Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.0% → 97.0%

Time: 10.9s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

2. Final simplification 96.7%

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

Alternative 2: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -860:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-158}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-137}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;\frac{-t}{\frac{z}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= x -860.0)
     t_1
     (if (<= x 3.4e-158)
       (* t (/ y (- y z)))
       (if (<= x 3e-137)
         (* (- x y) (/ t z))
         (if (<= x 2.15e-36) (/ (- t) (+ (/ z y) -1.0)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (x <= -860.0) {
		tmp = t_1;
	} else if (x <= 3.4e-158) {
		tmp = t * (y / (y - z));
	} else if (x <= 3e-137) {
		tmp = (x - y) * (t / z);
	} else if (x <= 2.15e-36) {
		tmp = -t / ((z / y) + -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    if (x <= (-860.0d0)) then
        tmp = t_1
    else if (x <= 3.4d-158) then
        tmp = t * (y / (y - z))
    else if (x <= 3d-137) then
        tmp = (x - y) * (t / z)
    else if (x <= 2.15d-36) then
        tmp = -t / ((z / y) + (-1.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (x <= -860.0) {
		tmp = t_1;
	} else if (x <= 3.4e-158) {
		tmp = t * (y / (y - z));
	} else if (x <= 3e-137) {
		tmp = (x - y) * (t / z);
	} else if (x <= 2.15e-36) {
		tmp = -t / ((z / y) + -1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if x <= -860.0:
		tmp = t_1
	elif x <= 3.4e-158:
		tmp = t * (y / (y - z))
	elif x <= 3e-137:
		tmp = (x - y) * (t / z)
	elif x <= 2.15e-36:
		tmp = -t / ((z / y) + -1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -860.0)
		tmp = t_1;
	elseif (x <= 3.4e-158)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (x <= 3e-137)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (x <= 2.15e-36)
		tmp = Float64(Float64(-t) / Float64(Float64(z / y) + -1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -860.0)
		tmp = t_1;
	elseif (x <= 3.4e-158)
		tmp = t * (y / (y - z));
	elseif (x <= 3e-137)
		tmp = (x - y) * (t / z);
	elseif (x <= 2.15e-36)
		tmp = -t / ((z / y) + -1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -860.0], t$95$1, If[LessEqual[x, 3.4e-158], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-137], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e-36], N[((-t) / N[(N[(z / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -860 or 2.1500000000000001e-36 < x

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 76.4%

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

   if -860 < x < 3.3999999999999999e-158

   1. Initial program 96.4%

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

      1. associate-*l/ 85.1%

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

      2. *-commutative 85.1%

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

      3. associate-*l/ 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in x around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-neg-frac 76.0%

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

      3. *-commutative 76.0%

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

      4. distribute-lft-neg-out 76.0%

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

   6. Simplified 76.0%

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

      1. frac-2neg 76.0%

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

      2. div-inv 75.9%

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

      3. distribute-lft-neg-out 75.9%

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

      4. remove-double-neg 75.9%

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

      5. *-commutative 75.9%

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

      6. sub-neg 75.9%

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

      7. distribute-neg-in 75.9%

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

      8. add-sqr-sqrt 33.3%

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

      9. sqrt-unprod 52.1%

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

      10. sqr-neg 52.1%

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

      11. sqrt-unprod 27.1%

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

      12. add-sqr-sqrt 43.1%

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

      13. add-sqr-sqrt 15.9%

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

      14. sqrt-unprod 51.0%

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

      15. sqr-neg 51.0%

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

      16. sqrt-unprod 42.5%

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

      17. add-sqr-sqrt 75.9%

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

   8. Applied egg-rr 75.9%

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

      1. associate-*l* 87.7%

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

      2. associate-*r/ 87.9%

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

      3. *-rgt-identity 87.9%

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

      4. +-commutative 87.9%

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

      5. unsub-neg 87.9%

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

   10. Simplified 87.9%

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

   if 3.3999999999999999e-158 < x < 2.9999999999999998e-137

   1. Initial program 72.7%

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

      1. associate-*l/ 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 86.2%

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

   if 2.9999999999999998e-137 < x < 2.1500000000000001e-36

   1. Initial program 94.3%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

      3. associate-*l/ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in x around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-/l* 83.3%

