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

Percentage Accurate: 97.0% → 97.0%

Time: 9.0s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Final simplification 97.9%

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

Alternative 2: 60.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e+86)
   t
   (if (<= y -6.4e-60) (/ (* t (- x)) y) (if (<= y 1.9e-8) (/ t (/ z x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e+86) {
		tmp = t;
	} else if (y <= -6.4e-60) {
		tmp = (t * -x) / y;
	} else if (y <= 1.9e-8) {
		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 <= (-7.2d+86)) then
        tmp = t
    else if (y <= (-6.4d-60)) then
        tmp = (t * -x) / y
    else if (y <= 1.9d-8) 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 <= -7.2e+86) {
		tmp = t;
	} else if (y <= -6.4e-60) {
		tmp = (t * -x) / y;
	} else if (y <= 1.9e-8) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e+86:
		tmp = t
	elif y <= -6.4e-60:
		tmp = (t * -x) / y
	elif y <= 1.9e-8:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e+86)
		tmp = t;
	elseif (y <= -6.4e-60)
		tmp = Float64(Float64(t * Float64(-x)) / y);
	elseif (y <= 1.9e-8)
		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 <= -7.2e+86)
		tmp = t;
	elseif (y <= -6.4e-60)
		tmp = (t * -x) / y;
	elseif (y <= 1.9e-8)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e+86], t, If[LessEqual[y, -6.4e-60], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.9e-8], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.20000000000000011e86 or 1.90000000000000014e-8 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 68.2%

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

   if -7.20000000000000011e86 < y < -6.4000000000000003e-60

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. associate-*r/ 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in z around 0 41.7%

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

      1. associate-*r/ 41.7%

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

      2. mul-1-neg 41.7%

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

      3. distribute-lft-neg-out 41.7%

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

      4. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if -6.4000000000000003e-60 < y < 1.90000000000000014e-8

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 66.8%

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

      1. associate-/l* 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+86}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e+54)
   (- t (* t (/ x y)))
   (if (<= y 8.8e-13) (* x (/ t (- z y))) (* t (- (/ y (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e+54) {
		tmp = t - (t * (x / y));
	} else if (y <= 8.8e-13) {
		tmp = x * (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 <= (-2.1d+54)) then
        tmp = t - (t * (x / y))
    else if (y <= 8.8d-13) then
        tmp = x * (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 <= -2.1e+54) {
		tmp = t - (t * (x / y));
	} else if (y <= 8.8e-13) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * -(y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e+54:
		tmp = t - (t * (x / y))
	elif y <= 8.8e-13:
		tmp = x * (t / (z - y))
	else:
		tmp = t * -(y / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e+54)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= 8.8e-13)
		tmp = Float64(x * 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 <= -2.1e+54)
		tmp = t - (t * (x / y));
	elseif (y <= 8.8e-13)
		tmp = x * (t / (z - y));
	else
		tmp = t * -(y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e+54], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-13], N[(x * 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 < -2.09999999999999986e54

   1. Initial program 99.8%

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

      1. associate-/r/ 63.2%

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

      2. div-inv 63.1%

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

      3. associate-/r* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 91.4%

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

      3. distribute-neg-frac 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in y around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-/l* 83.1%

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

      4. unsub-neg 83.1%

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

      5. associate-/r/ 91.4%

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

   10. Simplified 91.4%

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

   if -2.09999999999999986e54 < y < 8.79999999999999986e-13

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-*r/ 81.2%

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

   5. Simplified 81.2%

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

   if 8.79999999999999986e-13 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

      2. distribute-neg-frac 78.1%

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

   5. Simplified 78.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+54}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+53}:\\ \;\;\;\;\frac{-t}{\frac{y}{x - y}}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e+53)
   (/ (- t) (/ y (- x y)))
   (if (<= y 1.26e-13) (* x (/ t (- z y))) (* t (- (/ y (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e+53) {
		tmp = -t / (y / (x - y));
	} else if (y <= 1.26e-13) {
		tmp = x * (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 <= (-9d+53)) then
        tmp = -t / (y / (x - y))
    else if (y <= 1.26d-13) then
        tmp = x * (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 <= -9e+53) {
		tmp = -t / (y / (x - y));
	} else if (y <= 1.26e-13) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * -(y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e+53:
		tmp = -t / (y / (x - y))
	elif y <= 1.26e-13:
		tmp = x * (t / (z - y))
	else:
		tmp = t * -(y / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e+53)
		tmp = Float64(Float64(-t) / Float64(y / Float64(x - y)));
	elseif (y <= 1.26e-13)
		tmp = Float64(x * 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 <= -9e+53)
		tmp = -t / (y / (x - y));
	elseif (y <= 1.26e-13)
		tmp = x * (t / (z - y));
	else
		tmp = t * -(y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e+53], N[((-t) / N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e-13], N[(x * 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 < -9.0000000000000004e53

