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

Percentage Accurate: 96.8% → 96.8%

Time: 11.9s

Alternatives: 10

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: 96.8% 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: 96.8% 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 97.5%

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

3. Final simplification 97.5%

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

Alternative 2: 69.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.45 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-217}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -5.4e+25)
     t
     (if (<= y -4.45e-150)
       t_1
       (if (<= y -1.28e-217)
         (* (- x y) (/ t z))
         (if (<= y 4.2e+34)
           t_1
           (if (<= y 1.65e+182) (* y (/ t (- y z))) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -5.4e+25) {
		tmp = t;
	} else if (y <= -4.45e-150) {
		tmp = t_1;
	} else if (y <= -1.28e-217) {
		tmp = (x - y) * (t / z);
	} else if (y <= 4.2e+34) {
		tmp = t_1;
	} else if (y <= 1.65e+182) {
		tmp = y * (t / (y - 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) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    if (y <= (-5.4d+25)) then
        tmp = t
    else if (y <= (-4.45d-150)) then
        tmp = t_1
    else if (y <= (-1.28d-217)) then
        tmp = (x - y) * (t / z)
    else if (y <= 4.2d+34) then
        tmp = t_1
    else if (y <= 1.65d+182) then
        tmp = y * (t / (y - z))
    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 - y));
	double tmp;
	if (y <= -5.4e+25) {
		tmp = t;
	} else if (y <= -4.45e-150) {
		tmp = t_1;
	} else if (y <= -1.28e-217) {
		tmp = (x - y) * (t / z);
	} else if (y <= 4.2e+34) {
		tmp = t_1;
	} else if (y <= 1.65e+182) {
		tmp = y * (t / (y - z));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -5.4e+25:
		tmp = t
	elif y <= -4.45e-150:
		tmp = t_1
	elif y <= -1.28e-217:
		tmp = (x - y) * (t / z)
	elif y <= 4.2e+34:
		tmp = t_1
	elif y <= 1.65e+182:
		tmp = y * (t / (y - z))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -5.4e+25)
		tmp = t;
	elseif (y <= -4.45e-150)
		tmp = t_1;
	elseif (y <= -1.28e-217)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 4.2e+34)
		tmp = t_1;
	elseif (y <= 1.65e+182)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -5.4e+25)
		tmp = t;
	elseif (y <= -4.45e-150)
		tmp = t_1;
	elseif (y <= -1.28e-217)
		tmp = (x - y) * (t / z);
	elseif (y <= 4.2e+34)
		tmp = t_1;
	elseif (y <= 1.65e+182)
		tmp = y * (t / (y - z));
	else
		tmp = t;
	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[y, -5.4e+25], t, If[LessEqual[y, -4.45e-150], t$95$1, If[LessEqual[y, -1.28e-217], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+34], t$95$1, If[LessEqual[y, 1.65e+182], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4e25 or 1.65e182 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 75.5%

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

   if -5.4e25 < y < -4.45000000000000005e-150 or -1.28e-217 < y < 4.20000000000000035e34

