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

Percentage Accurate: 97.0% → 97.3%

Time: 8.6s

Alternatives: 11

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: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq 10^{+292}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) (- z y)))))
   (if (<= t_1 1e+292) t_1 (* x (/ t (- z y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / (z - y));
	double tmp;
	if (t_1 <= 1e+292) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((x - y) / (z - y))
    if (t_1 <= 1d+292) then
        tmp = t_1
    else
        tmp = x * (t / (z - y))
    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 - y));
	double tmp;
	if (t_1 <= 1e+292) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / (z - y))
	tmp = 0
	if t_1 <= 1e+292:
		tmp = t_1
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= 1e+292)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / (z - y));
	tmp = 0.0;
	if (t_1 <= 1e+292)
		tmp = t_1;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+292], t$95$1, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) < 1e292

   1. Initial program 98.2%

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

   if 1e292 < (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

   1. Initial program 68.4%

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

      1. associate-*l/ 99.8%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 99.8%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot \frac{x - y}{z - y} \leq 10^{+292}:\\ \;\;\;\;t \cdot \frac{x - y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 2: 69.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -3.5e+97)
     t
     (if (<= y -2.1e+26)
       t_1
       (if (<= y -8e+15)
         t
         (if (<= y 2.05e-246)
           (* x (/ t (- z y)))
           (if (<= y 5.2e+35) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -3.5e+97) {
		tmp = t;
	} else if (y <= -2.1e+26) {
		tmp = t_1;
	} else if (y <= -8e+15) {
		tmp = t;
	} else if (y <= 2.05e-246) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.2e+35) {
		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 - y))
    if (y <= (-3.5d+97)) then
        tmp = t
    else if (y <= (-2.1d+26)) then
        tmp = t_1
    else if (y <= (-8d+15)) then
        tmp = t
    else if (y <= 2.05d-246) then
        tmp = x * (t / (z - y))
    else if (y <= 5.2d+35) 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 - y));
	double tmp;
	if (y <= -3.5e+97) {
		tmp = t;
	} else if (y <= -2.1e+26) {
		tmp = t_1;
	} else if (y <= -8e+15) {
		tmp = t;
	} else if (y <= 2.05e-246) {
		tmp = x * (t / (z - y));
	} else if (y <= 5.2e+35) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -3.5e+97:
		tmp = t
	elif y <= -2.1e+26:
		tmp = t_1
	elif y <= -8e+15:
		tmp = t
	elif y <= 2.05e-246:
		tmp = x * (t / (z - y))
	elif y <= 5.2e+35:
		tmp = t_1
	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 <= -3.5e+97)
		tmp = t;
	elseif (y <= -2.1e+26)
		tmp = t_1;
	elseif (y <= -8e+15)
		tmp = t;
	elseif (y <= 2.05e-246)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 5.2e+35)
		tmp = t_1;
	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 <= -3.5e+97)
		tmp = t;
	elseif (y <= -2.1e+26)
		tmp = t_1;
	elseif (y <= -8e+15)
		tmp = t;
	elseif (y <= 2.05e-246)
		tmp = x * (t / (z - y));
	elseif (y <= 5.2e+35)
		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 / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+97], t, If[LessEqual[y, -2.1e+26], t$95$1, If[LessEqual[y, -8e+15], t, If[LessEqual[y, 2.05e-246], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+35], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e97 or -2.1000000000000001e26 < y < -8e15 or 5.20000000000000013e35 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 60.8%

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

      2. associate-*r/ 74.3%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in y around inf 68.2%

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

   if -3.5000000000000001e97 < y < -2.1000000000000001e26 or 2.04999999999999993e-246 < y < 5.20000000000000013e35

   1. Initial program 96.0%

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

   2. Taylor expanded in x around inf 67.5%

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

   if -8e15 < y < 2.04999999999999993e-246

   1. Initial program 92.3%

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

      1. associate-*l/ 98.5%

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

      2. associate-*r/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in x around inf 86.3%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