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

      3. distribute-neg-frac 83.3%

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

      4. div-sub 83.3%

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

      5. *-inverses 83.3%

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

   6. Simplified 83.3%

      \[\leadsto \color{blue}{\frac{-t}{\frac{z}{y} - 1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -860:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-158}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-137}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-36}:\\ \;\;\;\;\frac{-t}{\frac{z}{y} + -1}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 3: 58.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= y -2e+93)
     t
     (if (<= y -2.85e-43)
       t_1
       (if (<= y -7.1e-81)
         t
         (if (<= y -1.75e-207) (* x (/ t z)) (if (<= y 5e+97) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -2e+93) {
		tmp = t;
	} else if (y <= -2.85e-43) {
		tmp = t_1;
	} else if (y <= -7.1e-81) {
		tmp = t;
	} else if (y <= -1.75e-207) {
		tmp = x * (t / z);
	} else if (y <= 5e+97) {
		tmp = t_1;
	} else {
		tmp = 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 = t * (x / z)
    if (y <= (-2d+93)) then
        tmp = t
    else if (y <= (-2.85d-43)) then
        tmp = t_1
    else if (y <= (-7.1d-81)) then
        tmp = t
    else if (y <= (-1.75d-207)) then
        tmp = x * (t / z)
    else if (y <= 5d+97) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -2e+93) {
		tmp = t;
	} else if (y <= -2.85e-43) {
		tmp = t_1;
	} else if (y <= -7.1e-81) {
		tmp = t;
	} else if (y <= -1.75e-207) {
		tmp = x * (t / z);
	} else if (y <= 5e+97) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if y <= -2e+93:
		tmp = t
	elif y <= -2.85e-43:
		tmp = t_1
	elif y <= -7.1e-81:
		tmp = t
	elif y <= -1.75e-207:
		tmp = x * (t / z)
	elif y <= 5e+97:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (y <= -2e+93)
		tmp = t;
	elseif (y <= -2.85e-43)
		tmp = t_1;
	elseif (y <= -7.1e-81)
		tmp = t;
	elseif (y <= -1.75e-207)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 5e+97)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (y <= -2e+93)
		tmp = t;
	elseif (y <= -2.85e-43)
		tmp = t_1;
	elseif (y <= -7.1e-81)
		tmp = t;
	elseif (y <= -1.75e-207)
		tmp = x * (t / z);
	elseif (y <= 5e+97)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+93], t, If[LessEqual[y, -2.85e-43], t$95$1, If[LessEqual[y, -7.1e-81], t, If[LessEqual[y, -1.75e-207], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+97], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000009e93 or -2.85e-43 < y < -7.10000000000000019e-81 or 4.99999999999999999e97 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l/ 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in y around inf 68.7%

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

   if -2.00000000000000009e93 < y < -2.85e-43 or -1.7500000000000001e-207 < y < 4.99999999999999999e97

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0 61.0%

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

   if -7.10000000000000019e-81 < y < -1.7500000000000001e-207

   1. Initial program 84.4%

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

      1. associate-*l/ 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. clear-num 99.6%

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

      3. div-inv 99.6%

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

      4. div-inv 99.5%

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

      5. associate-/r* 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in y around 0 53.1%

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

      1. associate-*l/ 55.9%

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

   8. Simplified 55.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 58.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.26e+94)
   t
   (if (<= y -2.8e-44)
     (/ t (/ z x))
     (if (<= y -7.1e-81)
       t
       (if (<= y -6.4e-208)
         (* x (/ t z))
         (if (<= y 1.66e+97) (* t (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.26e+94) {
		tmp = t;
	} else if (y <= -2.8e-44) {
		tmp = t / (z / x);
	} else if (y <= -7.1e-81) {
		tmp = t;
	} else if (y <= -6.4e-208) {
		tmp = x * (t / z);
	} else if (y <= 1.66e+97) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.26d+94)) then
        tmp = t
    else if (y <= (-2.8d-44)) then
        tmp = t / (z / x)
    else if (y <= (-7.1d-81)) then
        tmp = t
    else if (y <= (-6.4d-208)) then
        tmp = x * (t / z)
    else if (y <= 1.66d+97) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.26e+94) {
		tmp = t;
	} else if (y <= -2.8e-44) {
		tmp = t / (z / x);
	} else if (y <= -7.1e-81) {
		tmp = t;
	} else if (y <= -6.4e-208) {
		tmp = x * (t / z);
	} else if (y <= 1.66e+97) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.26e+94:
		tmp = t
	elif y <= -2.8e-44:
		tmp = t / (z / x)
	elif y <= -7.1e-81:
		tmp = t
	elif y <= -6.4e-208:
		tmp = x * (t / z)
	elif y <= 1.66e+97:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.26e+94)
		tmp = t;
	elseif (y <= -2.8e-44)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -7.1e-81)
		tmp = t;
	elseif (y <= -6.4e-208)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 1.66e+97)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.26e+94)
		tmp = t;
	elseif (y <= -2.8e-44)
		tmp = t / (z / x);
	elseif (y <= -7.1e-81)
		tmp = t;
	elseif (y <= -6.4e-208)
		tmp = x * (t / z);
	elseif (y <= 1.66e+97)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.26e+94], t, If[LessEqual[y, -2.8e-44], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.1e-81], t, If[LessEqual[y, -6.4e-208], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.66e+97], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.25999999999999997e94 or -2.8e-44 < y < -7.10000000000000019e-81 or 1.6599999999999999e97 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l/ 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in y around inf 68.7%