   1. Initial program 97.6%

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

   3. Taylor expanded in x around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/l* 74.6%

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

      3. associate-/r/ 78.7%

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

   5. Simplified 78.7%

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

   if -4.45000000000000005e-150 < y < -1.28e-217

   1. Initial program 83.3%

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

   3. Taylor expanded in z around inf 94.3%

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

      1. associate-/l* 83.0%

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

      2. associate-/r/ 99.6%

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

   5. Simplified 99.6%

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

   if 4.20000000000000035e34 < y < 1.65e182

   1. Initial program 99.6%

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

      1. associate-/r/ 92.0%

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

      2. div-inv 91.6%

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

      3. associate-/r* 99.4%

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

   4. Applied egg-rr 99.4%

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

   5. Taylor expanded in x around 0 45.2%

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

      1. *-commutative 45.2%

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

      2. associate-/l* 69.7%

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

      3. neg-mul-1 69.7%

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

      4. distribute-neg-frac 69.7%

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

   7. Simplified 69.7%

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

      1. frac-2neg 69.7%

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

      2. div-inv 69.4%

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

      3. remove-double-neg 69.4%

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

      4. distribute-neg-frac 69.4%

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

      5. sub-neg 69.4%

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

      6. distribute-neg-in 69.4%

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

      7. remove-double-neg 69.4%

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

   9. Applied egg-rr 69.4%

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

       1. associate-/r/ 69.6%

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

       2. associate-*l/ 69.6%

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

       3. *-lft-identity 69.6%

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

       4. +-commutative 69.6%

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

       5. unsub-neg 69.6%

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

   11. Simplified 69.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.45 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-217}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+34}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.5:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-73}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.6e+52)
   t
   (if (<= y -3.5)
     (* (/ y z) (- t))
     (if (<= y -2e-73)
       t
       (if (<= y 4e-308)
         (/ x (/ z t))
         (if (<= y 7.8e+108) (/ t (/ z x)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.6e+52) {
		tmp = t;
	} else if (y <= -3.5) {
		tmp = (y / z) * -t;
	} else if (y <= -2e-73) {
		tmp = t;
	} else if (y <= 4e-308) {
		tmp = x / (z / t);
	} else if (y <= 7.8e+108) {
		tmp = t / (z / x);
	} 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 <= (-4.6d+52)) then
        tmp = t
    else if (y <= (-3.5d0)) then
        tmp = (y / z) * -t
    else if (y <= (-2d-73)) then
        tmp = t
    else if (y <= 4d-308) then
        tmp = x / (z / t)
    else if (y <= 7.8d+108) then
        tmp = t / (z / x)
    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 <= -4.6e+52) {
		tmp = t;
	} else if (y <= -3.5) {
		tmp = (y / z) * -t;
	} else if (y <= -2e-73) {
		tmp = t;
	} else if (y <= 4e-308) {
		tmp = x / (z / t);
	} else if (y <= 7.8e+108) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.6e+52:
		tmp = t
	elif y <= -3.5:
		tmp = (y / z) * -t
	elif y <= -2e-73:
		tmp = t
	elif y <= 4e-308:
		tmp = x / (z / t)
	elif y <= 7.8e+108:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.6e+52)
		tmp = t;
	elseif (y <= -3.5)
		tmp = Float64(Float64(y / z) * Float64(-t));
	elseif (y <= -2e-73)
		tmp = t;
	elseif (y <= 4e-308)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 7.8e+108)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.6e+52)
		tmp = t;
	elseif (y <= -3.5)
		tmp = (y / z) * -t;
	elseif (y <= -2e-73)
		tmp = t;
	elseif (y <= 4e-308)
		tmp = x / (z / t);
	elseif (y <= 7.8e+108)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.6e+52], t, If[LessEqual[y, -3.5], N[(N[(y / z), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[y, -2e-73], t, If[LessEqual[y, 4e-308], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e+108], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.6e52 or -3.5 < y < -1.99999999999999999e-73 or 7.79999999999999969e108 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 70.8%

