (x / t)
	tmp = 0
	if z <= -1.05e-106:
		tmp = x * ((z - y) / z)
	elif z <= -9.5e-172:
		tmp = t_1
	elif z <= -3e-180:
		tmp = (x * -y) / z
	elif z <= 5.4e+14:
		tmp = t_1
	elif z <= 1.3e+97:
		tmp = (z - y) * (x / z)
	elif z <= 1.55e+97:
		tmp = z * (x / -t)
	elif (z <= 2.15e+148) or not (z <= 2.2e+148):
		tmp = x * (1.0 - (y / z))
	else:
		tmp = x * (-z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / t))
	tmp = 0.0
	if (z <= -1.05e-106)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 5.4e+14)
		tmp = t_1;
	elseif (z <= 1.3e+97)
		tmp = Float64(Float64(z - y) * Float64(x / z));
	elseif (z <= 1.55e+97)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif ((z <= 2.15e+148) || !(z <= 2.2e+148))
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	else
		tmp = Float64(x * Float64(Float64(-z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (x / t);
	tmp = 0.0;
	if (z <= -1.05e-106)
		tmp = x * ((z - y) / z);
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = (x * -y) / z;
	elseif (z <= 5.4e+14)
		tmp = t_1;
	elseif (z <= 1.3e+97)
		tmp = (z - y) * (x / z);
	elseif (z <= 1.55e+97)
		tmp = z * (x / -t);
	elseif ((z <= 2.15e+148) || ~((z <= 2.2e+148)))
		tmp = x * (1.0 - (y / z));
	else
		tmp = x * (-z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-106], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-172], t$95$1, If[LessEqual[z, -3e-180], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.4e+14], t$95$1, If[LessEqual[z, 1.3e+97], N[(N[(z - y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+97], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.15e+148], N[Not[LessEqual[z, 2.2e+148]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[((-z) / t), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -1.05000000000000002e-106

   1. Initial program 84.1%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0 84.1%

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

      1. remove-double-neg 84.1%

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

      2. distribute-neg-frac2 84.1%

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

      3. *-commutative 84.1%

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

      4. associate-/l* 78.1%

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

      5. distribute-lft-neg-out 78.1%

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

      6. neg-sub0 78.1%

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

      7. associate--r- 78.1%

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

      8. neg-sub0 78.1%

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

      9. +-commutative 78.1%

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

      10. sub-neg 78.1%

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

      11. neg-sub0 78.1%

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

      12. associate--r- 78.1%

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

      13. neg-sub0 78.1%

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

      14. +-commutative 78.1%

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

      15. sub-neg 78.1%

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

      16. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in t around 0 59.1%

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

      1. associate-/l* 73.6%

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

   10. Simplified 73.6%

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

   if -1.05000000000000002e-106 < z < -9.50000000000000053e-172 or -3.0000000000000001e-180 < z < 5.4e14

   1. Initial program 91.6%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

      1. clear-num 89.8%

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

      2. un-div-inv 89.8%

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

   6. Applied egg-rr 89.8%

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

   7. Taylor expanded in t around inf 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-/l* 82.4%

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

   9. Simplified 82.4%

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

   if -9.50000000000000053e-172 < z < -3.0000000000000001e-180

   1. Initial program 99.8%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. remove-double-neg 99.8%

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

      2. distribute-neg-frac2 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate--r- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. neg-sub0 100.0%

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

      12. associate--r- 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. sub-neg 100.0%

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

      16. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 99.8%

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

      1. associate-/l* 33.0%

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

   10. Simplified 33.0%

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

   11. Taylor expanded in z around 0 99.8%

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

       1. associate-*r/ 99.8%

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

       2. neg-mul-1 99.8%

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

       3. distribute-rgt-neg-in 99.8%

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

   13. Simplified 99.8%

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

   if 5.4e14 < z < 1.3e97

   1. Initial program 77.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 77.5%

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

      1. remove-double-neg 77.5%

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

      2. distribute-neg-frac2 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. neg-sub0 99.7%

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

      7. associate--r- 99.7%

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

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-sub0 99.7%

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

      12. associate--r- 99.7%

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

      13. neg-sub0 99.7%

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

      14. +-commutative 99.7%

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

      15. sub-neg 99.7%

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

      16. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 63.0%

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

   if 1.3e97 < z < 1.54999999999999991e97

   1. Initial program 100.0%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

      1. clear-num 98.4%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in t around inf 100.0%

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

       1. associate-*r/ 100.0%

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

       2. mul-1-neg 100.0%

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

       3. distribute-rgt-neg-out 100.0%

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

       4. associate-*l/ 100.0%

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

   12. Simplified 100.0%

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

   if 1.54999999999999991e97 < z < 2.1500000000000001e148 or 2.1999999999999999e148 < z

   1. Initial program 72.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. associate-/l* 83.2%

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

      3. distribute-rgt-neg-in 83.2%

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

      4. distribute-frac-neg 83.2%

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

      5. neg-sub0 83.2%

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

      6. associate--r- 83.2%

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

      7. neg-sub0 83.2%

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

      8. +-commutative 83.2%

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

      9. sub-neg 83.2%

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

      10. div-sub 83.2%

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

      11. *-inverses 83.2%

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

   7. Simplified 83.2%

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

   if 2.1500000000000001e148 < z < 2.1999999999999999e148

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac2 100.0%

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

   10. Simplified 100.0%

       \[\leadsto x \cdot \color{blue}{\frac{z}{-t}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-172}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-180}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+14}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+97}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+148} \lor \neg \left(z \leq 2.2 \cdot 10^{+148}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 56.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-57}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-171}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+90)
   x
   (if (<= z -5.5e-15)
     (* y (/ x t))
     (if (<= z -9e-57)
       (/ (* z x) z)
       (if (<= z -1.15e-171)
         (/ (* z (- x)) t)
         (if (<= z -6.8e-176)
           (* y (/ x (- z)))
           (if (<= z 6e+15)
             (/ y (/ t x))
             (if (<= z 4.1e+70)
               x
               (if (<= z 9.5e+83) (/ y (/ z (- x))) x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+90) {
		tmp = x;
	} else if (z <= -5.5e-15) {
		tmp = y * (x / t);
	} else if (z <= -9e-57) {
		tmp = (z * x) / z;
	} else if (z <= -1.15e-171) {
		tmp = (z * -x) / t;
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= 6e+15) {
		tmp = y / (t / x);
	} else if (z <= 4.1e+70) {
		tmp = x;
	} else if (z <= 9.5e+83) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.2d+90)) then
        tmp = x
    else if (z <= (-5.5d-15)) then
        tmp = y * (x / t)
    else if (z <= (-9d-57)) then
        tmp = (z * x) / z
    else if (z <= (-1.15d-171)) then
        tmp = (z * -x) / t
    else if (z <= (-6.8d-176)) then
        tmp = y * (x / -z)
    else if (z <= 6d+15) then
        tmp = y / (t / x)
    else if (z <= 4.1d+70) then
        tmp = x
    else if (z <= 9.5d+83) then
        tmp = y / (z / -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+90) {
		tmp = x;
	} else if (z <= -5.5e-15) {
		tmp = y * (x / t);
	} else if (z <= -9e-57) {
		tmp = (z * x) / z;
	} else if (z <= -1.15e-171) {
		tmp = (z * -x) / t;
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= 6e+15) {
		tmp = y / (t / x);
	} else if (z <= 4.1e+70) {
		tmp = x;
	} else if (z <= 9.5e+83) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+90:
		tmp = x
	elif z <= -5.5e-15:
		tmp = y * (x / t)
	elif z <= -9e-57:
		tmp = (z * x) / z
	elif z <= -1.15e-171:
		tmp = (z * -x) / t
	elif z <= -6.8e-176:
		tmp = y * (x / -z)
	elif z <= 6e+15:
		tmp = y / (t / x)
	elif z <= 4.1e+70:
		tmp = x
	elif z <= 9.5e+83:
		tmp = y / (z / -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+90)
		tmp = x;
	elseif (z <= -5.5e-15)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= -9e-57)
		tmp = Float64(Float64(z * x) / z);
	elseif (z <= -1.15e-171)
		tmp = Float64(Float64(z * Float64(-x)) / t);
	elseif (z <= -6.8e-176)
		tmp = Float64(y * Float64(x / Float64(-z)));
	elseif (z <= 6e+15)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 4.1e+70)
		tmp = x;
	elseif (z <= 9.5e+83)
		tmp = Float64(y / Float64(z / Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+90)
		tmp = x;
	elseif (z <= -5.5e-15)
		tmp = y * (x / t);
	elseif (z <= -9e-57)
		tmp = (z * x) / z;
	elseif (z <= -1.15e-171)
		tmp = (z * -x) / t;
	elseif (z <= -6.8e-176)
		tmp = y * (x / -z);
	elseif (z <= 6e+15)
		tmp = y / (t / x);
	elseif (z <= 4.1e+70)
		tmp = x;
	elseif (z <= 9.5e+83)
		tmp = y / (z / -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+90], x, If[LessEqual[z, -5.5e-15], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-57], N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.15e-171], N[(N[(z * (-x)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -6.8e-176], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+15], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+70], x, If[LessEqual[z, 9.5e+83], N[(y / N[(z / (-x)), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.1999999999999999e90 or 6e15 < z < 4.1000000000000002e70 or 9.5000000000000002e83 < z

   1. Initial program 75.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 67.7%

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

   if -2.1999999999999999e90 < z < -5.5000000000000002e-15

   1. Initial program 90.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 38.4%

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

      1. associate-/r/ 38.4%

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

   9. Applied egg-rr 38.4%

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

   if -5.5000000000000002e-15 < z < -8.99999999999999945e-57

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in z around inf 55.8%

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

   if -8.99999999999999945e-57 < z < -1.14999999999999989e-171

   1. Initial program 97.8%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

   5. Taylor expanded in t around inf 66.4%

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

      1. associate-/l* 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in y around 0 52.9%

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

      1. associate-*r/ 52.9%

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

      2. neg-mul-1 52.9%

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

      3. *-commutative 52.9%

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

      4. distribute-lft-neg-in 52.9%

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

   10. Simplified 52.9%

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

   if -1.14999999999999989e-171 < z < -6.7999999999999994e-176

   1. Initial program 99.7%

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

      1. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around 0 99.7%

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

      1. remove-double-neg 99.7%

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

      2. distribute-neg-frac2 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate--r- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. neg-sub0 100.0%

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

      12. associate--r- 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. sub-neg 100.0%

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

      16. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 99.7%

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

      1. associate-/l* 43.9%

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

   10. Simplified 43.9%

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

   11. Taylor expanded in z around 0 99.7%

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

       1. associate-*r/ 99.7%

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

       2. neg-mul-1 99.7%

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

       3. distribute-rgt-neg-in 99.7%

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

   13. Simplified 99.7%

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

   14. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-*l/ 100.0%

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

   16. Simplified 100.0%

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

   if -6.7999999999999994e-176 < z < 6e15

   1. Initial program 90.8%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. clear-num 90.8%

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

      2. un-div-inv 90.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in z around 0 69.1%

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

      1. associate-/r/ 70.5%

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

   9. Applied egg-rr 70.5%

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

       1. *-commutative 70.5%

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

       2. clear-num 70.5%

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

       3. un-div-inv 70.5%

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

   11. Applied egg-rr 70.5%

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

   if 4.1000000000000002e70 < z < 9.5000000000000002e83

   1. Initial program 62.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 62.3%

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

      1. remove-double-neg 62.3%

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

      2. distribute-neg-frac2 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. neg-sub0 99.7%