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

   if -1.25999999999999997e94 < y < -2.8e-44

   1. Initial program 99.7%

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

      1. associate-*l/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 33.1%

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

      1. associate-/l* 40.4%

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

   6. Simplified 40.4%

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

   if -7.10000000000000019e-81 < y < -6.4000000000000003e-208

   1. Initial program 84.4%

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

      1. associate-*l/ 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. clear-num 99.6%

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

      3. div-inv 99.6%

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

      4. div-inv 99.5%

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

      5. associate-/r* 84.1%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in y around 0 53.1%

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

      1. associate-*l/ 55.9%

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

   8. Simplified 55.9%

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

   if -6.4000000000000003e-208 < y < 1.6599999999999999e97

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 65.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.26 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 58.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.82e+93)
   t
   (if (<= y -3.2e-44)
     (/ t (/ z x))
     (if (<= y -2.05e-82)
       t
       (if (<= y -1.3e-208)
         (/ x (/ z t))
         (if (<= y 1.8e+97) (* t (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.82e+93) {
		tmp = t;
	} else if (y <= -3.2e-44) {
		tmp = t / (z / x);
	} else if (y <= -2.05e-82) {
		tmp = t;
	} else if (y <= -1.3e-208) {
		tmp = x / (z / t);
	} else if (y <= 1.8e+97) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.82d+93)) then
        tmp = t
    else if (y <= (-3.2d-44)) then
        tmp = t / (z / x)
    else if (y <= (-2.05d-82)) then
        tmp = t
    else if (y <= (-1.3d-208)) then
        tmp = x / (z / t)
    else if (y <= 1.8d+97) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.82e+93) {
		tmp = t;
	} else if (y <= -3.2e-44) {
		tmp = t / (z / x);
	} else if (y <= -2.05e-82) {
		tmp = t;
	} else if (y <= -1.3e-208) {
		tmp = x / (z / t);
	} else if (y <= 1.8e+97) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.82e+93:
		tmp = t
	elif y <= -3.2e-44:
		tmp = t / (z / x)
	elif y <= -2.05e-82:
		tmp = t
	elif y <= -1.3e-208:
		tmp = x / (z / t)
	elif y <= 1.8e+97:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.82e+93)
		tmp = t;
	elseif (y <= -3.2e-44)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -2.05e-82)
		tmp = t;
	elseif (y <= -1.3e-208)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 1.8e+97)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.82e+93)
		tmp = t;
	elseif (y <= -3.2e-44)
		tmp = t / (z / x);
	elseif (y <= -2.05e-82)
		tmp = t;
	elseif (y <= -1.3e-208)
		tmp = x / (z / t);
	elseif (y <= 1.8e+97)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.82e+93], t, If[LessEqual[y, -3.2e-44], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.05e-82], t, If[LessEqual[y, -1.3e-208], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+97], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.82000000000000009e93 or -3.19999999999999995e-44 < y < -2.04999999999999998e-82 or 1.79999999999999983e97 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l/ 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in y around inf 68.7%

