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

Percentage Accurate: 96.9% → 96.9%

Time: 10.5s

Alternatives: 7

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: 96.9% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

   1. *-commutative 97.2%

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

   2. associate-*r/ 82.9%

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

   3. associate-/l* 97.2%

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

   4. sub-neg 97.2%

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

   5. +-commutative 97.2%

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

   6. neg-sub0 97.2%

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

   7. associate-+l- 97.2%

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

   8. sub0-neg 97.2%

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

   9. neg-mul-1 97.2%

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

   10. associate-/r* 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 2: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))))
   (if (<= y -5e+62)
     t
     (if (<= y -1.62e-248)
       t_1
       (if (<= y 2.8e-270) (* x (/ t z)) (if (<= y 1.05e+46) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double tmp;
	if (y <= -5e+62) {
		tmp = t;
	} else if (y <= -1.62e-248) {
		tmp = t_1;
	} else if (y <= 2.8e-270) {
		tmp = x * (t / z);
	} else if (y <= 1.05e+46) {
		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 - y) / z)
    if (y <= (-5d+62)) then
        tmp = t
    else if (y <= (-1.62d-248)) then
        tmp = t_1
    else if (y <= 2.8d-270) then
        tmp = x * (t / z)
    else if (y <= 1.05d+46) 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 - y) / z);
	double tmp;
	if (y <= -5e+62) {
		tmp = t;
	} else if (y <= -1.62e-248) {
		tmp = t_1;
	} else if (y <= 2.8e-270) {
		tmp = x * (t / z);
	} else if (y <= 1.05e+46) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	tmp = 0
	if y <= -5e+62:
		tmp = t
	elif y <= -1.62e-248:
		tmp = t_1
	elif y <= 2.8e-270:
		tmp = x * (t / z)
	elif y <= 1.05e+46:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (y <= -5e+62)
		tmp = t;
	elseif (y <= -1.62e-248)
		tmp = t_1;
	elseif (y <= 2.8e-270)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 1.05e+46)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	tmp = 0.0;
	if (y <= -5e+62)
		tmp = t;
	elseif (y <= -1.62e-248)
		tmp = t_1;
	elseif (y <= 2.8e-270)
		tmp = x * (t / z);
	elseif (y <= 1.05e+46)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+62], t, If[LessEqual[y, -1.62e-248], t$95$1, If[LessEqual[y, 2.8e-270], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+46], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000029e62 or 1.05e46 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 69.2%

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

   if -5.00000000000000029e62 < y < -1.6200000000000001e-248 or 2.7999999999999999e-270 < y < 1.05e46

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 67.2%

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

   if -1.6200000000000001e-248 < y < 2.7999999999999999e-270

   1. Initial program 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*r/ 87.4%

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

      3. associate-/l* 79.4%

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

      4. sub-neg 79.4%

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

      5. +-commutative 79.4%

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

      6. neg-sub0 79.4%

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

      7. associate-+l- 79.4%

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

      8. sub0-neg 79.4%

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

      9. neg-mul-1 79.4%

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

      10. associate-/r* 79.4%

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

   3. Simplified 79.4%

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

      1. div-inv 79.3%

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

      2. add-cube-cbrt 78.5%

         \[\leadsto \frac{t}{\color{blue}{\left(\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}\right)} \cdot \frac{1}{y - x}} \]

      3. associate-*l* 78.6%

         \[\leadsto \frac{t}{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\sqrt[3]{y - z} \cdot \frac{1}{y - x}\right)}} \]

      4. pow2 78.6%

         \[\leadsto \frac{t}{\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}} \cdot \left(\sqrt[3]{y - z} \cdot \frac{1}{y - x}\right)} \]

   5. Applied egg-rr 78.6%

      \[\leadsto \frac{t}{\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2} \cdot \left(\sqrt[3]{y - z} \cdot \frac{1}{y - x}\right)}} \]

