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

Percentage Accurate: 97.0% → 97.0%

Time: 9.5s

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 96.5%

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

3. Final simplification 96.5%

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

Alternative 2: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z - y}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.45e+19)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 3.7e+50) (* t (/ x (- z y))) (/ (- t) (/ (- z y) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e+19) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 3.7e+50) {
		tmp = t * (x / (z - y));
	} else {
		tmp = -t / ((z - y) / 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 <= (-2.45d+19)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 3.7d+50) then
        tmp = t * (x / (z - y))
    else
        tmp = -t / ((z - y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.45e+19) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 3.7e+50) {
		tmp = t * (x / (z - y));
	} else {
		tmp = -t / ((z - y) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.45e+19:
		tmp = t / (1.0 - (z / y))
	elif y <= 3.7e+50:
		tmp = t * (x / (z - y))
	else:
		tmp = -t / ((z - y) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.45e+19)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 3.7e+50)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(Float64(-t) / Float64(Float64(z - y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.45e+19)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 3.7e+50)
		tmp = t * (x / (z - y));
	else
		tmp = -t / ((z - y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.45e+19], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+50], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-t) / N[(N[(z - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.45e19

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. associate-/l* 85.0%

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

      3. distribute-neg-frac 85.0%

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

      4. div-sub 85.0%

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

      5. *-inverses 85.0%

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

   5. Simplified 85.0%

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

      1. frac-2neg 85.0%

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

      2. div-inv 85.0%

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

      3. remove-double-neg 85.0%

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

      4. sub-neg 85.0%

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

      5. metadata-eval 85.0%

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

      6. distribute-neg-in 85.0%

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

      7. metadata-eval 85.0%

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

   7. Applied egg-rr 85.0%

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

      1. associate-*r/ 85.0%

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

      2. *-rgt-identity 85.0%

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

      3. +-commutative 85.0%

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

      4. unsub-neg 85.0%

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

   9. Simplified 85.0%

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

   if -2.45e19 < y < 3.7000000000000001e50

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 78.4%

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

   if 3.7000000000000001e50 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 66.3%

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

      2. clear-num 66.1%

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

   4. Applied egg-rr 66.1%

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

   5. Taylor expanded in x around 0 56.1%

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

      1. mul-1-neg 56.1%

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

      2. associate-/l* 85.8%

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

      3. distribute-neg-frac 85.8%

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

   7. Simplified 85.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+19}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+50}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{z - y}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+20} \lor \neg \left(y \leq 3 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e+20) (not (<= y 3e+50)))
   (/ t (- 1.0 (/ z y)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e+20) || !(y <= 3e+50)) {
		tmp = t / (1.0 - (z / 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 <= (-8d+20)) .or. (.not. (y <= 3d+50))) then
        tmp = t / (1.0d0 - (z / 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 <= -8e+20) || !(y <= 3e+50)) {
		tmp = t / (1.0 - (z / y));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e+20) or not (y <= 3e+50):
		tmp = t / (1.0 - (z / y))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e+20) || !(y <= 3e+50))
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e+20) || ~((y <= 3e+50)))
		tmp = t / (1.0 - (z / y));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e+20], N[Not[LessEqual[y, 3e+50]], $MachinePrecision]], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e20 or 2.9999999999999998e50 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 58.7%

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

      1. mul-1-neg 58.7%

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

      2. associate-/l* 85.3%

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

      3. distribute-neg-frac 85.3%

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

      4. div-sub 85.3%

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

      5. *-inverses 85.3%

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

   5. Simplified 85.3%

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

      1. frac-2neg 85.3%

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

      2. div-inv 85.3%

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

      3. remove-double-neg 85.3%

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

      4. sub-neg 85.3%

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

      5. metadata-eval 85.3%

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

      6. distribute-neg-in 85.3%

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

      7. metadata-eval 85.3%

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

   7. Applied egg-rr 85.3%

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

      1. associate-*r/ 85.3%

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

      2. *-rgt-identity 85.3%

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

      3. +-commutative 85.3%

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

      4. unsub-neg 85.3%

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

   9. Simplified 85.3%

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

   if -8e20 < y < 2.9999999999999998e50

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 78.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+20} \lor \neg \left(y \leq 3 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.3e+54) t (if (<= y 4e+67) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.3e+54) {
		tmp = t;
	} else if (y <= 4e+67) {
		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 <= (-4.3d+54)) then
        tmp = t
    else if (y <= 4d+67) 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 <= -4.3e+54) {
		tmp = t;
	} else if (y <= 4e+67) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.3e+54:
		tmp = t
	elif y <= 4e+67:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.3e+54)
		tmp = t;
	elseif (y <= 4e+67)
		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 <= -4.3e+54)
		tmp = t;
	elseif (y <= 4e+67)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.3e+54], t, If[LessEqual[y, 4e+67], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -4.29999999999999976e54 or 3.99999999999999993e67 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 77.0%