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

   if -1.82000000000000009e93 < y < -3.19999999999999995e-44

   1. Initial program 99.7%

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

      1. associate-*l/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 33.1%

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

      1. associate-/l* 40.4%

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

   6. Simplified 40.4%

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

   if -2.04999999999999998e-82 < y < -1.30000000000000008e-208

   1. Initial program 84.4%

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

   2. Taylor expanded in y around 0 49.7%

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

      1. associate-/r/ 56.0%

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

   4. Applied egg-rr 56.0%

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

   if -1.30000000000000008e-208 < y < 1.79999999999999983e97

   1. Initial program 96.8%

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

   2. Taylor expanded in y around 0 65.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-82}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-246}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.12e+94)
   t
   (if (<= y -2.8e-42)
     (/ t (/ z x))
     (if (<= y -1.7e-102)
       t
       (if (<= y 9.2e-246)
         (/ (* x t) z)
         (if (<= y 1.66e+97) (* t (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+94) {
		tmp = t;
	} else if (y <= -2.8e-42) {
		tmp = t / (z / x);
	} else if (y <= -1.7e-102) {
		tmp = t;
	} else if (y <= 9.2e-246) {
		tmp = (x * t) / z;
	} else if (y <= 1.66e+97) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.12d+94)) then
        tmp = t
    else if (y <= (-2.8d-42)) then
        tmp = t / (z / x)
    else if (y <= (-1.7d-102)) then
        tmp = t
    else if (y <= 9.2d-246) then
        tmp = (x * t) / z
    else if (y <= 1.66d+97) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+94) {
		tmp = t;
	} else if (y <= -2.8e-42) {
		tmp = t / (z / x);
	} else if (y <= -1.7e-102) {
		tmp = t;
	} else if (y <= 9.2e-246) {
		tmp = (x * t) / z;
	} else if (y <= 1.66e+97) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e+94:
		tmp = t
	elif y <= -2.8e-42:
		tmp = t / (z / x)
	elif y <= -1.7e-102:
		tmp = t
	elif y <= 9.2e-246:
		tmp = (x * t) / z
	elif y <= 1.66e+97:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e+94)
		tmp = t;
	elseif (y <= -2.8e-42)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -1.7e-102)
		tmp = t;
	elseif (y <= 9.2e-246)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 1.66e+97)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.12e+94)
		tmp = t;
	elseif (y <= -2.8e-42)
		tmp = t / (z / x);
	elseif (y <= -1.7e-102)
		tmp = t;
	elseif (y <= 9.2e-246)
		tmp = (x * t) / z;
	elseif (y <= 1.66e+97)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.12e+94], t, If[LessEqual[y, -2.8e-42], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-102], t, If[LessEqual[y, 9.2e-246], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.66e+97], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.11999999999999996e94 or -2.79999999999999998e-42 < y < -1.70000000000000006e-102 or 1.6599999999999999e97 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 69.2%

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

      2. *-commutative 69.2%

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

      3. associate-*l/ 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in y around inf 67.7%