   6. Simplified 85.2%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-246}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 69.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= y -1.2e+100)
     t
     (if (<= y -1.65e+26)
       t_1
       (if (<= y -2e+15)
         t
         (if (<= y 3.4e-248)
           (* x (/ t (- z y)))
           (if (<= y 1.75e+35) t_1 (+ t (/ t (/ y z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (y <= -1.2e+100) {
		tmp = t;
	} else if (y <= -1.65e+26) {
		tmp = t_1;
	} else if (y <= -2e+15) {
		tmp = t;
	} else if (y <= 3.4e-248) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.75e+35) {
		tmp = t_1;
	} else {
		tmp = t + (t / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    if (y <= (-1.2d+100)) then
        tmp = t
    else if (y <= (-1.65d+26)) then
        tmp = t_1
    else if (y <= (-2d+15)) then
        tmp = t
    else if (y <= 3.4d-248) then
        tmp = x * (t / (z - y))
    else if (y <= 1.75d+35) then
        tmp = t_1
    else
        tmp = t + (t / (y / z))
    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 <= -1.2e+100) {
		tmp = t;
	} else if (y <= -1.65e+26) {
		tmp = t_1;
	} else if (y <= -2e+15) {
		tmp = t;
	} else if (y <= 3.4e-248) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.75e+35) {
		tmp = t_1;
	} else {
		tmp = t + (t / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if y <= -1.2e+100:
		tmp = t
	elif y <= -1.65e+26:
		tmp = t_1
	elif y <= -2e+15:
		tmp = t
	elif y <= 3.4e-248:
		tmp = x * (t / (z - y))
	elif y <= 1.75e+35:
		tmp = t_1
	else:
		tmp = t + (t / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.2e+100)
		tmp = t;
	elseif (y <= -1.65e+26)
		tmp = t_1;
	elseif (y <= -2e+15)
		tmp = t;
	elseif (y <= 3.4e-248)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.75e+35)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(t / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -1.2e+100)
		tmp = t;
	elseif (y <= -1.65e+26)
		tmp = t_1;
	elseif (y <= -2e+15)
		tmp = t;
	elseif (y <= 3.4e-248)
		tmp = x * (t / (z - y));
	elseif (y <= 1.75e+35)
		tmp = t_1;
	else
		tmp = t + (t / (y / z));
	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, -1.2e+100], t, If[LessEqual[y, -1.65e+26], t$95$1, If[LessEqual[y, -2e+15], t, If[LessEqual[y, 3.4e-248], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+35], t$95$1, N[(t + N[(t / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.20000000000000006e100 or -1.64999999999999997e26 < y < -2e15

   1. Initial program 99.8%

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

      1. associate-*l/ 58.6%

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

      2. associate-*r/ 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around inf 73.4%

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

   if -1.20000000000000006e100 < y < -1.64999999999999997e26 or 3.3999999999999998e-248 < y < 1.75e35

   1. Initial program 96.0%

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

   2. Taylor expanded in x around inf 67.5%

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

   if -2e15 < y < 3.3999999999999998e-248

   1. Initial program 92.3%

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

      1. associate-*l/ 98.5%

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

      2. associate-*r/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in x around inf 86.3%

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

      1. associate-*l/ 85.2%

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

      2. *-commutative 85.2%

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

   6. Simplified 85.2%

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

   if 1.75e35 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 62.7%

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

      2. associate-*r/ 76.3%

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

   3. Simplified 76.3%

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

   4. Taylor expanded in y around inf 72.2%

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

      1. associate--l+ 72.2%

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

      2. distribute-lft-out-- 72.2%

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

      3. div-sub 72.2%

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

      4. mul-1-neg 72.2%

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

      5. unsub-neg 72.2%

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

      6. distribute-lft-out-- 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in x around 0 59.0%

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

      1. sub-neg 59.0%

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

      2. mul-1-neg 59.0%

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

      3. remove-double-neg 59.0%

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

      4. associate-/l* 64.0%

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

   9. Simplified 64.0%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t}{\frac{y}{z}}\\ \end{array} \]

Alternative 4: 90.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+154}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+158}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e+154)
   (- t (* t (/ x y)))
   (if (<= y 3.8e+158) (* (- x y) (/ t (- z y))) (* t (/ (- y) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+154) {
		tmp = t - (t * (x / y));
	} else if (y <= 3.8e+158) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (-y / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d+154)) then
        tmp = t - (t * (x / y))
    else if (y <= 3.8d+158) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * (-y / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+154) {
		tmp = t - (t * (x / y));
	} else if (y <= 3.8e+158) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (-y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e+154:
		tmp = t - (t * (x / y))
	elif y <= 3.8e+158:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (-y / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e+154)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= 3.8e+158)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e+154)
		tmp = t - (t * (x / y));
	elseif (y <= 3.8e+158)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (-y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e+154], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+158], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000002e154