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

      7. associate--r- 99.7%

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

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-sub0 99.7%

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

      12. associate--r- 99.7%

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

      13. neg-sub0 99.7%

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

      14. +-commutative 99.7%

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

      15. sub-neg 99.7%

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

      16. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in t around 0 23.7%

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

      1. associate-/l* 42.3%

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

   10. Simplified 42.3%

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

   11. Taylor expanded in z around 0 33.0%

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

       1. associate-*r/ 33.0%

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

       2. neg-mul-1 33.0%

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

       3. distribute-rgt-neg-in 33.0%

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

   13. Simplified 33.0%

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

   14. Taylor expanded in x around 0 33.0%

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

       1. mul-1-neg 33.0%

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

       2. associate-*l/ 51.6%

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

   16. Simplified 51.6%

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

       1. *-commutative 51.6%

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

       2. clear-num 51.6%

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

       3. un-div-inv 51.6%

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

   18. Applied egg-rr 51.6%

       \[\leadsto -\color{blue}{\frac{y}{\frac{z}{x}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-57}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-171}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-158}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 33000000000000:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+90)
   x
   (if (<= z -5.2e-14)
     (* y (/ x t))
     (if (<= z -1.15e-55)
       (/ (* z x) z)
       (if (<= z -1.5e-111)
         (/ (* x (- y)) z)
         (if (<= z -5.5e-158)
           (* z (/ x (- t)))
           (if (<= z 33000000000000.0)
             (/ y (/ t x))
             (if (<= z 9e+74) x (if (<= z 3.4e+84) (/ y (/ z (- x))) x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+90) {
		tmp = x;
	} else if (z <= -5.2e-14) {
		tmp = y * (x / t);
	} else if (z <= -1.15e-55) {
		tmp = (z * x) / z;
	} else if (z <= -1.5e-111) {
		tmp = (x * -y) / z;
	} else if (z <= -5.5e-158) {
		tmp = z * (x / -t);
	} else if (z <= 33000000000000.0) {
		tmp = y / (t / x);
	} else if (z <= 9e+74) {
		tmp = x;
	} else if (z <= 3.4e+84) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.2d+90)) then
        tmp = x
    else if (z <= (-5.2d-14)) then
        tmp = y * (x / t)
    else if (z <= (-1.15d-55)) then
        tmp = (z * x) / z
    else if (z <= (-1.5d-111)) then
        tmp = (x * -y) / z
    else if (z <= (-5.5d-158)) then
        tmp = z * (x / -t)
    else if (z <= 33000000000000.0d0) then
        tmp = y / (t / x)
    else if (z <= 9d+74) then
        tmp = x
    else if (z <= 3.4d+84) then
        tmp = y / (z / -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+90) {
		tmp = x;
	} else if (z <= -5.2e-14) {
		tmp = y * (x / t);
	} else if (z <= -1.15e-55) {
		tmp = (z * x) / z;
	} else if (z <= -1.5e-111) {
		tmp = (x * -y) / z;
	} else if (z <= -5.5e-158) {
		tmp = z * (x / -t);
	} else if (z <= 33000000000000.0) {
		tmp = y / (t / x);
	} else if (z <= 9e+74) {
		tmp = x;
	} else if (z <= 3.4e+84) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+90:
		tmp = x
	elif z <= -5.2e-14:
		tmp = y * (x / t)
	elif z <= -1.15e-55:
		tmp = (z * x) / z
	elif z <= -1.5e-111:
		tmp = (x * -y) / z
	elif z <= -5.5e-158:
		tmp = z * (x / -t)
	elif z <= 33000000000000.0:
		tmp = y / (t / x)
	elif z <= 9e+74:
		tmp = x
	elif z <= 3.4e+84:
		tmp = y / (z / -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+90)
		tmp = x;
	elseif (z <= -5.2e-14)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= -1.15e-55)
		tmp = Float64(Float64(z * x) / z);
	elseif (z <= -1.5e-111)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= -5.5e-158)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (z <= 33000000000000.0)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 9e+74)
		tmp = x;
	elseif (z <= 3.4e+84)
		tmp = Float64(y / Float64(z / Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+90)
		tmp = x;
	elseif (z <= -5.2e-14)
		tmp = y * (x / t);
	elseif (z <= -1.15e-55)
		tmp = (z * x) / z;
	elseif (z <= -1.5e-111)
		tmp = (x * -y) / z;
	elseif (z <= -5.5e-158)
		tmp = z * (x / -t);
	elseif (z <= 33000000000000.0)
		tmp = y / (t / x);
	elseif (z <= 9e+74)
		tmp = x;
	elseif (z <= 3.4e+84)
		tmp = y / (z / -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+90], x, If[LessEqual[z, -5.2e-14], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-55], N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.5e-111], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -5.5e-158], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 33000000000000.0], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+74], x, If[LessEqual[z, 3.4e+84], N[(y / N[(z / (-x)), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.1999999999999999e90 or 3.3e13 < z < 8.9999999999999999e74 or 3.3999999999999998e84 < z

   1. Initial program 75.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 67.7%

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

   if -2.1999999999999999e90 < z < -5.19999999999999993e-14

   1. Initial program 90.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 38.4%

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

      1. associate-/r/ 38.4%

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

   9. Applied egg-rr 38.4%

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

   if -5.19999999999999993e-14 < z < -1.15000000000000006e-55

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in z around inf 55.8%

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

   if -1.15000000000000006e-55 < z < -1.50000000000000004e-111

   1. Initial program 95.9%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in x around 0 95.9%

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

      1. remove-double-neg 95.9%

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

      2. distribute-neg-frac2 95.9%

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

      3. *-commutative 95.9%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. neg-sub0 99.7%

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

      7. associate--r- 99.7%

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

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-sub0 99.7%

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

      12. associate--r- 99.7%

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

      13. neg-sub0 99.7%

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

      14. +-commutative 99.7%

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

      15. sub-neg 99.7%

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

      16. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in t around 0 63.3%

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

      1. associate-/l* 57.9%

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

   10. Simplified 57.9%

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

   11. Taylor expanded in z around 0 60.9%

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

       1. associate-*r/ 60.9%

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

       2. neg-mul-1 60.9%

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

       3. distribute-rgt-neg-in 60.9%

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

   13. Simplified 60.9%

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

   if -1.50000000000000004e-111 < z < -5.50000000000000025e-158

   1. Initial program 99.6%

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

      1. associate-/l* 86.0%

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

   3. Simplified 86.0%

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

      1. clear-num 86.0%

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

      2. un-div-inv 86.0%

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

   6. Applied egg-rr 86.0%

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

   7. Taylor expanded in y around 0 45.9%

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

      1. mul-1-neg 45.9%

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

   9. Simplified 45.9%

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

   10. Taylor expanded in t around inf 59.7%

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

       1. associate-*r/ 59.7%

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

       2. mul-1-neg 59.7%

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

       3. distribute-rgt-neg-out 59.7%

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

       4. associate-*l/ 59.2%

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

   12. Simplified 59.2%

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

   if -5.50000000000000025e-158 < z < 3.3e13

   1. Initial program 91.5%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

      1. clear-num 89.7%

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

      2. un-div-inv 89.7%

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

   6. Applied egg-rr 89.7%

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

   7. Taylor expanded in z around 0 67.8%

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

      1. associate-/r/ 69.0%

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

   9. Applied egg-rr 69.0%

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

       1. *-commutative 69.0%

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

       2. clear-num 69.0%

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

       3. un-div-inv 69.0%

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

   11. Applied egg-rr 69.0%

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

   if 8.9999999999999999e74 < z < 3.3999999999999998e84

   1. Initial program 62.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 62.3%

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

      1. remove-double-neg 62.3%

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

      2. distribute-neg-frac2 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. neg-sub0 99.7%

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

      7. associate--r- 99.7%

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

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-sub0 99.7%

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

      12. associate--r- 99.7%

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

      13. neg-sub0 99.7%

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

      14. +-commutative 99.7%

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

      15. sub-neg 99.7%

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

      16. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in t around 0 23.7%

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

      1. associate-/l* 42.3%

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

   10. Simplified 42.3%

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

   11. Taylor expanded in z around 0 33.0%

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

       1. associate-*r/ 33.0%

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

       2. neg-mul-1 33.0%

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

       3. distribute-rgt-neg-in 33.0%

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

   13. Simplified 33.0%

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

   14. Taylor expanded in x around 0 33.0%

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

       1. mul-1-neg 33.0%

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

       2. associate-*l/ 51.6%

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

   16. Simplified 51.6%

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

       1. *-commutative 51.6%

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

       2. clear-num 51.6%

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

       3. un-div-inv 51.6%

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

   18. Applied egg-rr 51.6%

       \[\leadsto -\color{blue}{\frac{y}{\frac{z}{x}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-158}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq 33000000000000:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+90)
   x
   (if (<= z -3.4e-13)
     (* y (/ x t))
     (if (<= z -1.15e-55)
       (/ (* z x) z)
       (if (<= z -3.7e-171)
         (* z (/ x (- t)))
         (if (<= z -6.8e-176)
           (* y (/ x (- z)))
           (if (<= z 4.9e+14)
             (/ y (/ t x))
             (if (<= z 2.3e+70)
               x
               (if (<= z 1.22e+84) (/ y (/ z (- x))) x)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+90) {
		tmp = x;
	} else if (z <= -3.4e-13) {
		tmp = y * (x / t);
	} else if (z <= -1.15e-55) {
		tmp = (z * x) / z;
	} else if (z <= -3.7e-171) {
		tmp = z * (x / -t);
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= 4.9e+14) {
		tmp = y / (t / x);
	} else if (z <= 2.3e+70) {
		tmp = x;
	} else if (z <= 1.22e+84) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.8d+90)) then
        tmp = x
    else if (z <= (-3.4d-13)) then
        tmp = y * (x / t)
    else if (z <= (-1.15d-55)) then
        tmp = (z * x) / z
    else if (z <= (-3.7d-171)) then
        tmp = z * (x / -t)
    else if (z <= (-6.8d-176)) then
        tmp = y * (x / -z)
    else if (z <= 4.9d+14) then
        tmp = y / (t / x)
    else if (z <= 2.3d+70) then
        tmp = x
    else if (z <= 1.22d+84) then
        tmp = y / (z / -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+90) {
		tmp = x;
	} else if (z <= -3.4e-13) {
		tmp = y * (x / t);
	} else if (z <= -1.15e-55) {
		tmp = (z * x) / z;
	} else if (z <= -3.7e-171) {
		tmp = z * (x / -t);
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= 4.9e+14) {
		tmp = y / (t / x);
	} else if (z <= 2.3e+70) {
		tmp = x;
	} else if (z <= 1.22e+84) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+90:
		tmp = x
	elif z <= -3.4e-13:
		tmp = y * (x / t)
	elif z <= -1.15e-55:
		tmp = (z * x) / z
	elif z <= -3.7e-171:
		tmp = z * (x / -t)
	elif z <= -6.8e-176:
		tmp = y * (x / -z)
	elif z <= 4.9e+14:
		tmp = y / (t / x)
	elif z <= 2.3e+70:
		tmp = x
	elif z <= 1.22e+84:
		tmp = y / (z / -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+90)
		tmp = x;
	elseif (z <= -3.4e-13)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= -1.15e-55)
		tmp = Float64(Float64(z * x) / z);
	elseif (z <= -3.7e-171)
		tmp = Float64(z * Float64(x / Float64(-t)));
	elseif (z <= -6.8e-176)
		tmp = Float64(y * Float64(x / Float64(-z)));
	elseif (z <= 4.9e+14)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 2.3e+70)
		tmp = x;
	elseif (z <= 1.22e+84)
		tmp = Float64(y / Float64(z / Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+90)
		tmp = x;
	elseif (z <= -3.4e-13)
		tmp = y * (x / t);
	elseif (z <= -1.15e-55)
		tmp = (z * x) / z;
	elseif (z <= -3.7e-171)
		tmp = z * (x / -t);
	elseif (z <= -6.8e-176)
		tmp = y * (x / -z);
	elseif (z <= 4.9e+14)
		tmp = y / (t / x);
	elseif (z <= 2.3e+70)
		tmp = x;
	elseif (z <= 1.22e+84)
		tmp = y / (z / -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+90], x, If[LessEqual[z, -3.4e-13], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-55], N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -3.7e-171], N[(z * N[(x / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-176], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+14], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+70], x, If[LessEqual[z, 1.22e+84], N[(y / N[(z / (-x)), $MachinePrecision]), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -2.8e90 or 4.9e14 < z < 2.29999999999999994e70 or 1.2200000000000001e84 < z

   1. Initial program 75.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 67.7%

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

   if -2.8e90 < z < -3.40000000000000015e-13

   1. Initial program 90.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 38.4%

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

      1. associate-/r/ 38.4%

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

   9. Applied egg-rr 38.4%

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

   if -3.40000000000000015e-13 < z < -1.15000000000000006e-55

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in z around inf 55.8%

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

   if -1.15000000000000006e-55 < z < -3.70000000000000012e-171

   1. Initial program 97.8%

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

      1. associate-/l* 87.2%

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

   3. Simplified 87.2%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.3%

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

   6. Applied egg-rr 85.3%

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

   7. Taylor expanded in y around 0 38.3%

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

      1. mul-1-neg 38.3%

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

   9. Simplified 38.3%

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

   10. Taylor expanded in t around inf 52.9%

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

       1. associate-*r/ 52.9%

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

       2. mul-1-neg 52.9%

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

       3. distribute-rgt-neg-out 52.9%

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

       4. associate-*l/ 52.7%

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

   12. Simplified 52.7%

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

   if -3.70000000000000012e-171 < z < -6.7999999999999994e-176

   1. Initial program 99.7%

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

      1. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in x around 0 99.7%

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

      1. remove-double-neg 99.7%

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

      2. distribute-neg-frac2 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate--r- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. neg-sub0 100.0%