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

   if -1.11999999999999996e94 < y < -2.79999999999999998e-42

   1. Initial program 99.7%

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

      1. associate-*l/ 92.5%

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

      2. *-commutative 92.5%

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

      3. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 33.1%

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

      1. associate-/l* 40.4%

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

   6. Simplified 40.4%

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

   if -1.70000000000000006e-102 < y < 9.199999999999999e-246

   1. Initial program 89.5%

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

      1. associate-*l/ 93.9%

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

      2. *-commutative 93.9%

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

      3. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around 0 71.5%

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

   if 9.199999999999999e-246 < y < 1.6599999999999999e97

   1. Initial program 97.2%

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

   2. Taylor expanded in y around 0 59.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-246}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 57.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.05e+85)
   t
   (if (<= y -1.7e-102)
     (* (/ t y) (- x))
     (if (<= y 4.8e-13)
       (/ (* x t) z)
       (if (<= y 3.2e+85)
         (* t (/ (- y) z))
         (if (<= y 1.66e+97) (* x (/ t z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.05e+85) {
		tmp = t;
	} else if (y <= -1.7e-102) {
		tmp = (t / y) * -x;
	} else if (y <= 4.8e-13) {
		tmp = (x * t) / z;
	} else if (y <= 3.2e+85) {
		tmp = t * (-y / z);
	} else if (y <= 1.66e+97) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.05d+85)) then
        tmp = t
    else if (y <= (-1.7d-102)) then
        tmp = (t / y) * -x
    else if (y <= 4.8d-13) then
        tmp = (x * t) / z
    else if (y <= 3.2d+85) then
        tmp = t * (-y / z)
    else if (y <= 1.66d+97) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.05e+85) {
		tmp = t;
	} else if (y <= -1.7e-102) {
		tmp = (t / y) * -x;
	} else if (y <= 4.8e-13) {
		tmp = (x * t) / z;
	} else if (y <= 3.2e+85) {
		tmp = t * (-y / z);
	} else if (y <= 1.66e+97) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.05e+85:
		tmp = t
	elif y <= -1.7e-102:
		tmp = (t / y) * -x
	elif y <= 4.8e-13:
		tmp = (x * t) / z
	elif y <= 3.2e+85:
		tmp = t * (-y / z)
	elif y <= 1.66e+97:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.05e+85)
		tmp = t;
	elseif (y <= -1.7e-102)
		tmp = Float64(Float64(t / y) * Float64(-x));
	elseif (y <= 4.8e-13)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 3.2e+85)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= 1.66e+97)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.05e+85)
		tmp = t;
	elseif (y <= -1.7e-102)
		tmp = (t / y) * -x;
	elseif (y <= 4.8e-13)
		tmp = (x * t) / z;
	elseif (y <= 3.2e+85)
		tmp = t * (-y / z);
	elseif (y <= 1.66e+97)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.05e+85], t, If[LessEqual[y, -1.7e-102], N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 4.8e-13], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 3.2e+85], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.66e+97], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.04999999999999991e85 or 1.6599999999999999e97 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*l/ 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in y around inf 69.7%

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

   if -3.04999999999999991e85 < y < -1.70000000000000006e-102

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 58.3%

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

   3. Taylor expanded in z around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. associate-*l/ 47.0%

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

      3. *-commutative 47.0%

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

      4. distribute-rgt-neg-in 47.0%

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

      5. distribute-neg-frac 47.0%

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

   5. Simplified 47.0%

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

   if -1.70000000000000006e-102 < y < 4.7999999999999997e-13

   1. Initial program 92.7%

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

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around 0 70.8%

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

   if 4.7999999999999997e-13 < y < 3.20000000000000018e85

   1. Initial program 99.8%

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

      1. associate-/r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around inf 44.1%

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

   5. Taylor expanded in x around 0 38.9%

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

      1. *-commutative 38.9%

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

      2. associate-*l/ 39.0%

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

      3. neg-mul-1 39.0%

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

      4. distribute-rgt-neg-in 39.0%

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

   7. Simplified 39.0%

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

   if 3.20000000000000018e85 < y < 1.6599999999999999e97

   1. Initial program 100.0%

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

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-/r* 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 99.2%

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

      1. associate-*l/ 100.0%

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

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{t}{z} \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{+85}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -2900:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* t (/ x (- z y)))))
   (if (<= x -2900.0)
     t_2
     (if (<= x 3.4e-158)
       t_1
       (if (<= x 4.8e-139) (* (- x y) (/ t z)) (if (<= x 5e-38) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -2900.0) {
		tmp = t_2;
	} else if (x <= 3.4e-158) {
		tmp = t_1;
	} else if (x <= 4.8e-139) {
		tmp = (x - y) * (t / z);
	} else if (x <= 5e-38) {
		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 = t * (y / (y - z))
    t_2 = t * (x / (z - y))
    if (x <= (-2900.0d0)) then
        tmp = t_2
    else if (x <= 3.4d-158) then
        tmp = t_1
    else if (x <= 4.8d-139) then
        tmp = (x - y) * (t / z)
    else if (x <= 5d-38) 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 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -2900.0) {
		tmp = t_2;
	} else if (x <= 3.4e-158) {
		tmp = t_1;
	} else if (x <= 4.8e-139) {
		tmp = (x - y) * (t / z);
	} else if (x <= 5e-38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t * (x / (z - y))
	tmp = 0
	if x <= -2900.0:
		tmp = t_2
	elif x <= 3.4e-158:
		tmp = t_1
	elif x <= 4.8e-139:
		tmp = (x - y) * (t / z)
	elif x <= 5e-38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -2900.0)
		tmp = t_2;
	elseif (x <= 3.4e-158)
		tmp = t_1;
	elseif (x <= 4.8e-139)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (x <= 5e-38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -2900.0)
		tmp = t_2;
	elseif (x <= 3.4e-158)
		tmp = t_1;
	elseif (x <= 4.8e-139)
		tmp = (x - y) * (t / z);
	elseif (x <= 5e-38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2900.0], t$95$2, If[LessEqual[x, 3.4e-158], t$95$1, If[LessEqual[x, 4.8e-139], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2900 or 5.00000000000000033e-38 < x