   1. Initial program 99.9%

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

      1. associate-*l/ 52.6%

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

      2. associate-*r/ 64.8%

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

   3. Simplified 64.8%

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

   4. Taylor expanded in y around inf 69.1%

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

      1. associate--l+ 69.1%

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

      2. distribute-lft-out-- 69.1%

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

      3. div-sub 69.1%

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

      4. mul-1-neg 69.1%

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

      5. unsub-neg 69.1%

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

      6. distribute-lft-out-- 69.1%

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

   6. Simplified 69.1%

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

   7. Taylor expanded in x around inf 77.8%

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

      1. associate-/l* 88.2%

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

   9. Simplified 88.2%

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

       1. clear-num 88.1%

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

       2. associate-/r/ 88.2%

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

       3. clear-num 88.2%

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

   11. Applied egg-rr 88.2%

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

   if -2.50000000000000002e154 < y < 3.7999999999999998e158

   1. Initial program 95.2%

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

      1. associate-*l/ 92.8%

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

      2. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   if 3.7999999999999998e158 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac 86.3%

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

   4. Simplified 86.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+154}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+158}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \]

Alternative 5: 75.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{-36} \lor \neg \left(y \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.24e-36) (not (<= y 4.7e-39)))
   (- t (* t (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.24e-36) || !(y <= 4.7e-39)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.24d-36)) .or. (.not. (y <= 4.7d-39))) then
        tmp = t - (t * (x / y))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.24e-36) || !(y <= 4.7e-39)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.24e-36) or not (y <= 4.7e-39):
		tmp = t - (t * (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.24e-36) || !(y <= 4.7e-39))
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.24e-36) || ~((y <= 4.7e-39)))
		tmp = t - (t * (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.24e-36], N[Not[LessEqual[y, 4.7e-39]], $MachinePrecision]], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.23999999999999997e-36 or 4.7000000000000002e-39 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 68.4%

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

      2. associate-*r/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in y around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. distribute-lft-out-- 68.8%

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

      3. div-sub 68.8%

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

      4. mul-1-neg 68.8%

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

      5. unsub-neg 68.8%

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

      6. distribute-lft-out-- 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in x around inf 72.8%

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

      1. associate-/l* 77.8%

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

   9. Simplified 77.8%

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

       1. clear-num 77.8%

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

       2. associate-/r/ 77.8%

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

       3. clear-num 77.8%

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

   11. Applied egg-rr 77.8%

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

   if -1.23999999999999997e-36 < y < 4.7000000000000002e-39

   1. Initial program 92.1%

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

      1. associate-*l/ 97.2%

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

      2. associate-*r/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around inf 85.4%

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

      1. associate-*l/ 80.9%

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

      2. *-commutative 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{-36} \lor \neg \left(y \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 6: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{-36} \lor \neg \left(y \leq 9.6 \cdot 10^{-39}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.48e-36) (not (<= y 9.6e-39)))
   (- t (* t (/ x y)))
   (/ (* t x) (- z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.48e-36) || !(y <= 9.6e-39)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.48d-36)) .or. (.not. (y <= 9.6d-39))) then
        tmp = t - (t * (x / y))
    else
        tmp = (t * x) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.48e-36) || !(y <= 9.6e-39)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.48e-36) or not (y <= 9.6e-39):
		tmp = t - (t * (x / y))
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.48e-36) || !(y <= 9.6e-39))
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.48e-36) || ~((y <= 9.6e-39)))
		tmp = t - (t * (x / y));
	else
		tmp = (t * x) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.48e-36], N[Not[LessEqual[y, 9.6e-39]], $MachinePrecision]], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.48e-36 or 9.60000000000000063e-39 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 68.4%

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

      2. associate-*r/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in y around inf 68.8%

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

      1. associate--l+ 68.8%

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

      2. distribute-lft-out-- 68.8%

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

      3. div-sub 68.8%

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

      4. mul-1-neg 68.8%

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

      5. unsub-neg 68.8%

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

      6. distribute-lft-out-- 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in x around inf 72.8%

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

      1. associate-/l* 77.8%

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

   9. Simplified 77.8%

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

       1. clear-num 77.8%

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

       2. associate-/r/ 77.8%

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

       3. clear-num 77.8%

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

   11. Applied egg-rr 77.8%

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

   if -1.48e-36 < y < 9.60000000000000063e-39

   1. Initial program 92.1%

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

      1. associate-*l/ 97.2%

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

      2. associate-*r/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in x around inf 85.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.48 \cdot 10^{-36} \lor \neg \left(y \leq 9.6 \cdot 10^{-39}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]