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

      12. associate--r- 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. sub-neg 100.0%

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

      16. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 99.7%

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

      1. associate-/l* 43.9%

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

   10. Simplified 43.9%

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

   11. Taylor expanded in z around 0 99.7%

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

       1. associate-*r/ 99.7%

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

       2. neg-mul-1 99.7%

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

       3. distribute-rgt-neg-in 99.7%

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

   13. Simplified 99.7%

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

   14. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-*l/ 100.0%

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

   16. Simplified 100.0%

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

   if -6.7999999999999994e-176 < z < 4.9e14

   1. Initial program 90.8%

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

      1. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

      1. clear-num 90.8%

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

      2. un-div-inv 90.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in z around 0 69.1%

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

      1. associate-/r/ 70.5%

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

   9. Applied egg-rr 70.5%

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

       1. *-commutative 70.5%

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

       2. clear-num 70.5%

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

       3. un-div-inv 70.5%

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

   11. Applied egg-rr 70.5%

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

   if 2.29999999999999994e70 < z < 1.2200000000000001e84

   1. Initial program 62.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 62.3%

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

      1. remove-double-neg 62.3%

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

      2. distribute-neg-frac2 62.3%

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

      3. *-commutative 62.3%

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

      4. associate-/l* 99.7%

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

      5. distribute-lft-neg-out 99.7%

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

      6. neg-sub0 99.7%

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

      7. associate--r- 99.7%

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

      8. neg-sub0 99.7%

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

      9. +-commutative 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-sub0 99.7%

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

      12. associate--r- 99.7%

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

      13. neg-sub0 99.7%

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

      14. +-commutative 99.7%

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

      15. sub-neg 99.7%

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

      16. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in t around 0 23.7%

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

      1. associate-/l* 42.3%

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

   10. Simplified 42.3%

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

   11. Taylor expanded in z around 0 33.0%

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

       1. associate-*r/ 33.0%

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

       2. neg-mul-1 33.0%

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

       3. distribute-rgt-neg-in 33.0%

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

   13. Simplified 33.0%

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

   14. Taylor expanded in x around 0 33.0%

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

       1. mul-1-neg 33.0%

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

       2. associate-*l/ 51.6%

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

   16. Simplified 51.6%

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

       1. *-commutative 51.6%

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

       2. clear-num 51.6%

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

       3. un-div-inv 51.6%

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

   18. Applied egg-rr 51.6%

       \[\leadsto -\color{blue}{\frac{y}{\frac{z}{x}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-55}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-171}:\\ \;\;\;\;z \cdot \frac{x}{-t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.95 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{elif}\;z \leq 34000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))))
   (if (<= z -1e-106)
     (* x (/ (- z y) z))
     (if (<= z -9.95e-173)
       t_1
       (if (<= z -6.8e-176)
         (* y (/ x (- z)))
         (if (<= z -3.5e-186)
           (* x (/ y t))
           (if (<= z -8.6e-187)
             (/ y (/ z (- x)))
             (if (<= z 34000000000000.0) t_1 (* x (- 1.0 (/ y z)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (z <= -1e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.95e-173) {
		tmp = t_1;
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= -3.5e-186) {
		tmp = x * (y / t);
	} else if (z <= -8.6e-187) {
		tmp = y / (z / -x);
	} else if (z <= 34000000000000.0) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - z) / t)
    if (z <= (-1d-106)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-9.95d-173)) then
        tmp = t_1
    else if (z <= (-6.8d-176)) then
        tmp = y * (x / -z)
    else if (z <= (-3.5d-186)) then
        tmp = x * (y / t)
    else if (z <= (-8.6d-187)) then
        tmp = y / (z / -x)
    else if (z <= 34000000000000.0d0) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double tmp;
	if (z <= -1e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.95e-173) {
		tmp = t_1;
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= -3.5e-186) {
		tmp = x * (y / t);
	} else if (z <= -8.6e-187) {
		tmp = y / (z / -x);
	} else if (z <= 34000000000000.0) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	tmp = 0
	if z <= -1e-106:
		tmp = x * ((z - y) / z)
	elif z <= -9.95e-173:
		tmp = t_1
	elif z <= -6.8e-176:
		tmp = y * (x / -z)
	elif z <= -3.5e-186:
		tmp = x * (y / t)
	elif z <= -8.6e-187:
		tmp = y / (z / -x)
	elif z <= 34000000000000.0:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	tmp = 0.0
	if (z <= -1e-106)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -9.95e-173)
		tmp = t_1;
	elseif (z <= -6.8e-176)
		tmp = Float64(y * Float64(x / Float64(-z)));
	elseif (z <= -3.5e-186)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= -8.6e-187)
		tmp = Float64(y / Float64(z / Float64(-x)));
	elseif (z <= 34000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	tmp = 0.0;
	if (z <= -1e-106)
		tmp = x * ((z - y) / z);
	elseif (z <= -9.95e-173)
		tmp = t_1;
	elseif (z <= -6.8e-176)
		tmp = y * (x / -z);
	elseif (z <= -3.5e-186)
		tmp = x * (y / t);
	elseif (z <= -8.6e-187)
		tmp = y / (z / -x);
	elseif (z <= 34000000000000.0)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-106], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.95e-173], t$95$1, If[LessEqual[z, -6.8e-176], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-186], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-187], N[(y / N[(z / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 34000000000000.0], t$95$1, N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -9.99999999999999941e-107

   1. Initial program 84.1%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around 0 84.1%

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

      1. remove-double-neg 84.1%

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

      2. distribute-neg-frac2 84.1%

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

      3. *-commutative 84.1%

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

      4. associate-/l* 78.1%

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

      5. distribute-lft-neg-out 78.1%

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

      6. neg-sub0 78.1%

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

      7. associate--r- 78.1%

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

      8. neg-sub0 78.1%

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

      9. +-commutative 78.1%

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

      10. sub-neg 78.1%

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

      11. neg-sub0 78.1%

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

      12. associate--r- 78.1%

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

      13. neg-sub0 78.1%

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

      14. +-commutative 78.1%

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

      15. sub-neg 78.1%

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

      16. *-commutative 78.1%

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

   7. Simplified 78.1%

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

   8. Taylor expanded in t around 0 59.1%

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

      1. associate-/l* 73.6%

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

   10. Simplified 73.6%

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

   if -9.99999999999999941e-107 < z < -9.9499999999999999e-173 or -8.60000000000000001e-187 < z < 3.4e13

   1. Initial program 92.4%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 79.3%

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

      1. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if -9.9499999999999999e-173 < z < -6.7999999999999994e-176

   1. Initial program 99.2%

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

      1. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in x around 0 99.2%

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

      1. remove-double-neg 99.2%

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

      2. distribute-neg-frac2 99.2%

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

      3. *-commutative 99.2%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate--r- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. neg-sub0 100.0%

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

      12. associate--r- 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. sub-neg 100.0%

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

      16. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 99.2%

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

      1. associate-/l* 52.4%

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

   10. Simplified 52.4%

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

   11. Taylor expanded in z around 0 99.2%

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

       1. associate-*r/ 99.2%

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

       2. neg-mul-1 99.2%

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

       3. distribute-rgt-neg-in 99.2%

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

   13. Simplified 99.2%

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

   14. Taylor expanded in x around 0 99.2%

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

       1. mul-1-neg 99.2%

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

       2. associate-*l/ 100.0%

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

   16. Simplified 100.0%

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

   if -6.7999999999999994e-176 < z < -3.49999999999999989e-186

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   if -3.49999999999999989e-186 < z < -8.60000000000000001e-187

   1. Initial program 68.2%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 68.2%

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

      1. remove-double-neg 68.2%

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

      2. distribute-neg-frac2 68.2%

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

      3. *-commutative 68.2%

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

      4. associate-/l* 99.5%

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

      5. distribute-lft-neg-out 99.5%

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

      6. neg-sub0 99.5%

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

      7. associate--r- 99.5%

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

      8. neg-sub0 99.5%

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

      9. +-commutative 99.5%

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

      10. sub-neg 99.5%

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

      11. neg-sub0 99.5%

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

      12. associate--r- 99.5%

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

      13. neg-sub0 99.5%

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

      14. +-commutative 99.5%

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

      15. sub-neg 99.5%

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

      16. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in t around 0 68.2%

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

      1. associate-/l* 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in z around 0 68.2%

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

       1. associate-*r/ 68.2%

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

       2. neg-mul-1 68.2%

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

       3. distribute-rgt-neg-in 68.2%

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

   13. Simplified 68.2%

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

   14. Taylor expanded in x around 0 68.2%

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

       1. mul-1-neg 68.2%

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

       2. associate-*l/ 99.5%

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

   16. Simplified 99.5%

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

       1. *-commutative 99.5%

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

       2. clear-num 99.5%

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

       3. un-div-inv 100.0%

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

   18. Applied egg-rr 100.0%

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

   if 3.4e13 < z

   1. Initial program 74.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-/l* 73.6%

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

      3. distribute-rgt-neg-in 73.6%

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

      4. distribute-frac-neg 73.6%

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

      5. neg-sub0 73.6%

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

      6. associate--r- 73.6%

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

      7. neg-sub0 73.6%

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

      8. +-commutative 73.6%

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

      9. sub-neg 73.6%

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

      10. div-sub 73.6%

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

      11. *-inverses 73.6%

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

   7. Simplified 73.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.95 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{elif}\;z \leq 34000000000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y - z}{t}\\ t_2 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -9.95 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{elif}\;z \leq 60000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y z) t))) (t_2 (* x (- 1.0 (/ y z)))))
   (if (<= z -7.2e-109)
     t_2
     (if (<= z -9.95e-173)
       t_1
       (if (<= z -6.8e-176)
         (* y (/ x (- z)))
         (if (<= z -2.5e-183)
           (* x (/ y t))
           (if (<= z -8.6e-187)
             (/ y (/ z (- x)))
             (if (<= z 60000000000000.0) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -7.2e-109) {
		tmp = t_2;
	} else if (z <= -9.95e-173) {
		tmp = t_1;
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= -2.5e-183) {
		tmp = x * (y / t);
	} else if (z <= -8.6e-187) {
		tmp = y / (z / -x);
	} else if (z <= 60000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y - z) / t)
    t_2 = x * (1.0d0 - (y / z))
    if (z <= (-7.2d-109)) then
        tmp = t_2
    else if (z <= (-9.95d-173)) then
        tmp = t_1
    else if (z <= (-6.8d-176)) then
        tmp = y * (x / -z)
    else if (z <= (-2.5d-183)) then
        tmp = x * (y / t)
    else if (z <= (-8.6d-187)) then
        tmp = y / (z / -x)
    else if (z <= 60000000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * ((y - z) / t);
	double t_2 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -7.2e-109) {
		tmp = t_2;
	} else if (z <= -9.95e-173) {
		tmp = t_1;
	} else if (z <= -6.8e-176) {
		tmp = y * (x / -z);
	} else if (z <= -2.5e-183) {
		tmp = x * (y / t);
	} else if (z <= -8.6e-187) {
		tmp = y / (z / -x);
	} else if (z <= 60000000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((y - z) / t)
	t_2 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -7.2e-109:
		tmp = t_2
	elif z <= -9.95e-173:
		tmp = t_1
	elif z <= -6.8e-176:
		tmp = y * (x / -z)
	elif z <= -2.5e-183:
		tmp = x * (y / t)
	elif z <= -8.6e-187:
		tmp = y / (z / -x)
	elif z <= 60000000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(y - z) / t))
	t_2 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -7.2e-109)
		tmp = t_2;
	elseif (z <= -9.95e-173)
		tmp = t_1;
	elseif (z <= -6.8e-176)
		tmp = Float64(y * Float64(x / Float64(-z)));
	elseif (z <= -2.5e-183)
		tmp = Float64(x * Float64(y / t));
	elseif (z <= -8.6e-187)
		tmp = Float64(y / Float64(z / Float64(-x)));
	elseif (z <= 60000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((y - z) / t);
	t_2 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -7.2e-109)
		tmp = t_2;
	elseif (z <= -9.95e-173)
		tmp = t_1;
	elseif (z <= -6.8e-176)
		tmp = y * (x / -z);
	elseif (z <= -2.5e-183)
		tmp = x * (y / t);
	elseif (z <= -8.6e-187)
		tmp = y / (z / -x);
	elseif (z <= 60000000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e-109], t$95$2, If[LessEqual[z, -9.95e-173], t$95$1, If[LessEqual[z, -6.8e-176], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-183], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-187], N[(y / N[(z / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 60000000000000.0], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.2000000000000001e-109 or 6e13 < z