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 76.4%

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

   if -2900 < x < 3.3999999999999999e-158 or 4.80000000000000029e-139 < x < 5.00000000000000033e-38

   1. Initial program 96.1%

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

      1. associate-*l/ 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*l/ 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in x around 0 74.6%

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

      1. mul-1-neg 74.6%

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

      2. distribute-neg-frac 74.6%

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

      3. *-commutative 74.6%

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

      4. distribute-lft-neg-out 74.6%

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

   6. Simplified 74.6%

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

      1. frac-2neg 74.6%

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

      2. div-inv 74.4%

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

      3. distribute-lft-neg-out 74.4%

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

      4. remove-double-neg 74.4%

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

      5. *-commutative 74.4%

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

      6. sub-neg 74.4%

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

      7. distribute-neg-in 74.4%

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

      8. add-sqr-sqrt 32.9%

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

      9. sqrt-unprod 50.7%

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

      10. sqr-neg 50.7%

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

      11. sqrt-unprod 24.8%

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

      12. add-sqr-sqrt 40.4%

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

      13. add-sqr-sqrt 15.5%

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

      14. sqrt-unprod 48.9%

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

      15. sqr-neg 48.9%

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

      16. sqrt-unprod 41.4%

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

      17. add-sqr-sqrt 74.4%

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

   8. Applied egg-rr 74.4%

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

      1. associate-*l* 87.0%

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

      2. associate-*r/ 87.1%

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

      3. *-rgt-identity 87.1%

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

      4. +-commutative 87.1%

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

      5. unsub-neg 87.1%

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

   10. Simplified 87.1%

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

   if 3.3999999999999999e-158 < x < 4.80000000000000029e-139

   1. Initial program 72.7%

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

      1. associate-*l/ 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 86.2%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2900:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-158}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-139}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 9: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+156}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e+155)
   (* t (/ y (- y z)))
   (if (<= y 6.4e+156) (* (- x y) (/ t (- z y))) (* t (/ (- y x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+155) {
		tmp = t * (y / (y - z));
	} else if (y <= 6.4e+156) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * ((y - x) / 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 (y <= (-4.6d+155)) then
        tmp = t * (y / (y - z))
    else if (y <= 6.4d+156) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+155) {
		tmp = t * (y / (y - z));
	} else if (y <= 6.4e+156) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e+155:
		tmp = t * (y / (y - z))
	elif y <= 6.4e+156:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e+155)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 6.4e+156)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e+155)
		tmp = t * (y / (y - z));
	elseif (y <= 6.4e+156)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e+155], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+156], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.59999999999999996e155

   1. Initial program 99.9%

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

      1. associate-*l/ 49.4%

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

      2. *-commutative 49.4%

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

      3. associate-*l/ 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in x around 0 46.3%

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

      1. mul-1-neg 46.3%

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

      2. distribute-neg-frac 46.3%

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

      3. *-commutative 46.3%

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

      4. distribute-lft-neg-out 46.3%

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

   6. Simplified 46.3%

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

      1. frac-2neg 46.3%

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

      2. div-inv 46.2%

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

      3. distribute-lft-neg-out 46.2%

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

      4. remove-double-neg 46.2%

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

      5. *-commutative 46.2%

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

      6. sub-neg 46.2%

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

      7. distribute-neg-in 46.2%

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

      8. add-sqr-sqrt 45.9%

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

      9. sqrt-unprod 2.3%

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

      10. sqr-neg 2.3%

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

      11. sqrt-unprod 0.0%

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

      12. add-sqr-sqrt 5.3%

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

      13. add-sqr-sqrt 5.3%

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

      14. sqrt-unprod 2.3%

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

      15. sqr-neg 2.3%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 46.2%

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

   8. Applied egg-rr 46.2%

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

      1. associate-*l* 96.6%

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

      2. associate-*r/ 96.8%

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

      3. *-rgt-identity 96.8%

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

      4. +-commutative 96.8%

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

      5. unsub-neg 96.8%

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

   10. Simplified 96.8%

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

   if -4.59999999999999996e155 < y < 6.40000000000000005e156

   1. Initial program 95.8%

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

      1. associate-*l/ 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*l/ 90.4%

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

   3. Simplified 90.4%

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

   if 6.40000000000000005e156 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 92.1%

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

      1. associate-*r/ 92.1%

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

      2. neg-mul-1 92.1%

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

   4. Simplified 92.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+156}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]