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

   if -4.6e52 < y < -3.5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 89.4%

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

   4. Taylor expanded in x around 0 68.3%

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

      1. neg-mul-1 68.3%

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

      2. distribute-neg-frac 68.3%

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

   6. Simplified 68.3%

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

   if -1.99999999999999999e-73 < y < 4.00000000000000013e-308

   1. Initial program 92.3%

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

      1. associate-/r/ 97.8%

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

      2. div-inv 97.8%

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

      3. associate-/r* 92.3%

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

   4. Applied egg-rr 92.3%

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

   5. Taylor expanded in y around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

   if 4.00000000000000013e-308 < y < 7.79999999999999969e108

   1. Initial program 97.7%

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

   3. Taylor expanded in y around 0 55.5%

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

      1. associate-/l* 60.6%

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

   5. Simplified 60.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+52}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.5:\\ \;\;\;\;\frac{y}{z} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-73}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{y - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+229}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ t (- y z)))))
   (if (<= y -1.75e+229)
     t
     (if (<= y -1.55e-73)
       t_1
       (if (<= y 7.6e-19) (/ t (/ z x)) (if (<= y 1.15e+183) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t / (y - z));
	double tmp;
	if (y <= -1.75e+229) {
		tmp = t;
	} else if (y <= -1.55e-73) {
		tmp = t_1;
	} else if (y <= 7.6e-19) {
		tmp = t / (z / x);
	} else if (y <= 1.15e+183) {
		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 = y * (t / (y - z))
    if (y <= (-1.75d+229)) then
        tmp = t
    else if (y <= (-1.55d-73)) then
        tmp = t_1
    else if (y <= 7.6d-19) then
        tmp = t / (z / x)
    else if (y <= 1.15d+183) 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 = y * (t / (y - z));
	double tmp;
	if (y <= -1.75e+229) {
		tmp = t;
	} else if (y <= -1.55e-73) {
		tmp = t_1;
	} else if (y <= 7.6e-19) {
		tmp = t / (z / x);
	} else if (y <= 1.15e+183) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t / (y - z))
	tmp = 0
	if y <= -1.75e+229:
		tmp = t
	elif y <= -1.55e-73:
		tmp = t_1
	elif y <= 7.6e-19:
		tmp = t / (z / x)
	elif y <= 1.15e+183:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.75e+229)
		tmp = t;
	elseif (y <= -1.55e-73)
		tmp = t_1;
	elseif (y <= 7.6e-19)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.15e+183)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t / (y - z));
	tmp = 0.0;
	if (y <= -1.75e+229)
		tmp = t;
	elseif (y <= -1.55e-73)
		tmp = t_1;
	elseif (y <= 7.6e-19)
		tmp = t / (z / x);
	elseif (y <= 1.15e+183)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+229], t, If[LessEqual[y, -1.55e-73], t$95$1, If[LessEqual[y, 7.6e-19], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+183], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7500000000000001e229 or 1.1499999999999999e183 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 86.4%

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

   if -1.7500000000000001e229 < y < -1.54999999999999985e-73 or 7.6e-19 < y < 1.1499999999999999e183

   1. Initial program 99.8%

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

      1. associate-/r/ 85.3%

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

      2. div-inv 85.1%

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

      3. associate-/r* 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around 0 53.8%

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

      1. *-commutative 53.8%

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

      2. associate-/l* 61.6%

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

      3. neg-mul-1 61.6%

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

      4. distribute-neg-frac 61.6%

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

   7. Simplified 61.6%

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

      1. frac-2neg 61.6%

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

      2. div-inv 61.4%

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

      3. remove-double-neg 61.4%

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

      4. distribute-neg-frac 61.4%

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

      5. sub-neg 61.4%

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

      6. distribute-neg-in 61.4%

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

      7. remove-double-neg 61.4%

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

   9. Applied egg-rr 61.4%

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

       1. associate-/r/ 63.0%

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

       2. associate-*l/ 63.1%

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

       3. *-lft-identity 63.1%

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

       4. +-commutative 63.1%

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

       5. unsub-neg 63.1%

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

   11. Simplified 63.1%

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

   if -1.54999999999999985e-73 < y < 7.6e-19

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 70.6%

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

      1. associate-/l* 72.2%

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

   5. Simplified 72.2%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+229}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-73}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-19}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+229}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+108}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e+229)
   t
   (if (<= y -1.42e-70)
     (* y (/ t (- y z)))
     (if (<= y -5.5e-129)
       (/ t (/ y (- x)))
       (if (<= y 9.4e+108) (* (- x y) (/ t z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e+229) {
		tmp = t;
	} else if (y <= -1.42e-70) {
		tmp = y * (t / (y - z));
	} else if (y <= -5.5e-129) {
		tmp = t / (y / -x);
	} else if (y <= 9.4e+108) {
		tmp = (x - y) * (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 <= (-2.7d+229)) then
        tmp = t
    else if (y <= (-1.42d-70)) then
        tmp = y * (t / (y - z))
    else if (y <= (-5.5d-129)) then
        tmp = t / (y / -x)
    else if (y <= 9.4d+108) then
        tmp = (x - y) * (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 <= -2.7e+229) {
		tmp = t;
	} else if (y <= -1.42e-70) {
		tmp = y * (t / (y - z));
	} else if (y <= -5.5e-129) {
		tmp = t / (y / -x);
	} else if (y <= 9.4e+108) {
		tmp = (x - y) * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e+229:
		tmp = t
	elif y <= -1.42e-70:
		tmp = y * (t / (y - z))
	elif y <= -5.5e-129:
		tmp = t / (y / -x)
	elif y <= 9.4e+108:
		tmp = (x - y) * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e+229)
		tmp = t;
	elseif (y <= -1.42e-70)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= -5.5e-129)
		tmp = Float64(t / Float64(y / Float64(-x)));
	elseif (y <= 9.4e+108)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e+229)
		tmp = t;
	elseif (y <= -1.42e-70)
		tmp = y * (t / (y - z));
	elseif (y <= -5.5e-129)
		tmp = t / (y / -x);
	elseif (y <= 9.4e+108)
		tmp = (x - y) * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e+229], t, If[LessEqual[y, -1.42e-70], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.5e-129], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.4e+108], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e229 or 9.3999999999999991e108 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 78.8%