   1. Initial program 79.6%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in t around 0 56.6%

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

      1. mul-1-neg 56.6%

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

      2. associate-/l* 73.6%

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

      3. distribute-rgt-neg-in 73.6%

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

      4. distribute-frac-neg 73.6%

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

      5. neg-sub0 73.6%

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

      6. associate--r- 73.6%

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

      7. neg-sub0 73.6%

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

      8. +-commutative 73.6%

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

      9. sub-neg 73.6%

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

      10. div-sub 73.6%

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

      11. *-inverses 73.6%

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

   7. Simplified 73.6%

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

   if -7.2000000000000001e-109 < z < -9.9499999999999999e-173 or -8.60000000000000001e-187 < z < 6e13

   1. Initial program 92.4%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 79.3%

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

      1. associate-/l* 78.4%

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

   7. Simplified 78.4%

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

   if -9.9499999999999999e-173 < z < -6.7999999999999994e-176

   1. Initial program 99.2%

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

      1. associate-/l* 52.4%

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

   3. Simplified 52.4%

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

   5. Taylor expanded in x around 0 99.2%

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

      1. remove-double-neg 99.2%

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

      2. distribute-neg-frac2 99.2%

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

      3. *-commutative 99.2%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. neg-sub0 100.0%

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

      7. associate--r- 100.0%

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

      8. neg-sub0 100.0%

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

      9. +-commutative 100.0%

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

      10. sub-neg 100.0%

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

      11. neg-sub0 100.0%

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

      12. associate--r- 100.0%

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

      13. neg-sub0 100.0%

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

      14. +-commutative 100.0%

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

      15. sub-neg 100.0%

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

      16. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 99.2%

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

      1. associate-/l* 52.4%

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

   10. Simplified 52.4%

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

   11. Taylor expanded in z around 0 99.2%

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

       1. associate-*r/ 99.2%

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

       2. neg-mul-1 99.2%

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

       3. distribute-rgt-neg-in 99.2%

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

   13. Simplified 99.2%

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

   14. Taylor expanded in x around 0 99.2%

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

       1. mul-1-neg 99.2%

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

       2. associate-*l/ 100.0%

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

   16. Simplified 100.0%

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

   if -6.7999999999999994e-176 < z < -2.5000000000000001e-183

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

      1. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   if -2.5000000000000001e-183 < z < -8.60000000000000001e-187

   1. Initial program 76.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 76.1%

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

      1. remove-double-neg 76.1%

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

      2. distribute-neg-frac2 76.1%

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

      3. *-commutative 76.1%

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

      4. associate-/l* 99.6%

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

      5. distribute-lft-neg-out 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate--r- 99.6%

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

      8. neg-sub0 99.6%

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

      9. +-commutative 99.6%

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

      10. sub-neg 99.6%

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

      11. neg-sub0 99.6%

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

      12. associate--r- 99.6%

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

      13. neg-sub0 99.6%

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

      14. +-commutative 99.6%

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

      15. sub-neg 99.6%

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

      16. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in t around 0 76.1%

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

      1. associate-/l* 77.8%

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

   10. Simplified 77.8%

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

   11. Taylor expanded in z around 0 76.1%

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

       1. associate-*r/ 76.1%

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

       2. neg-mul-1 76.1%

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

       3. distribute-rgt-neg-in 76.1%

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

   13. Simplified 76.1%

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

   14. Taylor expanded in x around 0 76.1%

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

       1. mul-1-neg 76.1%

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

       2. associate-*l/ 99.6%

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

   16. Simplified 99.6%

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

       1. *-commutative 99.6%

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

       2. clear-num 99.6%

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

       3. un-div-inv 100.0%

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

   18. Applied egg-rr 100.0%

       \[\leadsto -\color{blue}{\frac{y}{\frac{z}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -9.95 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{elif}\;z \leq 60000000000000:\\ \;\;\;\;x \cdot \frac{y - z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq 42000000000000:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e+90)
   x
   (if (<= z -3.2e-14)
     (* y (/ x t))
     (if (<= z -3.9e-56)
       (/ (* z x) z)
       (if (<= z 42000000000000.0)
         (/ y (/ t x))
         (if (<= z 2e+73) x (if (<= z 1.45e+84) (/ y (/ z (- x))) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+90) {
		tmp = x;
	} else if (z <= -3.2e-14) {
		tmp = y * (x / t);
	} else if (z <= -3.9e-56) {
		tmp = (z * x) / z;
	} else if (z <= 42000000000000.0) {
		tmp = y / (t / x);
	} else if (z <= 2e+73) {
		tmp = x;
	} else if (z <= 1.45e+84) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.2d+90)) then
        tmp = x
    else if (z <= (-3.2d-14)) then
        tmp = y * (x / t)
    else if (z <= (-3.9d-56)) then
        tmp = (z * x) / z
    else if (z <= 42000000000000.0d0) then
        tmp = y / (t / x)
    else if (z <= 2d+73) then
        tmp = x
    else if (z <= 1.45d+84) then
        tmp = y / (z / -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e+90) {
		tmp = x;
	} else if (z <= -3.2e-14) {
		tmp = y * (x / t);
	} else if (z <= -3.9e-56) {
		tmp = (z * x) / z;
	} else if (z <= 42000000000000.0) {
		tmp = y / (t / x);
	} else if (z <= 2e+73) {
		tmp = x;
	} else if (z <= 1.45e+84) {
		tmp = y / (z / -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e+90:
		tmp = x
	elif z <= -3.2e-14:
		tmp = y * (x / t)
	elif z <= -3.9e-56:
		tmp = (z * x) / z
	elif z <= 42000000000000.0:
		tmp = y / (t / x)
	elif z <= 2e+73:
		tmp = x
	elif z <= 1.45e+84:
		tmp = y / (z / -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e+90)
		tmp = x;
	elseif (z <= -3.2e-14)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= -3.9e-56)
		tmp = Float64(Float64(z * x) / z);
	elseif (z <= 42000000000000.0)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 2e+73)
		tmp = x;
	elseif (z <= 1.45e+84)
		tmp = Float64(y / Float64(z / Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e+90)
		tmp = x;
	elseif (z <= -3.2e-14)
		tmp = y * (x / t);
	elseif (z <= -3.9e-56)
		tmp = (z * x) / z;
	elseif (z <= 42000000000000.0)
		tmp = y / (t / x);
	elseif (z <= 2e+73)
		tmp = x;
	elseif (z <= 1.45e+84)
		tmp = y / (z / -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e+90], x, If[LessEqual[z, -3.2e-14], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-56], N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 42000000000000.0], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+73], x, If[LessEqual[z, 1.45e+84], N[(y / N[(z / (-x)), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.1999999999999999e90 or 4.2e13 < z < 1.99999999999999997e73 or 1.44999999999999994e84 < z

   1. Initial program 75.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 67.7%

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

   if -2.1999999999999999e90 < z < -3.2000000000000002e-14

   1. Initial program 90.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 38.4%

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

      1. associate-/r/ 38.4%

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

   9. Applied egg-rr 38.4%

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

   if -3.2000000000000002e-14 < z < -3.9e-56

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-neg-frac2 100.0%

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

      5. distribute-lft-neg-out 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. sub-neg 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. remove-double-neg 100.0%

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

      10. +-commutative 100.0%

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

      11. sub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. distribute-neg-in 100.0%

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

      14. remove-double-neg 100.0%

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

      15. +-commutative 100.0%

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

      16. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in t around 0 66.8%

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

   6. Taylor expanded in z around inf 55.8%

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

   if -3.9e-56 < z < 4.2e13

   1. Initial program 92.4%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.5%

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

      2. un-div-inv 89.5%

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

   6. Applied egg-rr 89.5%

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

   7. Taylor expanded in z around 0 62.8%

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

      1. associate-/r/ 63.9%

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

   9. Applied egg-rr 63.9%

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

       1. *-commutative 63.9%

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

       2. clear-num 63.9%

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

       3. un-div-inv 63.9%

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

   11. Applied egg-rr 63.9%

       \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]

   if 1.99999999999999997e73 < z < 1.44999999999999994e84

   1. Initial program 62.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 62.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 62.3%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 62.3%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 62.3%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 99.7%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 99.7%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 99.7%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 99.7%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 99.7%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 99.7%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 99.7%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 23.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 42.3%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 42.3%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   11. Taylor expanded in z around 0 33.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 33.0%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. neg-mul-1 33.0%

          \[\leadsto \frac{\color{blue}{-x \cdot y}}{z} \]

       3. distribute-rgt-neg-in 33.0%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{z} \]

   13. Simplified 33.0%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-y\right)}{z}} \]

   14. Taylor expanded in x around 0 33.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   15. Step-by-step derivation

       1. mul-1-neg 33.0%

          \[\leadsto \color{blue}{-\frac{x \cdot y}{z}} \]

       2. associate-*l/ 51.6%

          \[\leadsto -\color{blue}{\frac{x}{z} \cdot y} \]

   16. Simplified 51.6%

       \[\leadsto \color{blue}{-\frac{x}{z} \cdot y} \]
   17. Step-by-step derivation

       1. *-commutative 51.6%

          \[\leadsto -\color{blue}{y \cdot \frac{x}{z}} \]

       2. clear-num 51.6%

          \[\leadsto -y \cdot \color{blue}{\frac{1}{\frac{z}{x}}} \]

       3. un-div-inv 51.6%

          \[\leadsto -\color{blue}{\frac{y}{\frac{z}{x}}} \]

   18. Applied egg-rr 51.6%

       \[\leadsto -\color{blue}{\frac{y}{\frac{z}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-56}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq 42000000000000:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{\frac{z}{-x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.26e+91)
   x
   (if (<= z -2.15e-13)
     (* y (/ x t))
     (if (<= z -3.1e-56)
       (/ (* z x) z)
       (if (<= z 4.4e+15)
         (/ y (/ t x))
         (if (<= z 1.3e+74) x (if (<= z 2.7e+84) (* y (/ x (- z))) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e+91) {
		tmp = x;
	} else if (z <= -2.15e-13) {
		tmp = y * (x / t);
	} else if (z <= -3.1e-56) {
		tmp = (z * x) / z;
	} else if (z <= 4.4e+15) {
		tmp = y / (t / x);
	} else if (z <= 1.3e+74) {
		tmp = x;
	} else if (z <= 2.7e+84) {
		tmp = y * (x / -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.26d+91)) then
        tmp = x
    else if (z <= (-2.15d-13)) then
        tmp = y * (x / t)
    else if (z <= (-3.1d-56)) then
        tmp = (z * x) / z
    else if (z <= 4.4d+15) then
        tmp = y / (t / x)
    else if (z <= 1.3d+74) then
        tmp = x
    else if (z <= 2.7d+84) then
        tmp = y * (x / -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.26e+91) {
		tmp = x;
	} else if (z <= -2.15e-13) {
		tmp = y * (x / t);
	} else if (z <= -3.1e-56) {
		tmp = (z * x) / z;
	} else if (z <= 4.4e+15) {
		tmp = y / (t / x);
	} else if (z <= 1.3e+74) {
		tmp = x;
	} else if (z <= 2.7e+84) {
		tmp = y * (x / -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.26e+91:
		tmp = x
	elif z <= -2.15e-13:
		tmp = y * (x / t)
	elif z <= -3.1e-56:
		tmp = (z * x) / z
	elif z <= 4.4e+15:
		tmp = y / (t / x)
	elif z <= 1.3e+74:
		tmp = x
	elif z <= 2.7e+84:
		tmp = y * (x / -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.26e+91)
		tmp = x;
	elseif (z <= -2.15e-13)
		tmp = Float64(y * Float64(x / t));
	elseif (z <= -3.1e-56)
		tmp = Float64(Float64(z * x) / z);
	elseif (z <= 4.4e+15)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 1.3e+74)
		tmp = x;
	elseif (z <= 2.7e+84)
		tmp = Float64(y * Float64(x / Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.26e+91)
		tmp = x;
	elseif (z <= -2.15e-13)
		tmp = y * (x / t);
	elseif (z <= -3.1e-56)
		tmp = (z * x) / z;
	elseif (z <= 4.4e+15)
		tmp = y / (t / x);
	elseif (z <= 1.3e+74)
		tmp = x;
	elseif (z <= 2.7e+84)
		tmp = y * (x / -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.26e+91], x, If[LessEqual[z, -2.15e-13], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-56], N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.4e+15], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+74], x, If[LessEqual[z, 2.7e+84], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.26e91 or 4.4e15 < z < 1.3e74 or 2.7e84 < z