Alternative 10: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e+81)
   t
   (if (<= y -1.7e-102)
     (* (/ t y) (- x))
     (if (<= y 2.3e+97) (/ (* x t) z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+81) {
		tmp = t;
	} else if (y <= -1.7e-102) {
		tmp = (t / y) * -x;
	} else if (y <= 2.3e+97) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8d+81)) then
        tmp = t
    else if (y <= (-1.7d-102)) then
        tmp = (t / y) * -x
    else if (y <= 2.3d+97) then
        tmp = (x * t) / z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+81) {
		tmp = t;
	} else if (y <= -1.7e-102) {
		tmp = (t / y) * -x;
	} else if (y <= 2.3e+97) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e+81:
		tmp = t
	elif y <= -1.7e-102:
		tmp = (t / y) * -x
	elif y <= 2.3e+97:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e+81)
		tmp = t;
	elseif (y <= -1.7e-102)
		tmp = Float64(Float64(t / y) * Float64(-x));
	elseif (y <= 2.3e+97)
		tmp = Float64(Float64(x * t) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e+81)
		tmp = t;
	elseif (y <= -1.7e-102)
		tmp = (t / y) * -x;
	elseif (y <= 2.3e+97)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e+81], t, If[LessEqual[y, -1.7e-102], N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 2.3e+97], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.99999999999999937e81 or 2.30000000000000006e97 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*l/ 67.0%

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

   3. Simplified 67.0%

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

   4. Taylor expanded in y around inf 69.7%

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

   if -7.99999999999999937e81 < y < -1.70000000000000006e-102

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 58.3%

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

   3. Taylor expanded in z around 0 44.3%

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

      1. mul-1-neg 44.3%

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

      2. associate-*l/ 47.0%

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

      3. *-commutative 47.0%

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

      4. distribute-rgt-neg-in 47.0%

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

      5. distribute-neg-frac 47.0%

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

   5. Simplified 47.0%

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

   if -1.70000000000000006e-102 < y < 2.30000000000000006e97

   1. Initial program 93.8%

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

      1. associate-*l/ 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around 0 63.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+81}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 68.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-103} \lor \neg \left(y \leq 2.7 \cdot 10^{-14}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e-103) (not (<= y 2.7e-14)))
   (* t (/ y (- y z)))
   (/ (* x t) z)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-103) || !(y <= 2.7e-14)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x * t) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.85d-103)) .or. (.not. (y <= 2.7d-14))) then
        tmp = t * (y / (y - z))
    else
        tmp = (x * t) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e-103) || !(y <= 2.7e-14)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x * t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.85e-103) or not (y <= 2.7e-14):
		tmp = t * (y / (y - z))
	else:
		tmp = (x * t) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.85e-103) || !(y <= 2.7e-14))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(x * t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.85e-103) || ~((y <= 2.7e-14)))
		tmp = t * (y / (y - z));
	else
		tmp = (x * t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.85e-103], N[Not[LessEqual[y, 2.7e-14]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e-103 or 2.6999999999999999e-14 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*l/ 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in x around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. distribute-neg-frac 51.9%

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

      3. *-commutative 51.9%

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

      4. distribute-lft-neg-out 51.9%

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

   6. Simplified 51.9%

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

      1. frac-2neg 51.9%

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

      2. div-inv 51.8%

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

      3. distribute-lft-neg-out 51.8%

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

      4. remove-double-neg 51.8%

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

      5. *-commutative 51.8%

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

      6. sub-neg 51.8%

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

      7. distribute-neg-in 51.8%

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

      8. add-sqr-sqrt 27.9%

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

      9. sqrt-unprod 25.7%

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

      10. sqr-neg 25.7%

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

      11. sqrt-unprod 9.1%

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

      12. add-sqr-sqrt 17.5%

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

      13. add-sqr-sqrt 8.3%

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

      14. sqrt-unprod 22.2%

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

      15. sqr-neg 22.2%

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

      16. sqrt-unprod 23.7%

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

      17. add-sqr-sqrt 51.8%

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

   8. Applied egg-rr 51.8%

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

      1. associate-*l* 69.4%

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

      2. associate-*r/ 69.6%

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

      3. *-rgt-identity 69.6%

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

      4. +-commutative 69.6%

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

      5. unsub-neg 69.6%

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

   10. Simplified 69.6%

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

   if -1.85e-103 < y < 2.6999999999999999e-14

   1. Initial program 92.7%

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

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in y around 0 70.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-103} \lor \neg \left(y \leq 2.7 \cdot 10^{-14}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \end{array} \]