   6. Taylor expanded in y around 0 87.4%

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

      1. associate-*l/ 95.9%

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

   8. Simplified 95.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+62}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.62 \cdot 10^{-248}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+46}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ t_2 := t \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))) (t_2 (* t (/ (- x y) z))))
   (if (<= z -4.9e+38)
     t_2
     (if (<= z 2.4e-152)
       t_1
       (if (<= z 4e-104) (/ (* t x) z) (if (<= z 1.14e+61) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double t_2 = t * ((x - y) / z);
	double tmp;
	if (z <= -4.9e+38) {
		tmp = t_2;
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		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 - x) / y)
    t_2 = t * ((x - y) / z)
    if (z <= (-4.9d+38)) then
        tmp = t_2
    else if (z <= 2.4d-152) then
        tmp = t_1
    else if (z <= 4d-104) then
        tmp = (t * x) / z
    else if (z <= 1.14d+61) 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 - x) / y);
	double t_2 = t * ((x - y) / z);
	double tmp;
	if (z <= -4.9e+38) {
		tmp = t_2;
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	t_2 = t * ((x - y) / z)
	tmp = 0
	if z <= -4.9e+38:
		tmp = t_2
	elif z <= 2.4e-152:
		tmp = t_1
	elif z <= 4e-104:
		tmp = (t * x) / z
	elif z <= 1.14e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	t_2 = Float64(t * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (z <= -4.9e+38)
		tmp = t_2;
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = Float64(Float64(t * x) / z);
	elseif (z <= 1.14e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	t_2 = t * ((x - y) / z);
	tmp = 0.0;
	if (z <= -4.9e+38)
		tmp = t_2;
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = (t * x) / z;
	elseif (z <= 1.14e+61)
		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[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.9e+38], t$95$2, If[LessEqual[z, 2.4e-152], t$95$1, If[LessEqual[z, 4e-104], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.14e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.90000000000000002e38 or 1.13999999999999996e61 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 78.5%

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

   if -4.90000000000000002e38 < z < 2.4e-152 or 3.99999999999999971e-104 < z < 1.13999999999999996e61

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

      3. neg-sub0 83.9%

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

      4. associate--r- 83.9%

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

      5. neg-sub0 83.9%

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

      6. +-commutative 83.9%

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

      7. sub-neg 83.9%

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

   4. Simplified 83.9%

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

   if 2.4e-152 < z < 3.99999999999999971e-104

   1. Initial program 73.8%

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

   2. Taylor expanded in y around 0 99.6%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- y x) y))))
   (if (<= z -4.6e+38)
     (* t (/ (- x y) z))
     (if (<= z 2.4e-152)
       t_1
       (if (<= z 4e-104)
         (/ (* t x) z)
         (if (<= z 1.14e+61) t_1 (/ t (/ z (- x y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (z <= -4.6e+38) {
		tmp = t * ((x - y) / z);
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		tmp = t_1;
	} else {
		tmp = t / (z / (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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y - x) / y)
    if (z <= (-4.6d+38)) then
        tmp = t * ((x - y) / z)
    else if (z <= 2.4d-152) then
        tmp = t_1
    else if (z <= 4d-104) then
        tmp = (t * x) / z
    else if (z <= 1.14d+61) then
        tmp = t_1
    else
        tmp = t / (z / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((y - x) / y);
	double tmp;
	if (z <= -4.6e+38) {
		tmp = t * ((x - y) / z);
	} else if (z <= 2.4e-152) {
		tmp = t_1;
	} else if (z <= 4e-104) {
		tmp = (t * x) / z;
	} else if (z <= 1.14e+61) {
		tmp = t_1;
	} else {
		tmp = t / (z / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((y - x) / y)
	tmp = 0
	if z <= -4.6e+38:
		tmp = t * ((x - y) / z)
	elif z <= 2.4e-152:
		tmp = t_1
	elif z <= 4e-104:
		tmp = (t * x) / z
	elif z <= 1.14e+61:
		tmp = t_1
	else:
		tmp = t / (z / (x - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (z <= -4.6e+38)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = Float64(Float64(t * x) / z);
	elseif (z <= 1.14e+61)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(z / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((y - x) / y);
	tmp = 0.0;
	if (z <= -4.6e+38)
		tmp = t * ((x - y) / z);
	elseif (z <= 2.4e-152)
		tmp = t_1;
	elseif (z <= 4e-104)
		tmp = (t * x) / z;
	elseif (z <= 1.14e+61)
		tmp = t_1;
	else
		tmp = t / (z / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+38], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-152], t$95$1, If[LessEqual[z, 4e-104], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.14e+61], t$95$1, N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.6000000000000002e38