   1. Initial program 75.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.7%

      \[\leadsto \color{blue}{x} \]

   if -1.26e91 < z < -2.1499999999999999e-13

   1. Initial program 90.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 38.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 38.4%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 38.4%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   if -2.1499999999999999e-13 < z < -3.09999999999999987e-56

   1. Initial program 100.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(-x \cdot \left(y - z\right)\right)}}{t - z} \]

      2. distribute-lft-neg-out 100.0%

         \[\leadsto \frac{-\color{blue}{\left(-x\right) \cdot \left(y - z\right)}}{t - z} \]

      3. distribute-neg-frac 100.0%

         \[\leadsto \color{blue}{-\frac{\left(-x\right) \cdot \left(y - z\right)}{t - z}} \]

      4. distribute-neg-frac2 100.0%

         \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto \frac{\color{blue}{-x \cdot \left(y - z\right)}}{-\left(t - z\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-\left(y - z\right)\right)}}{-\left(t - z\right)} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{x \cdot \left(-\color{blue}{\left(y + \left(-z\right)\right)}\right)}{-\left(t - z\right)} \]

      8. distribute-neg-in 100.0%

         \[\leadsto \frac{x \cdot \color{blue}{\left(\left(-y\right) + \left(-\left(-z\right)\right)\right)}}{-\left(t - z\right)} \]

      9. remove-double-neg 100.0%

         \[\leadsto \frac{x \cdot \left(\left(-y\right) + \color{blue}{z}\right)}{-\left(t - z\right)} \]

      10. +-commutative 100.0%

          \[\leadsto \frac{x \cdot \color{blue}{\left(z + \left(-y\right)\right)}}{-\left(t - z\right)} \]

      11. sub-neg 100.0%

          \[\leadsto \frac{x \cdot \color{blue}{\left(z - y\right)}}{-\left(t - z\right)} \]

      12. sub-neg 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{-\color{blue}{\left(t + \left(-z\right)\right)}} \]

      13. distribute-neg-in 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\color{blue}{\left(-t\right) + \left(-\left(-z\right)\right)}} \]

      14. remove-double-neg 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\left(-t\right) + \color{blue}{z}} \]

      15. +-commutative 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\color{blue}{z + \left(-t\right)}} \]

      16. sub-neg 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\color{blue}{z - t}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]

   6. Taylor expanded in z around inf 55.8%

      \[\leadsto \frac{\color{blue}{x \cdot z}}{z} \]

   if -3.09999999999999987e-56 < z < 4.4e15

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 89.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 89.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 89.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 62.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 63.9%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 63.9%

          \[\leadsto \color{blue}{y \cdot \frac{x}{t}} \]

       2. clear-num 63.9%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{t}{x}}} \]

       3. un-div-inv 63.9%

          \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]

   11. Applied egg-rr 63.9%

       \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]

   if 1.3e74 < z < 2.7e84

   1. Initial program 62.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 62.3%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 62.3%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 62.3%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 62.3%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 99.7%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 99.7%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 99.7%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 99.7%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 99.7%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 99.7%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 99.7%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 99.7%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 23.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 42.3%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 42.3%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   11. Taylor expanded in z around 0 33.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 33.0%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. neg-mul-1 33.0%

          \[\leadsto \frac{\color{blue}{-x \cdot y}}{z} \]

       3. distribute-rgt-neg-in 33.0%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{z} \]

   13. Simplified 33.0%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-y\right)}{z}} \]

   14. Taylor expanded in x around 0 33.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   15. Step-by-step derivation

       1. mul-1-neg 33.0%

          \[\leadsto \color{blue}{-\frac{x \cdot y}{z}} \]

       2. associate-*l/ 51.6%

          \[\leadsto -\color{blue}{\frac{x}{z} \cdot y} \]

   16. Simplified 51.6%

       \[\leadsto \color{blue}{-\frac{x}{z} \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-15} \lor \neg \left(z \leq -1.45 \cdot 10^{-55}\right) \land \left(z \leq 52000000000000 \lor \neg \left(z \leq 8.5 \cdot 10^{+71}\right) \land z \leq 1.25 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+90)
   x
   (if (or (<= z -9.2e-15)
           (and (not (<= z -1.45e-55))
                (or (<= z 52000000000000.0)
                    (and (not (<= z 8.5e+71)) (<= z 1.25e+84)))))
     (* y (/ x t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+90) {
		tmp = x;
	} else if ((z <= -9.2e-15) || (!(z <= -1.45e-55) && ((z <= 52000000000000.0) || (!(z <= 8.5e+71) && (z <= 1.25e+84))))) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.2d+90)) then
        tmp = x
    else if ((z <= (-9.2d-15)) .or. (.not. (z <= (-1.45d-55))) .and. (z <= 52000000000000.0d0) .or. (.not. (z <= 8.5d+71)) .and. (z <= 1.25d+84)) then
        tmp = y * (x / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+90) {
		tmp = x;
	} else if ((z <= -9.2e-15) || (!(z <= -1.45e-55) && ((z <= 52000000000000.0) || (!(z <= 8.5e+71) && (z <= 1.25e+84))))) {
		tmp = y * (x / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+90:
		tmp = x
	elif (z <= -9.2e-15) or (not (z <= -1.45e-55) and ((z <= 52000000000000.0) or (not (z <= 8.5e+71) and (z <= 1.25e+84)))):
		tmp = y * (x / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+90)
		tmp = x;
	elseif ((z <= -9.2e-15) || (!(z <= -1.45e-55) && ((z <= 52000000000000.0) || (!(z <= 8.5e+71) && (z <= 1.25e+84)))))
		tmp = Float64(y * Float64(x / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+90)
		tmp = x;
	elseif ((z <= -9.2e-15) || (~((z <= -1.45e-55)) && ((z <= 52000000000000.0) || (~((z <= 8.5e+71)) && (z <= 1.25e+84)))))
		tmp = y * (x / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+90], x, If[Or[LessEqual[z, -9.2e-15], And[N[Not[LessEqual[z, -1.45e-55]], $MachinePrecision], Or[LessEqual[z, 52000000000000.0], And[N[Not[LessEqual[z, 8.5e+71]], $MachinePrecision], LessEqual[z, 1.25e+84]]]]], N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999997e90 or -9.19999999999999961e-15 < z < -1.45e-55 or 5.2e13 < z < 8.4999999999999996e71 or 1.25e84 < z

   1. Initial program 77.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{x} \]

   if -5.1999999999999997e90 < z < -9.19999999999999961e-15 or -1.45e-55 < z < 5.2e13 or 8.4999999999999996e71 < z < 1.25e84

   1. Initial program 91.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.5%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 91.2%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 91.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 91.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 58.9%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 59.8%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 59.8%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-15} \lor \neg \left(z \leq -1.45 \cdot 10^{-55}\right) \land \left(z \leq 52000000000000 \lor \neg \left(z \leq 8.5 \cdot 10^{+71}\right) \land z \leq 1.25 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-14} \lor \neg \left(z \leq -2.6 \cdot 10^{-58}\right) \land \left(z \leq 1.2 \cdot 10^{+14} \lor \neg \left(z \leq 3.5 \cdot 10^{+74}\right) \land z \leq 4.2 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e+90)
   x
   (if (or (<= z -1.32e-14)
           (and (not (<= z -2.6e-58))
                (or (<= z 1.2e+14) (and (not (<= z 3.5e+74)) (<= z 4.2e+84)))))
     (* x (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+90) {
		tmp = x;
	} else if ((z <= -1.32e-14) || (!(z <= -2.6e-58) && ((z <= 1.2e+14) || (!(z <= 3.5e+74) && (z <= 4.2e+84))))) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.5d+90)) then
        tmp = x
    else if ((z <= (-1.32d-14)) .or. (.not. (z <= (-2.6d-58))) .and. (z <= 1.2d+14) .or. (.not. (z <= 3.5d+74)) .and. (z <= 4.2d+84)) then
        tmp = x * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+90) {
		tmp = x;
	} else if ((z <= -1.32e-14) || (!(z <= -2.6e-58) && ((z <= 1.2e+14) || (!(z <= 3.5e+74) && (z <= 4.2e+84))))) {
		tmp = x * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+90:
		tmp = x
	elif (z <= -1.32e-14) or (not (z <= -2.6e-58) and ((z <= 1.2e+14) or (not (z <= 3.5e+74) and (z <= 4.2e+84)))):
		tmp = x * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+90)
		tmp = x;
	elseif ((z <= -1.32e-14) || (!(z <= -2.6e-58) && ((z <= 1.2e+14) || (!(z <= 3.5e+74) && (z <= 4.2e+84)))))
		tmp = Float64(x * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e+90)
		tmp = x;
	elseif ((z <= -1.32e-14) || (~((z <= -2.6e-58)) && ((z <= 1.2e+14) || (~((z <= 3.5e+74)) && (z <= 4.2e+84)))))
		tmp = x * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e+90], x, If[Or[LessEqual[z, -1.32e-14], And[N[Not[LessEqual[z, -2.6e-58]], $MachinePrecision], Or[LessEqual[z, 1.2e+14], And[N[Not[LessEqual[z, 3.5e+74]], $MachinePrecision], LessEqual[z, 4.2e+84]]]]], N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000002e90 or -1.32e-14 < z < -2.60000000000000007e-58 or 1.2e14 < z < 3.50000000000000014e74 or 4.20000000000000037e84 < z

   1. Initial program 77.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{x} \]

   if -2.5000000000000002e90 < z < -1.32e-14 or -2.60000000000000007e-58 < z < 1.2e14 or 3.50000000000000014e74 < z < 4.20000000000000037e84

   1. Initial program 91.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.5%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 91.5%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 57.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 58.9%

         \[\leadsto \color{blue}{x \cdot \frac{y}{t}} \]

   7. Simplified 58.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-14} \lor \neg \left(z \leq -2.6 \cdot 10^{-58}\right) \land \left(z \leq 1.2 \cdot 10^{+14} \lor \neg \left(z \leq 3.5 \cdot 10^{+74}\right) \land z \leq 4.2 \cdot 10^{+84}\right):\\ \;\;\;\;x \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{-55}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x t))))
   (if (<= z -2.35e+90)
     x
     (if (<= z -1.2e-12)
       t_1
       (if (<= z -1.48e-55)
         (/ (* z x) z)
         (if (<= z 5e+14)
           (/ y (/ t x))
           (if (<= z 1.4e+74) x (if (<= z 1.1e+84) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / t);
	double tmp;
	if (z <= -2.35e+90) {
		tmp = x;
	} else if (z <= -1.2e-12) {
		tmp = t_1;
	} else if (z <= -1.48e-55) {
		tmp = (z * x) / z;
	} else if (z <= 5e+14) {
		tmp = y / (t / x);
	} else if (z <= 1.4e+74) {
		tmp = x;
	} else if (z <= 1.1e+84) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / t)
    if (z <= (-2.35d+90)) then
        tmp = x
    else if (z <= (-1.2d-12)) then
        tmp = t_1
    else if (z <= (-1.48d-55)) then
        tmp = (z * x) / z
    else if (z <= 5d+14) then
        tmp = y / (t / x)
    else if (z <= 1.4d+74) then
        tmp = x
    else if (z <= 1.1d+84) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / t);
	double tmp;
	if (z <= -2.35e+90) {
		tmp = x;
	} else if (z <= -1.2e-12) {
		tmp = t_1;
	} else if (z <= -1.48e-55) {
		tmp = (z * x) / z;
	} else if (z <= 5e+14) {
		tmp = y / (t / x);
	} else if (z <= 1.4e+74) {
		tmp = x;
	} else if (z <= 1.1e+84) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / t)
	tmp = 0
	if z <= -2.35e+90:
		tmp = x
	elif z <= -1.2e-12:
		tmp = t_1
	elif z <= -1.48e-55:
		tmp = (z * x) / z
	elif z <= 5e+14:
		tmp = y / (t / x)
	elif z <= 1.4e+74:
		tmp = x
	elif z <= 1.1e+84:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / t))
	tmp = 0.0
	if (z <= -2.35e+90)
		tmp = x;
	elseif (z <= -1.2e-12)
		tmp = t_1;
	elseif (z <= -1.48e-55)
		tmp = Float64(Float64(z * x) / z);
	elseif (z <= 5e+14)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 1.4e+74)
		tmp = x;
	elseif (z <= 1.1e+84)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / t);
	tmp = 0.0;
	if (z <= -2.35e+90)
		tmp = x;
	elseif (z <= -1.2e-12)
		tmp = t_1;
	elseif (z <= -1.48e-55)
		tmp = (z * x) / z;
	elseif (z <= 5e+14)
		tmp = y / (t / x);
	elseif (z <= 1.4e+74)
		tmp = x;
	elseif (z <= 1.1e+84)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.35e+90], x, If[LessEqual[z, -1.2e-12], t$95$1, If[LessEqual[z, -1.48e-55], N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5e+14], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+74], x, If[LessEqual[z, 1.1e+84], t$95$1, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.3500000000000001e90 or 5e14 < z < 1.40000000000000001e74 or 1.0999999999999999e84 < z