Alternative 12: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-81} \lor \neg \left(y \leq 4.8 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7e-81) (not (<= y 4.8e-13)))
   (* t (/ y (- y z)))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-81) || !(y <= 4.8e-13)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7d-81)) .or. (.not. (y <= 4.8d-13))) then
        tmp = t * (y / (y - z))
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-81) || !(y <= 4.8e-13)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7e-81) or not (y <= 4.8e-13):
		tmp = t * (y / (y - z))
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7e-81) || !(y <= 4.8e-13))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7e-81) || ~((y <= 4.8e-13)))
		tmp = t * (y / (y - z));
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7e-81], N[Not[LessEqual[y, 4.8e-13]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999973e-81 or 4.7999999999999997e-13 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 78.4%

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

      2. *-commutative 78.4%

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

      3. associate-*l/ 76.8%

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

   3. Simplified 76.8%

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

   4. Taylor expanded in x around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. distribute-neg-frac 52.9%

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

      3. *-commutative 52.9%

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

      4. distribute-lft-neg-out 52.9%

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

   6. Simplified 52.9%

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

      1. frac-2neg 52.9%

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

      2. div-inv 52.7%

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

      3. distribute-lft-neg-out 52.7%

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

      4. remove-double-neg 52.7%

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

      5. *-commutative 52.7%

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

      6. sub-neg 52.7%

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

      7. distribute-neg-in 52.7%

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

      8. add-sqr-sqrt 28.4%

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

      9. sqrt-unprod 26.1%

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

      10. sqr-neg 26.1%

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

      11. sqrt-unprod 9.3%

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

      12. add-sqr-sqrt 17.8%

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

      13. add-sqr-sqrt 8.4%

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

      14. sqrt-unprod 22.5%

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

      15. sqr-neg 22.5%

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

      16. sqrt-unprod 24.2%

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

      17. add-sqr-sqrt 52.7%

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

   8. Applied egg-rr 52.7%

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

      1. associate-*l* 70.1%

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

      2. associate-*r/ 70.3%

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

      3. *-rgt-identity 70.3%

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

      4. +-commutative 70.3%

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

      5. unsub-neg 70.3%

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

   10. Simplified 70.3%

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

   if -6.99999999999999973e-81 < y < 4.7999999999999997e-13

   1. Initial program 92.8%

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

      1. associate-*l/ 92.6%

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

      2. *-commutative 92.6%

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

      3. associate-*l/ 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around inf 77.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-81} \lor \neg \left(y \leq 4.8 \cdot 10^{-13}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]

Alternative 13: 58.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.65e+93) t (if (<= y 1.66e+97) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.65e+93) {
		tmp = t;
	} else if (y <= 1.66e+97) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.65d+93)) then
        tmp = t
    else if (y <= 1.66d+97) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.65e+93) {
		tmp = t;
	} else if (y <= 1.66e+97) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.65e+93:
		tmp = t
	elif y <= 1.66e+97:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.65e+93)
		tmp = t;
	elseif (y <= 1.66e+97)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.65e+93)
		tmp = t;
	elseif (y <= 1.66e+97)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.65e+93], t, If[LessEqual[y, 1.66e+97], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6500000000000002e93 or 1.6599999999999999e97 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*l/ 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in y around inf 70.5%

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

   if -2.6500000000000002e93 < y < 1.6599999999999999e97

   1. Initial program 95.1%

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

      1. associate-*l/ 93.3%

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

      2. *-commutative 93.3%

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

      3. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

      1. *-commutative 92.1%

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

      2. clear-num 91.5%

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

      3. div-inv 92.1%

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

      4. div-inv 92.0%

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

      5. associate-/r* 94.9%

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

   5. Applied egg-rr 94.9%

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

   6. Taylor expanded in y around 0 54.9%

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

      1. associate-*l/ 54.0%

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

   8. Simplified 54.0%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+93}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.66 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 35.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.7%

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

   1. associate-*l/ 84.7%

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

   2. *-commutative 84.7%

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

   3. associate-*l/ 83.3%

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

3. Simplified 83.3%

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

4. Taylor expanded in y around inf 33.5%

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

5. Final simplification 33.5%

   \[\leadsto t \]

Developer target: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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