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

   if -2.7e229 < y < -1.42000000000000002e-70

   1. Initial program 99.9%

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

      1. associate-/r/ 78.4%

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

      2. div-inv 78.3%

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

      3. associate-/r* 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-/l* 60.8%

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

      3. neg-mul-1 60.8%

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

      4. distribute-neg-frac 60.8%

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

   7. Simplified 60.8%

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

      1. frac-2neg 60.8%

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

      2. div-inv 60.6%

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

      3. remove-double-neg 60.6%

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

      4. distribute-neg-frac 60.6%

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

      5. sub-neg 60.6%

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

      6. distribute-neg-in 60.6%

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

      7. remove-double-neg 60.6%

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

   9. Applied egg-rr 60.6%

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

       1. associate-/r/ 63.5%

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

       2. associate-*l/ 63.6%

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

       3. *-lft-identity 63.6%

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

       4. +-commutative 63.6%

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

       5. unsub-neg 63.6%

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

   11. Simplified 63.6%

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

   if -1.42000000000000002e-70 < y < -5.50000000000000023e-129

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

      3. associate-/r/ 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0 71.9%

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

      1. associate-*r/ 71.9%

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

      2. *-commutative 71.9%

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

      3. neg-mul-1 71.9%

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

      4. distribute-lft-neg-in 71.9%

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

      5. *-commutative 71.9%

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

      6. associate-/l* 71.9%

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

   8. Simplified 71.9%

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

   if -5.50000000000000023e-129 < y < 9.3999999999999991e108

   1. Initial program 95.6%

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

   3. Taylor expanded in z around inf 72.9%

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

      1. associate-/l* 76.4%

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

      2. associate-/r/ 75.9%

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

   5. Simplified 75.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+229}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-129}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{+108}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ t_2 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-218}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))) (t_2 (/ t (- 1.0 (/ z y)))))
   (if (<= y -1.55e-21)
     t_2
     (if (<= y -3.9e-148)
       t_1
       (if (<= y -3.3e-218)
         (* (- x y) (/ t z))
         (if (<= y 9.8e+33) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double t_2 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.55e-21) {
		tmp = t_2;
	} else if (y <= -3.9e-148) {
		tmp = t_1;
	} else if (y <= -3.3e-218) {
		tmp = (x - y) * (t / z);
	} else if (y <= 9.8e+33) {
		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 * (x / (z - y))
    t_2 = t / (1.0d0 - (z / y))
    if (y <= (-1.55d-21)) then
        tmp = t_2
    else if (y <= (-3.9d-148)) then
        tmp = t_1
    else if (y <= (-3.3d-218)) then
        tmp = (x - y) * (t / z)
    else if (y <= 9.8d+33) 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 * (x / (z - y));
	double t_2 = t / (1.0 - (z / y));
	double tmp;
	if (y <= -1.55e-21) {
		tmp = t_2;
	} else if (y <= -3.9e-148) {
		tmp = t_1;
	} else if (y <= -3.3e-218) {
		tmp = (x - y) * (t / z);
	} else if (y <= 9.8e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	t_2 = t / (1.0 - (z / y))
	tmp = 0
	if y <= -1.55e-21:
		tmp = t_2
	elif y <= -3.9e-148:
		tmp = t_1
	elif y <= -3.3e-218:
		tmp = (x - y) * (t / z)
	elif y <= 9.8e+33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	t_2 = Float64(t / Float64(1.0 - Float64(z / y)))
	tmp = 0.0
	if (y <= -1.55e-21)
		tmp = t_2;
	elseif (y <= -3.9e-148)
		tmp = t_1;
	elseif (y <= -3.3e-218)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 9.8e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	t_2 = t / (1.0 - (z / y));
	tmp = 0.0;
	if (y <= -1.55e-21)
		tmp = t_2;
	elseif (y <= -3.9e-148)
		tmp = t_1;
	elseif (y <= -3.3e-218)
		tmp = (x - y) * (t / z);
	elseif (y <= 9.8e+33)
		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[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e-21], t$95$2, If[LessEqual[y, -3.9e-148], t$95$1, If[LessEqual[y, -3.3e-218], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5499999999999999e-21 or 9.80000000000000027e33 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 59.7%