   1. Initial program 75.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 67.7%

      \[\leadsto \color{blue}{x} \]

   if -2.3500000000000001e90 < z < -1.19999999999999994e-12 or 1.40000000000000001e74 < z < 1.0999999999999999e84

   1. Initial program 84.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 39.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 39.3%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 39.3%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   if -1.19999999999999994e-12 < z < -1.4800000000000001e-55

   1. Initial program 100.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto \frac{\color{blue}{-\left(-x \cdot \left(y - z\right)\right)}}{t - z} \]

      2. distribute-lft-neg-out 100.0%

         \[\leadsto \frac{-\color{blue}{\left(-x\right) \cdot \left(y - z\right)}}{t - z} \]

      3. distribute-neg-frac 100.0%

         \[\leadsto \color{blue}{-\frac{\left(-x\right) \cdot \left(y - z\right)}{t - z}} \]

      4. distribute-neg-frac2 100.0%

         \[\leadsto \color{blue}{\frac{\left(-x\right) \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto \frac{\color{blue}{-x \cdot \left(y - z\right)}}{-\left(t - z\right)} \]

      6. distribute-rgt-neg-in 100.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-\left(y - z\right)\right)}}{-\left(t - z\right)} \]

      7. sub-neg 100.0%

         \[\leadsto \frac{x \cdot \left(-\color{blue}{\left(y + \left(-z\right)\right)}\right)}{-\left(t - z\right)} \]

      8. distribute-neg-in 100.0%

         \[\leadsto \frac{x \cdot \color{blue}{\left(\left(-y\right) + \left(-\left(-z\right)\right)\right)}}{-\left(t - z\right)} \]

      9. remove-double-neg 100.0%

         \[\leadsto \frac{x \cdot \left(\left(-y\right) + \color{blue}{z}\right)}{-\left(t - z\right)} \]

      10. +-commutative 100.0%

          \[\leadsto \frac{x \cdot \color{blue}{\left(z + \left(-y\right)\right)}}{-\left(t - z\right)} \]

      11. sub-neg 100.0%

          \[\leadsto \frac{x \cdot \color{blue}{\left(z - y\right)}}{-\left(t - z\right)} \]

      12. sub-neg 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{-\color{blue}{\left(t + \left(-z\right)\right)}} \]

      13. distribute-neg-in 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\color{blue}{\left(-t\right) + \left(-\left(-z\right)\right)}} \]

      14. remove-double-neg 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\left(-t\right) + \color{blue}{z}} \]

      15. +-commutative 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\color{blue}{z + \left(-t\right)}} \]

      16. sub-neg 100.0%

          \[\leadsto \frac{x \cdot \left(z - y\right)}{\color{blue}{z - t}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z - t}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]

   6. Taylor expanded in z around inf 55.8%

      \[\leadsto \frac{\color{blue}{x \cdot z}}{z} \]

   if -1.4800000000000001e-55 < z < 5e14

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 89.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 89.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 89.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 62.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 63.9%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 63.9%

          \[\leadsto \color{blue}{y \cdot \frac{x}{t}} \]

       2. clear-num 63.9%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{t}{x}}} \]

       3. un-div-inv 63.9%

          \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]

   11. Applied egg-rr 63.9%

       \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.48 \cdot 10^{-55}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+74}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ x t))))
   (if (<= z -5.2e+90)
     x
     (if (<= z -3.2e-13)
       t_1
       (if (<= z -1.75e-55)
         x
         (if (<= z 1.1e+14)
           (/ y (/ t x))
           (if (<= z 2.4e+70) x (if (<= z 9.5e+83) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x / t);
	double tmp;
	if (z <= -5.2e+90) {
		tmp = x;
	} else if (z <= -3.2e-13) {
		tmp = t_1;
	} else if (z <= -1.75e-55) {
		tmp = x;
	} else if (z <= 1.1e+14) {
		tmp = y / (t / x);
	} else if (z <= 2.4e+70) {
		tmp = x;
	} else if (z <= 9.5e+83) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x / t)
    if (z <= (-5.2d+90)) then
        tmp = x
    else if (z <= (-3.2d-13)) then
        tmp = t_1
    else if (z <= (-1.75d-55)) then
        tmp = x
    else if (z <= 1.1d+14) then
        tmp = y / (t / x)
    else if (z <= 2.4d+70) then
        tmp = x
    else if (z <= 9.5d+83) then
        tmp = t_1
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (x / t);
	double tmp;
	if (z <= -5.2e+90) {
		tmp = x;
	} else if (z <= -3.2e-13) {
		tmp = t_1;
	} else if (z <= -1.75e-55) {
		tmp = x;
	} else if (z <= 1.1e+14) {
		tmp = y / (t / x);
	} else if (z <= 2.4e+70) {
		tmp = x;
	} else if (z <= 9.5e+83) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x / t)
	tmp = 0
	if z <= -5.2e+90:
		tmp = x
	elif z <= -3.2e-13:
		tmp = t_1
	elif z <= -1.75e-55:
		tmp = x
	elif z <= 1.1e+14:
		tmp = y / (t / x)
	elif z <= 2.4e+70:
		tmp = x
	elif z <= 9.5e+83:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x / t))
	tmp = 0.0
	if (z <= -5.2e+90)
		tmp = x;
	elseif (z <= -3.2e-13)
		tmp = t_1;
	elseif (z <= -1.75e-55)
		tmp = x;
	elseif (z <= 1.1e+14)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 2.4e+70)
		tmp = x;
	elseif (z <= 9.5e+83)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x / t);
	tmp = 0.0;
	if (z <= -5.2e+90)
		tmp = x;
	elseif (z <= -3.2e-13)
		tmp = t_1;
	elseif (z <= -1.75e-55)
		tmp = x;
	elseif (z <= 1.1e+14)
		tmp = y / (t / x);
	elseif (z <= 2.4e+70)
		tmp = x;
	elseif (z <= 9.5e+83)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+90], x, If[LessEqual[z, -3.2e-13], t$95$1, If[LessEqual[z, -1.75e-55], x, If[LessEqual[z, 1.1e+14], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+70], x, If[LessEqual[z, 9.5e+83], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1999999999999997e90 or -3.2e-13 < z < -1.75000000000000013e-55 or 1.1e14 < z < 2.39999999999999987e70 or 9.5000000000000002e83 < z

   1. Initial program 77.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 66.8%

      \[\leadsto \color{blue}{x} \]

   if -5.1999999999999997e90 < z < -3.2e-13 or 2.39999999999999987e70 < z < 9.5000000000000002e83

   1. Initial program 84.3%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 39.2%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 39.3%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 39.3%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   if -1.75000000000000013e-55 < z < 1.1e14

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 89.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 89.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 89.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 62.8%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 63.9%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 63.9%

          \[\leadsto \color{blue}{y \cdot \frac{x}{t}} \]

       2. clear-num 63.9%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{t}{x}}} \]

       3. un-div-inv 63.9%

          \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]

   11. Applied egg-rr 63.9%

       \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-107}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-180}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 130000000000:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+203}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8e-107)
   (* x (/ (- z y) z))
   (if (<= z -9.5e-172)
     (/ (* x (- y z)) t)
     (if (<= z -3e-180)
       (/ (* x (- y)) z)
       (if (<= z 130000000000.0)
         (* (- y z) (/ x t))
         (if (<= z 4e+203) (/ x (- 1.0 (/ t z))) (/ x (/ z (- z y)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e-107) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = (x * (y - z)) / t;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 130000000000.0) {
		tmp = (y - z) * (x / t);
	} else if (z <= 4e+203) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x / (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-8d-107)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-9.5d-172)) then
        tmp = (x * (y - z)) / t
    else if (z <= (-3d-180)) then
        tmp = (x * -y) / z
    else if (z <= 130000000000.0d0) then
        tmp = (y - z) * (x / t)
    else if (z <= 4d+203) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = x / (z / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e-107) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = (x * (y - z)) / t;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 130000000000.0) {
		tmp = (y - z) * (x / t);
	} else if (z <= 4e+203) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x / (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8e-107:
		tmp = x * ((z - y) / z)
	elif z <= -9.5e-172:
		tmp = (x * (y - z)) / t
	elif z <= -3e-180:
		tmp = (x * -y) / z
	elif z <= 130000000000.0:
		tmp = (y - z) * (x / t)
	elif z <= 4e+203:
		tmp = x / (1.0 - (t / z))
	else:
		tmp = x / (z / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8e-107)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -9.5e-172)
		tmp = Float64(Float64(x * Float64(y - z)) / t);
	elseif (z <= -3e-180)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 130000000000.0)
		tmp = Float64(Float64(y - z) * Float64(x / t));
	elseif (z <= 4e+203)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x / Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8e-107)
		tmp = x * ((z - y) / z);
	elseif (z <= -9.5e-172)
		tmp = (x * (y - z)) / t;
	elseif (z <= -3e-180)
		tmp = (x * -y) / z;
	elseif (z <= 130000000000.0)
		tmp = (y - z) * (x / t);
	elseif (z <= 4e+203)
		tmp = x / (1.0 - (t / z));
	else
		tmp = x / (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8e-107], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-172], N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -3e-180], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 130000000000.0], N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+203], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8e-107

   1. Initial program 84.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 84.1%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 84.1%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 84.1%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 78.1%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 78.1%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 78.1%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 78.1%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 78.1%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 78.1%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 78.1%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 78.1%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 59.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 73.6%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 73.6%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   if -8e-107 < z < -9.50000000000000053e-172

   1. Initial program 99.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 82.3%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 82.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 90.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t}} \]

   if -9.50000000000000053e-172 < z < -3.0000000000000001e-180

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 86.4%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 99.8%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 99.8%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 100.0%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 100.0%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 100.0%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 33.0%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 33.0%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   11. Taylor expanded in z around 0 99.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 99.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. neg-mul-1 99.8%

          \[\leadsto \frac{\color{blue}{-x \cdot y}}{z} \]

       3. distribute-rgt-neg-in 99.8%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{z} \]

   13. Simplified 99.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-y\right)}{z}} \]

   if -3.0000000000000001e-180 < z < 1.3e11

   1. Initial program 90.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.6%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 90.5%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 90.6%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 90.6%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in t around inf 77.2%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{t} \]

      2. associate-/l* 81.2%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   9. Simplified 81.2%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   if 1.3e11 < z < 4e203

   1. Initial program 76.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in y around 0 78.5%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{t - z}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 78.5%

         \[\leadsto \frac{x}{\color{blue}{-\frac{t - z}{z}}} \]

   9. Simplified 78.5%

      \[\leadsto \frac{x}{\color{blue}{-\frac{t - z}{z}}} \]

   10. Taylor expanded in x around 0 78.5%

       \[\leadsto \color{blue}{\frac{x}{1 - \frac{t}{z}}} \]

   if 4e203 < z

   1. Initial program 72.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in t around 0 94.0%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{z}{y - z}}} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.0%

         \[\leadsto \frac{x}{\color{blue}{-\frac{z}{y - z}}} \]

      2. distribute-neg-frac2 94.0%

         \[\leadsto \frac{x}{\color{blue}{\frac{z}{-\left(y - z\right)}}} \]

      3. neg-sub0 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{0 - \left(y - z\right)}}} \]

      4. associate-+l- 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(0 - y\right) + z}}} \]

      5. neg-sub0 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(-y\right)} + z}} \]

      6. +-commutative 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{z + \left(-y\right)}}} \]