   1. Initial program 99.8%

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

      1. associate-/r/ 63.2%

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

      2. div-inv 63.1%

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

      3. associate-/r* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 91.4%

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

      3. distribute-neg-frac 91.4%

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

   7. Simplified 91.4%

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

   if -9.0000000000000004e53 < y < 1.25999999999999993e-13

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. associate-*r/ 81.2%

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

   5. Simplified 81.2%

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

   if 1.25999999999999993e-13 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 78.1%

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

      1. neg-mul-1 78.1%

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

      2. distribute-neg-frac 78.1%

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

   5. Simplified 78.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+53}:\\ \;\;\;\;\frac{-t}{\frac{y}{x - y}}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{y}{z - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+53} \lor \neg \left(y \leq 4.1 \cdot 10^{-11}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+53) (not (<= y 4.1e-11)))
   (- t (* t (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+53) || !(y <= 4.1e-11)) {
		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 <= (-9d+53)) .or. (.not. (y <= 4.1d-11))) 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 <= -9e+53) || !(y <= 4.1e-11)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+53) or not (y <= 4.1e-11):
		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 <= -9e+53) || !(y <= 4.1e-11))
		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 <= -9e+53) || ~((y <= 4.1e-11)))
		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, -9e+53], N[Not[LessEqual[y, 4.1e-11]], $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 < -9.0000000000000004e53 or 4.1000000000000001e-11 < y

   1. Initial program 99.8%

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

      1. associate-/r/ 72.5%

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

      2. div-inv 72.4%

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

      3. associate-/r* 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-/l* 83.7%

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

      3. distribute-neg-frac 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in y around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-/l* 79.7%

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

      4. unsub-neg 79.7%

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

      5. associate-/r/ 83.7%

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

   10. Simplified 83.7%

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

   if -9.0000000000000004e53 < y < 4.1000000000000001e-11

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-*r/ 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+53} \lor \neg \left(y \leq 4.1 \cdot 10^{-11}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e+88) t (if (<= y 8.6e+104) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+88) {
		tmp = t;
	} else if (y <= 8.6e+104) {
		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 <= (-1.15d+88)) then
        tmp = t
    else if (y <= 8.6d+104) 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 <= -1.15e+88) {
		tmp = t;
	} else if (y <= 8.6e+104) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e+88:
		tmp = t
	elif y <= 8.6e+104:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e+88)
		tmp = t;
	elseif (y <= 8.6e+104)
		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 <= -1.15e+88)
		tmp = t;
	elseif (y <= 8.6e+104)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e+88], t, If[LessEqual[y, 8.6e+104], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1500000000000001e88 or 8.6000000000000003e104 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 75.1%

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

   if -1.1500000000000001e88 < y < 8.6000000000000003e104

   1. Initial program 96.8%

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

   3. Taylor expanded in x around inf 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r/ 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e+84) t (if (<= y 1.7e-8) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e+84) {
		tmp = t;
	} else if (y <= 1.7e-8) {
		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 <= (-1.6d+84)) then
        tmp = t
    else if (y <= 1.7d-8) 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 <= -1.6e+84) {
		tmp = t;
	} else if (y <= 1.7e-8) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e+84:
		tmp = t
	elif y <= 1.7e-8:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e+84)
		tmp = t;
	elseif (y <= 1.7e-8)
		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 <= -1.6e+84)
		tmp = t;
	elseif (y <= 1.7e-8)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e+84], t, If[LessEqual[y, 1.7e-8], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000005e84 or 1.7e-8 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 67.1%

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

   if -1.60000000000000005e84 < y < 1.7e-8

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 55.8%

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

      1. associate-/l* 63.7%

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

      2. associate-/r/ 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e+84) t (if (<= y 1.4e-8) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+84) {
		tmp = t;
	} else if (y <= 1.4e-8) {
		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 <= (-5.2d+84)) then
        tmp = t
    else if (y <= 1.4d-8) 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 <= -5.2e+84) {
		tmp = t;
	} else if (y <= 1.4e-8) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e+84:
		tmp = t
	elif y <= 1.4e-8:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e+84)
		tmp = t;
	elseif (y <= 1.4e-8)
		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 <= -5.2e+84)
		tmp = t;
	elseif (y <= 1.4e-8)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e+84], t, If[LessEqual[y, 1.4e-8], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000002e84 or 1.4e-8 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 67.1%

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

   if -5.2000000000000002e84 < y < 1.4e-8

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 55.8%

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

      1. associate-/l* 63.7%

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

   5. Simplified 63.7%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+84}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.0% 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 97.9%

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

3. Taylor expanded in y around inf 38.6%

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

4. Final simplification 38.6%

   \[\leadsto t \]
5. Add Preprocessing

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 2024027 
(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))