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

      1. mul-1-neg 59.7%

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

      2. associate-/l* 81.5%

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

      3. distribute-neg-frac 81.5%

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

      4. div-sub 81.5%

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

      5. *-inverses 81.5%

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

   5. Simplified 81.5%

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

      1. frac-2neg 81.5%

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

      2. div-inv 81.4%

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

      3. remove-double-neg 81.4%

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

      4. sub-neg 81.4%

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

      5. metadata-eval 81.4%

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

      6. distribute-neg-in 81.4%

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

      7. metadata-eval 81.4%

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

   7. Applied egg-rr 81.4%

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

      1. associate-*r/ 81.5%

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

      2. *-rgt-identity 81.5%

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

      3. neg-mul-1 81.5%

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

      4. +-commutative 81.5%

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

      5. neg-mul-1 81.5%

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

      6. unsub-neg 81.5%

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

   9. Simplified 81.5%

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

   if -1.5499999999999999e-21 < y < -3.89999999999999994e-148 or -3.30000000000000023e-218 < y < 9.80000000000000027e33

   1. Initial program 97.4%

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

   3. Taylor expanded in x around inf 78.2%

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

      1. *-commutative 78.2%

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

      2. associate-/l* 78.2%

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

      3. associate-/r/ 82.0%

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

   5. Simplified 82.0%

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

   if -3.89999999999999994e-148 < y < -3.30000000000000023e-218

   1. Initial program 83.3%

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

   3. Taylor expanded in z around inf 94.3%

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

      1. associate-/l* 83.0%

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

      2. associate-/r/ 99.6%

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

   5. Simplified 99.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-21}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-148}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-218}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-73}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e-73) t (if (<= y 1.85e+33) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-73) {
		tmp = t;
	} else if (y <= 1.85e+33) {
		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 <= (-2d-73)) then
        tmp = t
    else if (y <= 1.85d+33) 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 <= -2e-73) {
		tmp = t;
	} else if (y <= 1.85e+33) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e-73:
		tmp = t
	elif y <= 1.85e+33:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e-73)
		tmp = t;
	elseif (y <= 1.85e+33)
		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 <= -2e-73)
		tmp = t;
	elseif (y <= 1.85e+33)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e-73], t, If[LessEqual[y, 1.85e+33], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999999e-73 or 1.8499999999999999e33 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 62.5%

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

   if -1.99999999999999999e-73 < y < 1.8499999999999999e33

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 0 67.5%

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

      1. associate-/l* 69.7%

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

      2. associate-/r/ 68.8%

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

   5. Simplified 68.8%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-73}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e+25) t (if (<= y 7.8e+108) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+25) {
		tmp = t;
	} else if (y <= 7.8e+108) {
		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 <= (-3d+25)) then
        tmp = t
    else if (y <= 7.8d+108) 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 <= -3e+25) {
		tmp = t;
	} else if (y <= 7.8e+108) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e+25:
		tmp = t
	elif y <= 7.8e+108:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e+25)
		tmp = t;
	elseif (y <= 7.8e+108)
		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 <= -3e+25)
		tmp = t;
	elseif (y <= 7.8e+108)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e+25], t, If[LessEqual[y, 7.8e+108], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000006e25 or 7.79999999999999969e108 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 73.3%

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

   if -3.00000000000000006e25 < y < 7.79999999999999969e108

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 62.7%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+25) t (if (<= y 7.8e+108) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+25) {
		tmp = t;
	} else if (y <= 7.8e+108) {
		tmp = t / (z / x);
	} 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 <= (-1.85d+25)) then
        tmp = t
    else if (y <= 7.8d+108) then
        tmp = t / (z / x)
    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 <= -1.85e+25) {
		tmp = t;
	} else if (y <= 7.8e+108) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+25:
		tmp = t
	elif y <= 7.8e+108:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+25)
		tmp = t;
	elseif (y <= 7.8e+108)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.85e+25)
		tmp = t;
	elseif (y <= 7.8e+108)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+25], t, If[LessEqual[y, 7.8e+108], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8499999999999999e25 or 7.79999999999999969e108 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 73.3%

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

   if -1.8499999999999999e25 < y < 7.79999999999999969e108

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 60.2%

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

      1. associate-/l* 63.0%

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

   5. Simplified 63.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.9% 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 97.5%

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

3. Taylor expanded in y around inf 35.3%

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

4. Final simplification 35.3%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 96.8% 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 2024031 
(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))