   1. Initial program 96.2%

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

   2. Taylor expanded in z around inf 75.7%

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

   if -4.6000000000000002e38 < z < 2.4e-152 or 3.99999999999999971e-104 < z < 1.13999999999999996e61

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

      3. neg-sub0 83.9%

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

      4. associate--r- 83.9%

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

      5. neg-sub0 83.9%

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

      6. +-commutative 83.9%

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

      7. sub-neg 83.9%

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

   4. Simplified 83.9%

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

   if 2.4e-152 < z < 3.99999999999999971e-104

   1. Initial program 73.8%

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

   2. Taylor expanded in y around 0 99.6%

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

   if 1.13999999999999996e61 < z

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 74.4%

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

      1. associate-/l* 81.3%

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

   4. Simplified 81.3%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-152}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-104}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 5: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-20) t (if (<= y 7.2e-34) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-20) {
		tmp = t;
	} else if (y <= 7.2e-34) {
		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 <= (-1.45d-20)) then
        tmp = t
    else if (y <= 7.2d-34) 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 <= -1.45e-20) {
		tmp = t;
	} else if (y <= 7.2e-34) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-20:
		tmp = t
	elif y <= 7.2e-34:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-20)
		tmp = t;
	elseif (y <= 7.2e-34)
		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 <= -1.45e-20)
		tmp = t;
	elseif (y <= 7.2e-34)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-20], t, If[LessEqual[y, 7.2e-34], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e-20 or 7.20000000000000016e-34 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 59.7%

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

   if -1.45e-20 < y < 7.20000000000000016e-34

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*r/ 89.9%

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

      3. associate-/l* 94.1%

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

      4. sub-neg 94.1%

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

      5. +-commutative 94.1%

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

      6. neg-sub0 94.1%

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

      7. associate-+l- 94.1%

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

      8. sub0-neg 94.1%

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

      9. neg-mul-1 94.1%

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

      10. associate-/r* 94.1%

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

   3. Simplified 94.1%

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

      1. div-inv 93.9%

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

      2. add-cube-cbrt 92.9%

         \[\leadsto \frac{t}{\color{blue}{\left(\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}\right)} \cdot \frac{1}{y - x}} \]

      3. associate-*l* 93.0%

         \[\leadsto \frac{t}{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \left(\sqrt[3]{y - z} \cdot \frac{1}{y - x}\right)}} \]

      4. pow2 93.0%

         \[\leadsto \frac{t}{\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2}} \cdot \left(\sqrt[3]{y - z} \cdot \frac{1}{y - x}\right)} \]

   5. Applied egg-rr 93.0%

      \[\leadsto \frac{t}{\color{blue}{{\left(\sqrt[3]{y - z}\right)}^{2} \cdot \left(\sqrt[3]{y - z} \cdot \frac{1}{y - x}\right)}} \]

   6. Taylor expanded in y around 0 66.3%

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

      1. associate-*l/ 69.6%

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

   8. Simplified 69.6%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

2. Final simplification 97.2%

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

Alternative 7: 35.8% 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 97.2%

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

2. Taylor expanded in y around inf 37.4%

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

3. Final simplification 37.4%

   \[\leadsto t \]

Developer target: 96.9% 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 2023279 
(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))