Alternative 7: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+16) t (if (<= y 4.5e+34) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+16) {
		tmp = t;
	} else if (y <= 4.5e+34) {
		tmp = x * (t / (z - y));
	} 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+16)) then
        tmp = t
    else if (y <= 4.5d+34) then
        tmp = x * (t / (z - y))
    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+16) {
		tmp = t;
	} else if (y <= 4.5e+34) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+16:
		tmp = t
	elif y <= 4.5e+34:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+16)
		tmp = t;
	elseif (y <= 4.5e+34)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e+16)
		tmp = t;
	elseif (y <= 4.5e+34)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+16], t, If[LessEqual[y, 4.5e+34], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45e16 or 4.5e34 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 62.8%

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

      2. associate-*r/ 74.8%

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

   3. Simplified 74.8%

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

   4. Taylor expanded in y around inf 63.5%

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

   if -1.45e16 < y < 4.5e34

   1. Initial program 93.3%

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

      1. associate-*l/ 97.6%

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

      2. associate-*r/ 93.3%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in x around inf 80.6%

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

      1. associate-*l/ 77.0%

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

      2. *-commutative 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-36) t (if (<= y 1.1e+22) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-36) {
		tmp = t;
	} else if (y <= 1.1e+22) {
		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-36)) then
        tmp = t
    else if (y <= 1.1d+22) 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-36) {
		tmp = t;
	} else if (y <= 1.1e+22) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-36:
		tmp = t
	elif y <= 1.1e+22:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-36)
		tmp = t;
	elseif (y <= 1.1e+22)
		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-36)
		tmp = t;
	elseif (y <= 1.1e+22)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-36], t, If[LessEqual[y, 1.1e+22], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.45000000000000006e-36 or 1.1e22 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 66.1%

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

      2. associate-*r/ 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in y around inf 60.3%

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

   if -1.45000000000000006e-36 < y < 1.1e22

   1. Initial program 92.7%

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

      1. associate-*l/ 97.4%

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

      2. associate-*r/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in x around inf 82.7%

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

      1. associate-*l/ 78.6%

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

      2. *-commutative 78.6%

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

   6. Simplified 78.6%

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

   7. Taylor expanded in z around inf 67.8%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.18e-36) t (if (<= y 2.8e+27) (/ (* t x) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.18e-36) {
		tmp = t;
	} else if (y <= 2.8e+27) {
		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 <= (-1.18d-36)) then
        tmp = t
    else if (y <= 2.8d+27) 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 <= -1.18e-36) {
		tmp = t;
	} else if (y <= 2.8e+27) {
		tmp = (t * x) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.18e-36:
		tmp = t
	elif y <= 2.8e+27:
		tmp = (t * x) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.18e-36)
		tmp = t;
	elseif (y <= 2.8e+27)
		tmp = Float64(Float64(t * x) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.18e-36)
		tmp = t;
	elseif (y <= 2.8e+27)
		tmp = (t * x) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.18e-36], t, If[LessEqual[y, 2.8e+27], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1799999999999999e-36 or 2.7999999999999999e27 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 66.1%

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

      2. associate-*r/ 77.1%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in y around inf 60.3%

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

   if -1.1799999999999999e-36 < y < 2.7999999999999999e27

   1. Initial program 92.7%

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

      1. associate-*l/ 97.4%

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

      2. associate-*r/ 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in y around 0 70.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 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]

Derivation

1. Initial program 96.4%

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

   1. associate-*l/ 81.0%

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

   2. associate-*r/ 84.5%

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

3. Simplified 84.5%

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

   1. associate-*r/ 81.0%

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

   2. associate-*l/ 96.4%

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

   3. *-commutative 96.4%

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

   4. clear-num 96.4%

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

   5. un-div-inv 96.8%

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

5. Applied egg-rr 96.8%

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

6. Final simplification 96.8%

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

Alternative 11: 35.5% 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 96.4%

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

   1. associate-*l/ 81.0%

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

   2. associate-*r/ 84.5%

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

3. Simplified 84.5%

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

4. Taylor expanded in y around inf 36.7%

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

5. Final simplification 36.7%

   \[\leadsto t \]

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 2023224 
(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))