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

Percentage Accurate: 97.5% → 97.6%

Time: 7.6s

Alternatives: 9

Speedup: 1.0×

• 25.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \cdot \left(z - t\right) + t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{x}{y}\right), t\right) \]

   2. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{y}{x}}\right), t\right) \]

   3. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{y}{x}}\right), t\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{y}{x}\right)\right), t\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{y}{x}\right)\right), t\right) \]

   6. /-lowering-/.f64 98.5%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, x\right)\right), t\right) \]

4. Applied egg-rr 98.5%

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

5. Final simplification 98.5%

   \[\leadsto t + \frac{z - t}{\frac{y}{x}} \]
6. Add Preprocessing

Alternative 2: 93.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) x) y)))
   (if (<= (/ x y) -1e+32)
     t_1
     (if (<= (/ x y) 2e+74) (+ t (* z (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -1e+32) {
		tmp = t_1;
	} else if ((x / y) <= 2e+74) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	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 = ((z - t) * x) / y
    if ((x / y) <= (-1d+32)) then
        tmp = t_1
    else if ((x / y) <= 2d+74) then
        tmp = t + (z * (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z - t) * x) / y;
	double tmp;
	if ((x / y) <= -1e+32) {
		tmp = t_1;
	} else if ((x / y) <= 2e+74) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - t) * x) / y
	tmp = 0
	if (x / y) <= -1e+32:
		tmp = t_1
	elif (x / y) <= 2e+74:
		tmp = t + (z * (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - t) * x) / y)
	tmp = 0.0
	if (Float64(x / y) <= -1e+32)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e+74)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - t) * x) / y;
	tmp = 0.0;
	if ((x / y) <= -1e+32)
		tmp = t_1;
	elseif ((x / y) <= 2e+74)
		tmp = t + (z * (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+32], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e+74], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000005e32 or 1.9999999999999999e74 < (/.f64 x y)

   1. Initial program 97.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 97.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 97.3%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 97.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 97.3%

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

   if -1.00000000000000005e32 < (/.f64 x y) < 1.9999999999999999e74

   1. Initial program 99.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 96.7%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+32}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+74}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e-43)
   (* z (/ x y))
   (if (<= (/ x y) 5e-52) t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-43) {
		tmp = z * (x / y);
	} else if ((x / y) <= 5e-52) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	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 ((x / y) <= (-1d-43)) then
        tmp = z * (x / y)
    else if ((x / y) <= 5d-52) then
        tmp = t
    else
        tmp = z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-43) {
		tmp = z * (x / y);
	} else if ((x / y) <= 5e-52) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e-43:
		tmp = z * (x / y)
	elif (x / y) <= 5e-52:
		tmp = t
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e-43)
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= 5e-52)
		tmp = t;
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e-43)
		tmp = z * (x / y);
	elseif ((x / y) <= 5e-52)
		tmp = t;
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e-43], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-52], t, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.00000000000000008e-43

   1. Initial program 99.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 90.9%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 56.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 56.1%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 66.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right) \]

   9. Applied egg-rr 66.4%

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

   if -1.00000000000000008e-43 < (/.f64 x y) < 5e-52

   1. Initial program 99.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 78.7%

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

   if 5e-52 < (/.f64 x y)

   1. Initial program 95.7%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.0%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 63.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 63.1%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. associate-/r/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      5. /-lowering-/.f64 67.1%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 67.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -1e-43) t_1 (if (<= (/ x y) 5e-52) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -1e-43) {
		tmp = t_1;
	} else if ((x / y) <= 5e-52) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	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 = z * (x / y)
    if ((x / y) <= (-1d-43)) then
        tmp = t_1
    else if ((x / y) <= 5d-52) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -1e-43) {
		tmp = t_1;
	} else if ((x / y) <= 5e-52) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -1e-43:
		tmp = t_1
	elif (x / y) <= 5e-52:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e-43)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-52)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -1e-43)
		tmp = t_1;
	elseif ((x / y) <= 5e-52)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-43], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-52], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000008e-43 or 5e-52 < (/.f64 x y)

   1. Initial program 97.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 91.5%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 91.5%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 59.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 59.6%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 66.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right) \]