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

   if -4.29999999999999976e54 < y < 3.99999999999999993e67

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-*r/ 73.9%

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

   5. Simplified 73.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e+61) t (if (<= y 2.9e+68) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+61) {
		tmp = t;
	} else if (y <= 2.9e+68) {
		tmp = t * (x / (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 <= (-1.02d+61)) then
        tmp = t
    else if (y <= 2.9d+68) then
        tmp = t * (x / (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 <= -1.02e+61) {
		tmp = t;
	} else if (y <= 2.9e+68) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e+61:
		tmp = t
	elif y <= 2.9e+68:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e+61)
		tmp = t;
	elseif (y <= 2.9e+68)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.02e+61)
		tmp = t;
	elseif (y <= 2.9e+68)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e+61], t, If[LessEqual[y, 2.9e+68], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999999e61 or 2.90000000000000011e68 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 78.3%

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

   if -1.01999999999999999e61 < y < 2.90000000000000011e68

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 75.3%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+61}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.95e-100) t (if (<= y 3.5e+67) (* y (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.95e-100) {
		tmp = t;
	} else if (y <= 3.5e+67) {
		tmp = y * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.95d-100)) then
        tmp = t
    else if (y <= 3.5d+67) then
        tmp = y * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.95e-100) {
		tmp = t;
	} else if (y <= 3.5e+67) {
		tmp = y * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.95e-100:
		tmp = t
	elif y <= 3.5e+67:
		tmp = y * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.95e-100)
		tmp = t;
	elseif (y <= 3.5e+67)
		tmp = Float64(y * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.95e-100)
		tmp = t;
	elseif (y <= 3.5e+67)
		tmp = y * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.95e-100], t, If[LessEqual[y, 3.5e+67], N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9500000000000002e-100 or 3.5e67 < y

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 61.6%

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

   if -2.9500000000000002e-100 < y < 3.5e67

   1. Initial program 93.6%

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

   3. Taylor expanded in z around inf 73.2%

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

      1. associate-/l* 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around 0 25.7%

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

      1. associate-*r/ 25.7%

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

      2. mul-1-neg 25.7%

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

      3. distribute-rgt-neg-out 25.7%

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

      4. associate-*l/ 28.8%

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

   8. Simplified 28.8%

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

      1. expm1-log1p-u 25.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{z} \cdot \left(-y\right)\right)\right)} \]

      2. expm1-udef 20.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t}{z} \cdot \left(-y\right)\right)} - 1} \]

      3. *-commutative 20.5%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(-y\right) \cdot \frac{t}{z}}\right)} - 1 \]

      4. clear-num 20.5%

         \[\leadsto e^{\mathsf{log1p}\left(\left(-y\right) \cdot \color{blue}{\frac{1}{\frac{z}{t}}}\right)} - 1 \]

      5. un-div-inv 20.5%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{-y}{\frac{z}{t}}}\right)} - 1 \]

      6. add-sqr-sqrt 6.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}{\frac{z}{t}}\right)} - 1 \]

      7. sqrt-unprod 18.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}}{\frac{z}{t}}\right)} - 1 \]

      8. sqr-neg 18.8%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{y \cdot y}}}{\frac{z}{t}}\right)} - 1 \]

      9. sqrt-unprod 12.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}{\frac{z}{t}}\right)} - 1 \]

      10. add-sqr-sqrt 19.7%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{y}}{\frac{z}{t}}\right)} - 1 \]

   10. Applied egg-rr 19.7%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{z}{t}}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 19.7%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{z}{t}}\right)\right)} \]

       2. expm1-log1p 22.5%

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

       3. associate-/l* 18.8%

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

       4. associate-*r/ 22.5%

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

   12. Simplified 22.5%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-100}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+67}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e+55) t (if (<= y 4.2e+69) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+55) {
		tmp = t;
	} else if (y <= 4.2e+69) {
		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 <= (-1.02d+55)) then
        tmp = t
    else if (y <= 4.2d+69) 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 <= -1.02e+55) {
		tmp = t;
	} else if (y <= 4.2e+69) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e+55:
		tmp = t
	elif y <= 4.2e+69:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e+55)
		tmp = t;
	elseif (y <= 4.2e+69)
		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 <= -1.02e+55)
		tmp = t;
	elseif (y <= 4.2e+69)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e+55], t, If[LessEqual[y, 4.2e+69], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02000000000000002e55 or 4.2000000000000003e69 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 77.0%

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

   if -1.02000000000000002e55 < y < 4.2000000000000003e69

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 56.2%

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

      1. associate-/l* 60.4%

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

      2. associate-/r/ 57.2%

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

   5. Simplified 57.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+55}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e+54) t (if (<= y 4e+67) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e+54) {
		tmp = t;
	} else if (y <= 4e+67) {
		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 <= (-3.1d+54)) then
        tmp = t
    else if (y <= 4d+67) 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 <= -3.1e+54) {
		tmp = t;
	} else if (y <= 4e+67) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.1e+54:
		tmp = t
	elif y <= 4e+67:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.1e+54)
		tmp = t;
	elseif (y <= 4e+67)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.1e+54)
		tmp = t;
	elseif (y <= 4e+67)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.1e+54], t, If[LessEqual[y, 4e+67], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e54 or 3.99999999999999993e67 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 77.0%

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

   if -3.0999999999999999e54 < y < 3.99999999999999993e67

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 60.5%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 34.8% 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 96.5%

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

3. Taylor expanded in y around inf 36.6%

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

4. Final simplification 36.6%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.0% 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 2024018 
(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))