      7. sub-neg 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{z - y}}} \]

   9. Simplified 94.0%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{z - y}}} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 15: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-180}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 330000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x t))))
   (if (<= z -1.05e-106)
     (* x (/ (- z y) z))
     (if (<= z -9.5e-172)
       t_1
       (if (<= z -3e-180)
         (/ (* x (- y)) z)
         (if (<= z 330000000000.0)
           t_1
           (if (<= z 7e+202) (/ x (- 1.0 (/ t z))) (/ x (/ z (- z y))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 330000000000.0) {
		tmp = t_1;
	} else if (z <= 7e+202) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x / (z / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (x / t)
    if (z <= (-1.05d-106)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-9.5d-172)) then
        tmp = t_1
    else if (z <= (-3d-180)) then
        tmp = (x * -y) / z
    else if (z <= 330000000000.0d0) then
        tmp = t_1
    else if (z <= 7d+202) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = x / (z / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 330000000000.0) {
		tmp = t_1;
	} else if (z <= 7e+202) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x / (z / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (x / t)
	tmp = 0
	if z <= -1.05e-106:
		tmp = x * ((z - y) / z)
	elif z <= -9.5e-172:
		tmp = t_1
	elif z <= -3e-180:
		tmp = (x * -y) / z
	elif z <= 330000000000.0:
		tmp = t_1
	elif z <= 7e+202:
		tmp = x / (1.0 - (t / z))
	else:
		tmp = x / (z / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / t))
	tmp = 0.0
	if (z <= -1.05e-106)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 330000000000.0)
		tmp = t_1;
	elseif (z <= 7e+202)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x / Float64(z / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (x / t);
	tmp = 0.0;
	if (z <= -1.05e-106)
		tmp = x * ((z - y) / z);
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = (x * -y) / z;
	elseif (z <= 330000000000.0)
		tmp = t_1;
	elseif (z <= 7e+202)
		tmp = x / (1.0 - (t / z));
	else
		tmp = x / (z / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-106], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-172], t$95$1, If[LessEqual[z, -3e-180], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 330000000000.0], t$95$1, If[LessEqual[z, 7e+202], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.05000000000000002e-106

   1. Initial program 84.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 84.1%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 84.1%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 84.1%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 78.1%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 78.1%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 78.1%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 78.1%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 78.1%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 78.1%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 78.1%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 78.1%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 59.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 73.6%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 73.6%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   if -1.05000000000000002e-106 < z < -9.50000000000000053e-172 or -3.0000000000000001e-180 < z < 3.3e11

   1. Initial program 91.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 89.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in t around inf 78.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 78.6%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{t} \]

      2. associate-/l* 82.2%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   9. Simplified 82.2%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   if -9.50000000000000053e-172 < z < -3.0000000000000001e-180

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 86.4%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 99.8%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 99.8%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 100.0%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 100.0%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 100.0%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 33.0%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 33.0%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   11. Taylor expanded in z around 0 99.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 99.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. neg-mul-1 99.8%

          \[\leadsto \frac{\color{blue}{-x \cdot y}}{z} \]

       3. distribute-rgt-neg-in 99.8%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{z} \]

   13. Simplified 99.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-y\right)}{z}} \]

   if 3.3e11 < z < 6.99999999999999975e202

   1. Initial program 76.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in y around 0 78.5%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{t - z}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 78.5%

         \[\leadsto \frac{x}{\color{blue}{-\frac{t - z}{z}}} \]

   9. Simplified 78.5%

      \[\leadsto \frac{x}{\color{blue}{-\frac{t - z}{z}}} \]

   10. Taylor expanded in x around 0 78.5%

       \[\leadsto \color{blue}{\frac{x}{1 - \frac{t}{z}}} \]

   if 6.99999999999999975e202 < z

   1. Initial program 72.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in t around 0 94.0%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{z}{y - z}}} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.0%

         \[\leadsto \frac{x}{\color{blue}{-\frac{z}{y - z}}} \]

      2. distribute-neg-frac2 94.0%

         \[\leadsto \frac{x}{\color{blue}{\frac{z}{-\left(y - z\right)}}} \]

      3. neg-sub0 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{0 - \left(y - z\right)}}} \]

      4. associate-+l- 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(0 - y\right) + z}}} \]

      5. neg-sub0 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{\left(-y\right)} + z}} \]

      6. +-commutative 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{z + \left(-y\right)}}} \]

      7. sub-neg 94.0%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{z - y}}} \]

   9. Simplified 94.0%

      \[\leadsto \frac{x}{\color{blue}{\frac{z}{z - y}}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 16: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-180}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 90000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+202}:\\ \;\;\;\;\frac{x}{1 - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x t))))
   (if (<= z -1.05e-106)
     (* x (/ (- z y) z))
     (if (<= z -9.5e-172)
       t_1
       (if (<= z -3e-180)
         (/ (* x (- y)) z)
         (if (<= z 90000000000.0)
           t_1
           (if (<= z 6.6e+202)
             (/ x (- 1.0 (/ t z)))
             (* x (- 1.0 (/ y z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 90000000000.0) {
		tmp = t_1;
	} else if (z <= 6.6e+202) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (x / t)
    if (z <= (-1.05d-106)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-9.5d-172)) then
        tmp = t_1
    else if (z <= (-3d-180)) then
        tmp = (x * -y) / z
    else if (z <= 90000000000.0d0) then
        tmp = t_1
    else if (z <= 6.6d+202) then
        tmp = x / (1.0d0 - (t / z))
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 90000000000.0) {
		tmp = t_1;
	} else if (z <= 6.6e+202) {
		tmp = x / (1.0 - (t / z));
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (x / t)
	tmp = 0
	if z <= -1.05e-106:
		tmp = x * ((z - y) / z)
	elif z <= -9.5e-172:
		tmp = t_1
	elif z <= -3e-180:
		tmp = (x * -y) / z
	elif z <= 90000000000.0:
		tmp = t_1
	elif z <= 6.6e+202:
		tmp = x / (1.0 - (t / z))
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / t))
	tmp = 0.0
	if (z <= -1.05e-106)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 90000000000.0)
		tmp = t_1;
	elseif (z <= 6.6e+202)
		tmp = Float64(x / Float64(1.0 - Float64(t / z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (x / t);
	tmp = 0.0;
	if (z <= -1.05e-106)
		tmp = x * ((z - y) / z);
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = (x * -y) / z;
	elseif (z <= 90000000000.0)
		tmp = t_1;
	elseif (z <= 6.6e+202)
		tmp = x / (1.0 - (t / z));
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-106], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-172], t$95$1, If[LessEqual[z, -3e-180], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 90000000000.0], t$95$1, If[LessEqual[z, 6.6e+202], N[(x / N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.05000000000000002e-106

   1. Initial program 84.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 84.1%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 84.1%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 84.1%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 78.1%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 78.1%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 78.1%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 78.1%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 78.1%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 78.1%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 78.1%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 78.1%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 59.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 73.6%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 73.6%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   if -1.05000000000000002e-106 < z < -9.50000000000000053e-172 or -3.0000000000000001e-180 < z < 9e10

   1. Initial program 91.5%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 89.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 89.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in t around inf 78.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 78.6%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{t} \]

      2. associate-/l* 82.2%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   9. Simplified 82.2%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   if -9.50000000000000053e-172 < z < -3.0000000000000001e-180

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 86.4%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 99.8%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 99.8%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 100.0%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 100.0%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 100.0%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 33.0%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 33.0%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   11. Taylor expanded in z around 0 99.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 99.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. neg-mul-1 99.8%

          \[\leadsto \frac{\color{blue}{-x \cdot y}}{z} \]

       3. distribute-rgt-neg-in 99.8%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{z} \]

   13. Simplified 99.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-y\right)}{z}} \]

   if 9e10 < z < 6.5999999999999998e202

   1. Initial program 76.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.6%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 99.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in y around 0 78.5%

      \[\leadsto \frac{x}{\color{blue}{-1 \cdot \frac{t - z}{z}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 78.5%

         \[\leadsto \frac{x}{\color{blue}{-\frac{t - z}{z}}} \]

   9. Simplified 78.5%

      \[\leadsto \frac{x}{\color{blue}{-\frac{t - z}{z}}} \]

   10. Taylor expanded in x around 0 78.5%

       \[\leadsto \color{blue}{\frac{x}{1 - \frac{t}{z}}} \]

   if 6.5999999999999998e202 < z

   1. Initial program 72.7%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 66.8%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{z}} \]

      2. associate-/l* 94.0%

         \[\leadsto -\color{blue}{x \cdot \frac{y - z}{z}} \]

      3. distribute-rgt-neg-in 94.0%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{y - z}{z}\right)} \]

      4. distribute-frac-neg 94.0%

         \[\leadsto x \cdot \color{blue}{\frac{-\left(y - z\right)}{z}} \]

      5. neg-sub0 94.0%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 94.0%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 94.0%

         \[\leadsto x \cdot \frac{\color{blue}{\left(-y\right)} + z}{z} \]

      8. +-commutative 94.0%

         \[\leadsto x \cdot \frac{\color{blue}{z + \left(-y\right)}}{z} \]

      9. sub-neg 94.0%

         \[\leadsto x \cdot \frac{\color{blue}{z - y}}{z} \]

      10. div-sub 94.0%

          \[\leadsto x \cdot \color{blue}{\left(\frac{z}{z} - \frac{y}{z}\right)} \]

      11. *-inverses 94.0%

          \[\leadsto x \cdot \left(\color{blue}{1} - \frac{y}{z}\right) \]

   7. Simplified 94.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 17: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \frac{x}{t}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-180}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{z}\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (/ x t))))
   (if (<= z -1.05e-106)
     (* x (/ (- z y) z))
     (if (<= z -9.5e-172)
       t_1
       (if (<= z -3e-180)
         (/ (* x (- y)) z)
         (if (<= z 8.4e-52) t_1 (* x (- 1.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 8.4e-52) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (x / t)
    if (z <= (-1.05d-106)) then
        tmp = x * ((z - y) / z)
    else if (z <= (-9.5d-172)) then
        tmp = t_1
    else if (z <= (-3d-180)) then
        tmp = (x * -y) / z
    else if (z <= 8.4d-52) then
        tmp = t_1
    else
        tmp = x * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (x / t);
	double tmp;
	if (z <= -1.05e-106) {
		tmp = x * ((z - y) / z);
	} else if (z <= -9.5e-172) {
		tmp = t_1;
	} else if (z <= -3e-180) {
		tmp = (x * -y) / z;
	} else if (z <= 8.4e-52) {
		tmp = t_1;
	} else {
		tmp = x * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (x / t)
	tmp = 0
	if z <= -1.05e-106:
		tmp = x * ((z - y) / z)
	elif z <= -9.5e-172:
		tmp = t_1
	elif z <= -3e-180:
		tmp = (x * -y) / z
	elif z <= 8.4e-52:
		tmp = t_1
	else:
		tmp = x * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(x / t))
	tmp = 0.0
	if (z <= -1.05e-106)
		tmp = Float64(x * Float64(Float64(z - y) / z));
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = Float64(Float64(x * Float64(-y)) / z);
	elseif (z <= 8.4e-52)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (x / t);
	tmp = 0.0;
	if (z <= -1.05e-106)
		tmp = x * ((z - y) / z);
	elseif (z <= -9.5e-172)
		tmp = t_1;
	elseif (z <= -3e-180)
		tmp = (x * -y) / z;
	elseif (z <= 8.4e-52)
		tmp = t_1;
	else
		tmp = x * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e-106], N[(x * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-172], t$95$1, If[LessEqual[z, -3e-180], N[(N[(x * (-y)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 8.4e-52], t$95$1, N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05000000000000002e-106

   1. Initial program 84.1%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 84.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 84.1%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 84.1%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 84.1%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 78.1%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 78.1%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 78.1%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 78.1%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 78.1%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 78.1%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 78.1%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 78.1%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 78.1%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 59.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 73.6%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 73.6%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   if -1.05000000000000002e-106 < z < -9.50000000000000053e-172 or -3.0000000000000001e-180 < z < 8.3999999999999995e-52

   1. Initial program 89.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 87.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 87.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 87.7%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 87.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 87.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in t around inf 81.2%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t}} \]
   8. Step-by-step derivation

      1. *-commutative 81.2%

         \[\leadsto \frac{\color{blue}{\left(y - z\right) \cdot x}}{t} \]