   9. Applied egg-rr 66.7%

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

   if -1.00000000000000008e-43 < (/.f64 x y) < 5e-52

   1. Initial program 99.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 93.4%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 78.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-43}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-52}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+74}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -1e+184) t_1 (if (<= t 6.5e+74) (+ t (* z (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1e+184) {
		tmp = t_1;
	} else if (t <= 6.5e+74) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	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 * (1.0d0 - (x / y))
    if (t <= (-1d+184)) then
        tmp = t_1
    else if (t <= 6.5d+74) then
        tmp = t + (z * (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1e+184) {
		tmp = t_1;
	} else if (t <= 6.5e+74) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -1e+184:
		tmp = t_1
	elif t <= 6.5e+74:
		tmp = t + (z * (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -1e+184)
		tmp = t_1;
	elseif (t <= 6.5e+74)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -1e+184)
		tmp = t_1;
	elseif (t <= 6.5e+74)
		tmp = t + (z * (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e+184], t$95$1, If[LessEqual[t, 6.5e+74], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000002e184 or 6.49999999999999962e74 < t

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 89.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 89.4%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 92.4%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 92.4%

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

   if -1.00000000000000002e184 < t < 6.49999999999999962e74

   1. Initial program 97.6%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 90.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+74}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{-138}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 320000:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -1.16e-138) t_1 (if (<= t 320000.0) (* z (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1.16e-138) {
		tmp = t_1;
	} else if (t <= 320000.0) {
		tmp = z * (x / y);
	} else {
		tmp = t_1;
	}
	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 * (1.0d0 - (x / y))
    if (t <= (-1.16d-138)) then
        tmp = t_1
    else if (t <= 320000.0d0) then
        tmp = z * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1.16e-138) {
		tmp = t_1;
	} else if (t <= 320000.0) {
		tmp = z * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -1.16e-138:
		tmp = t_1
	elif t <= 320000.0:
		tmp = z * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -1.16e-138)
		tmp = t_1;
	elseif (t <= 320000.0)
		tmp = Float64(z * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -1.16e-138)
		tmp = t_1;
	elseif (t <= 320000.0)
		tmp = z * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.16e-138], t$95$1, If[LessEqual[t, 320000.0], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.16e-138 or 3.2e5 < t

   1. Initial program 99.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 90.8%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 90.8%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 77.2%

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

   if -1.16e-138 < t < 3.2e5

   1. Initial program 96.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.0%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 68.6%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 73.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right) \]

   9. Applied egg-rr 73.4%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 320000:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.7% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e+50) (+ t (/ x (/ y z))) (+ t (/ (* (- z t) x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+50) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t + (((z - t) * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3d+50)) then
        tmp = t + (x / (y / z))
    else
        tmp = t + (((z - t) * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+50) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t + (((z - t) * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e+50:
		tmp = t + (x / (y / z))
	else:
		tmp = t + (((z - t) * x) / y)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e+50], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999998e50

   1. Initial program 98.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 96.6%

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

      1. *-commutative N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{\frac{y}{x}}\right), \color{blue}{t}\right) \]

      5. associate-/r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z}{y} \cdot x\right), t\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{z}{y}\right), t\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \frac{1}{\frac{y}{z}}\right), t\right) \]

      8. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{\frac{y}{z}}\right), t\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \left(\frac{y}{z}\right)\right), t\right) \]

      10. /-lowering-/.f64 98.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, z\right)\right), t\right) \]

   7. Applied egg-rr 98.4%

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

   if -2.9999999999999998e50 < y

   1. Initial program 98.4%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.8%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.3%

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

Alternative 8: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \left(z - t\right) \cdot \frac{x}{y} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Final simplification 98.3%

   \[\leadsto t + \left(z - t\right) \cdot \frac{x}{y} \]
4. Add Preprocessing

Alternative 9: 38.1% 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 98.3%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Step-by-step derivation

   1. +-commutative N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

   3. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

   6. --lowering--.f64 92.3%

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

3. Simplified 92.3%

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

5. Taylor expanded in x around 0

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

7. Simplified 38.4%

   \[\leadsto \color{blue}{t} \]
8. Add Preprocessing

Developer Target 1: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	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 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

  (+ (* (/ x y) (- z t)) t))