      2. associate-/l* 87.6%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   9. Simplified 87.6%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{x}{t}} \]

   if -9.50000000000000053e-172 < z < -3.0000000000000001e-180

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 86.4%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 86.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 99.8%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 99.8%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 99.8%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 100.0%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 100.0%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 100.0%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 100.0%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 100.0%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 100.0%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   8. Taylor expanded in t around 0 99.8%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - y\right)}{z}} \]
   9. Step-by-step derivation

      1. associate-/l* 33.0%

         \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   10. Simplified 33.0%

       \[\leadsto \color{blue}{x \cdot \frac{z - y}{z}} \]

   11. Taylor expanded in z around 0 99.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot y}{z}} \]
   12. Step-by-step derivation

       1. associate-*r/ 99.8%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot y\right)}{z}} \]

       2. neg-mul-1 99.8%

          \[\leadsto \frac{\color{blue}{-x \cdot y}}{z} \]

       3. distribute-rgt-neg-in 99.8%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-y\right)}}{z} \]

   13. Simplified 99.8%

       \[\leadsto \color{blue}{\frac{x \cdot \left(-y\right)}{z}} \]

   if 8.3999999999999995e-52 < z

   1. Initial program 79.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 52.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 52.4%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{z}} \]

      2. associate-/l* 68.1%

         \[\leadsto -\color{blue}{x \cdot \frac{y - z}{z}} \]

      3. distribute-rgt-neg-in 68.1%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{y - z}{z}\right)} \]

      4. distribute-frac-neg 68.1%

         \[\leadsto x \cdot \color{blue}{\frac{-\left(y - z\right)}{z}} \]

      5. neg-sub0 68.1%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 68.1%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 68.1%

         \[\leadsto x \cdot \frac{\color{blue}{\left(-y\right)} + z}{z} \]

      8. +-commutative 68.1%

         \[\leadsto x \cdot \frac{\color{blue}{z + \left(-y\right)}}{z} \]

      9. sub-neg 68.1%

         \[\leadsto x \cdot \frac{\color{blue}{z - y}}{z} \]

      10. div-sub 68.1%

          \[\leadsto x \cdot \color{blue}{\left(\frac{z}{z} - \frac{y}{z}\right)} \]

      11. *-inverses 68.1%

          \[\leadsto x \cdot \left(\color{blue}{1} - \frac{y}{z}\right) \]

   7. Simplified 68.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 67.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-242}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y z)))))
   (if (<= z -2.5e-72)
     t_1
     (if (<= z -4.2e-158)
       (/ (* z (- x)) t)
       (if (<= z 2.8e-242)
         (/ y (/ t x))
         (if (<= z 4.4e-9) (/ x (/ t y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.5e-72) {
		tmp = t_1;
	} else if (z <= -4.2e-158) {
		tmp = (z * -x) / t;
	} else if (z <= 2.8e-242) {
		tmp = y / (t / x);
	} else if (z <= 4.4e-9) {
		tmp = x / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / z))
    if (z <= (-2.5d-72)) then
        tmp = t_1
    else if (z <= (-4.2d-158)) then
        tmp = (z * -x) / t
    else if (z <= 2.8d-242) then
        tmp = y / (t / x)
    else if (z <= 4.4d-9) then
        tmp = x / (t / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / z));
	double tmp;
	if (z <= -2.5e-72) {
		tmp = t_1;
	} else if (z <= -4.2e-158) {
		tmp = (z * -x) / t;
	} else if (z <= 2.8e-242) {
		tmp = y / (t / x);
	} else if (z <= 4.4e-9) {
		tmp = x / (t / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / z))
	tmp = 0
	if z <= -2.5e-72:
		tmp = t_1
	elif z <= -4.2e-158:
		tmp = (z * -x) / t
	elif z <= 2.8e-242:
		tmp = y / (t / x)
	elif z <= 4.4e-9:
		tmp = x / (t / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -2.5e-72)
		tmp = t_1;
	elseif (z <= -4.2e-158)
		tmp = Float64(Float64(z * Float64(-x)) / t);
	elseif (z <= 2.8e-242)
		tmp = Float64(y / Float64(t / x));
	elseif (z <= 4.4e-9)
		tmp = Float64(x / Float64(t / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -2.5e-72)
		tmp = t_1;
	elseif (z <= -4.2e-158)
		tmp = (z * -x) / t;
	elseif (z <= 2.8e-242)
		tmp = y / (t / x);
	elseif (z <= 4.4e-9)
		tmp = x / (t / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e-72], t$95$1, If[LessEqual[z, -4.2e-158], N[(N[(z * (-x)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.8e-242], N[(y / N[(t / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e-9], N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4999999999999998e-72 or 4.3999999999999997e-9 < z

   1. Initial program 79.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.3%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 56.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(y - z\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 56.1%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{z}} \]

      2. associate-/l* 72.9%

         \[\leadsto -\color{blue}{x \cdot \frac{y - z}{z}} \]

      3. distribute-rgt-neg-in 72.9%

         \[\leadsto \color{blue}{x \cdot \left(-\frac{y - z}{z}\right)} \]

      4. distribute-frac-neg 72.9%

         \[\leadsto x \cdot \color{blue}{\frac{-\left(y - z\right)}{z}} \]

      5. neg-sub0 72.9%

         \[\leadsto x \cdot \frac{\color{blue}{0 - \left(y - z\right)}}{z} \]

      6. associate--r- 72.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(0 - y\right) + z}}{z} \]

      7. neg-sub0 72.9%

         \[\leadsto x \cdot \frac{\color{blue}{\left(-y\right)} + z}{z} \]

      8. +-commutative 72.9%

         \[\leadsto x \cdot \frac{\color{blue}{z + \left(-y\right)}}{z} \]

      9. sub-neg 72.9%

         \[\leadsto x \cdot \frac{\color{blue}{z - y}}{z} \]

      10. div-sub 72.9%

          \[\leadsto x \cdot \color{blue}{\left(\frac{z}{z} - \frac{y}{z}\right)} \]

      11. *-inverses 72.9%

          \[\leadsto x \cdot \left(\color{blue}{1} - \frac{y}{z}\right) \]

   7. Simplified 72.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{z}\right)} \]

   if -2.4999999999999998e-72 < z < -4.19999999999999983e-158

   1. Initial program 99.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 93.0%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 72.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 65.2%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t}} \]

   7. Simplified 65.2%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t}} \]

   8. Taylor expanded in y around 0 60.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 60.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(x \cdot z\right)}{t}} \]

      2. neg-mul-1 60.0%

         \[\leadsto \frac{\color{blue}{-x \cdot z}}{t} \]

      3. *-commutative 60.0%

         \[\leadsto \frac{-\color{blue}{z \cdot x}}{t} \]

      4. distribute-lft-neg-in 60.0%

         \[\leadsto \frac{\color{blue}{\left(-z\right) \cdot x}}{t} \]

   10. Simplified 60.0%

       \[\leadsto \color{blue}{\frac{\left(-z\right) \cdot x}{t}} \]

   if -4.19999999999999983e-158 < z < 2.79999999999999983e-242

   1. Initial program 89.0%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 82.4%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 82.4%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 82.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 82.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 75.0%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 84.4%

         \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]

   9. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{\frac{x}{t} \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 84.4%

          \[\leadsto \color{blue}{y \cdot \frac{x}{t}} \]

       2. clear-num 84.3%

          \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{t}{x}}} \]

       3. un-div-inv 84.4%

          \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]

   11. Applied egg-rr 84.4%

       \[\leadsto \color{blue}{\frac{y}{\frac{t}{x}}} \]

   if 2.79999999999999983e-242 < z < 4.3999999999999997e-9

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 94.3%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 94.2%

         \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{t - z}{y - z}}} \]

      2. un-div-inv 94.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   6. Applied egg-rr 94.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}} \]

   7. Taylor expanded in z around 0 65.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{t}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-242}:\\ \;\;\;\;\frac{y}{\frac{t}{x}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+81} \lor \neg \left(z \leq 3.8 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.6e+81) (not (<= z 3.8e-90)))
   (* x (/ (- y z) (- t z)))
   (* (/ x (- z t)) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+81) || !(z <= 3.8e-90)) {
		tmp = x * ((y - z) / (t - z));
	} else {
		tmp = (x / (z - t)) * (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.6d+81)) .or. (.not. (z <= 3.8d-90))) then
        tmp = x * ((y - z) / (t - z))
    else
        tmp = (x / (z - t)) * (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+81) || !(z <= 3.8e-90)) {
		tmp = x * ((y - z) / (t - z));
	} else {
		tmp = (x / (z - t)) * (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.6e+81) or not (z <= 3.8e-90):
		tmp = x * ((y - z) / (t - z))
	else:
		tmp = (x / (z - t)) * (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.6e+81) || !(z <= 3.8e-90))
		tmp = Float64(x * Float64(Float64(y - z) / Float64(t - z)));
	else
		tmp = Float64(Float64(x / Float64(z - t)) * Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.6e+81) || ~((z <= 3.8e-90)))
		tmp = x * ((y - z) / (t - z));
	else
		tmp = (x / (z - t)) * (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.6e+81], N[Not[LessEqual[z, 3.8e-90]], $MachinePrecision]], N[(x * N[(N[(y - z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6000000000000003e81 or 3.8e-90 < z

   1. Initial program 79.8%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   if -8.6000000000000003e81 < z < 3.8e-90

   1. Initial program 90.9%

      \[\frac{x \cdot \left(y - z\right)}{t - z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.9%

         \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 90.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(y - z\right)}{t - z}} \]
   6. Step-by-step derivation

      1. remove-double-neg 90.9%

         \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{-\left(-\left(t - z\right)\right)}} \]

      2. distribute-neg-frac2 90.9%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(y - z\right)}{-\left(t - z\right)}} \]

      3. *-commutative 90.9%

         \[\leadsto -\frac{\color{blue}{\left(y - z\right) \cdot x}}{-\left(t - z\right)} \]

      4. associate-/l* 97.4%

         \[\leadsto -\color{blue}{\left(y - z\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      5. distribute-lft-neg-out 97.4%

         \[\leadsto \color{blue}{\left(-\left(y - z\right)\right) \cdot \frac{x}{-\left(t - z\right)}} \]

      6. neg-sub0 97.4%

         \[\leadsto \color{blue}{\left(0 - \left(y - z\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      7. associate--r- 97.4%

         \[\leadsto \color{blue}{\left(\left(0 - y\right) + z\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      8. neg-sub0 97.4%

         \[\leadsto \left(\color{blue}{\left(-y\right)} + z\right) \cdot \frac{x}{-\left(t - z\right)} \]

      9. +-commutative 97.4%

         \[\leadsto \color{blue}{\left(z + \left(-y\right)\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      10. sub-neg 97.4%

          \[\leadsto \color{blue}{\left(z - y\right)} \cdot \frac{x}{-\left(t - z\right)} \]

      11. neg-sub0 97.4%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{0 - \left(t - z\right)}} \]

      12. associate--r- 97.4%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(0 - t\right) + z}} \]

      13. neg-sub0 97.4%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{\left(-t\right)} + z} \]

      14. +-commutative 97.4%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z + \left(-t\right)}} \]

      15. sub-neg 97.4%

          \[\leadsto \left(z - y\right) \cdot \frac{x}{\color{blue}{z - t}} \]

      16. *-commutative 97.4%

          \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]

   7. Simplified 97.4%

      \[\leadsto \color{blue}{\frac{x}{z - t} \cdot \left(z - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+81} \lor \neg \left(z \leq 3.8 \cdot 10^{-90}\right):\\ \;\;\;\;x \cdot \frac{y - z}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - t} \cdot \left(z - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{y - z}{t - z} \end{array} \]

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]

Derivation

1. Initial program 85.0%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. associate-/l* 95.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

3. Simplified 95.1%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 21: 35.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

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
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 85.0%

   \[\frac{x \cdot \left(y - z\right)}{t - z} \]
2. Step-by-step derivation

   1. associate-/l* 95.1%

      \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]

3. Simplified 95.1%

   \[\leadsto \color{blue}{x \cdot \frac{y - z}{t - z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 33.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{t - z}{y - z}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ x (/ (- t z) (- y z))))

C

double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - 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 / ((t - z) / (y - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x / ((t - z) / (y - z));
}

Python

def code(x, y, z, t):
	return x / ((t - z) / (y - z))

Julia

function code(x, y, z, t)
	return Float64(x / Float64(Float64(t - z) / Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x / ((t - z) / (y - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x / N[(N[(t - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024105 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

  :alt
  (/ x (/ (- t z) (- y z)))

  (/ (* x (- y z)) (- t z)))