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

Percentage Accurate: 97.6% → 97.6%

Time: 6.1s

Alternatives: 11

Speedup: 1.0×

• 25.3% 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: 97.6% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Final simplification 97.0%

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

Alternative 2: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))))
   (if (<= (/ x y) -1e+20)
     t_1
     (if (<= (/ x y) 1e-7)
       t
       (if (or (<= (/ x y) 2e+114) (not (<= (/ x y) 2e+193)))
         (* (/ x y) z)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -1e+20) {
		tmp = t_1;
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else if (((x / y) <= 2e+114) || !((x / y) <= 2e+193)) {
		tmp = (x / y) * z;
	} 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) * -t
    if ((x / y) <= (-1d+20)) then
        tmp = t_1
    else if ((x / y) <= 1d-7) then
        tmp = t
    else if (((x / y) <= 2d+114) .or. (.not. ((x / y) <= 2d+193))) then
        tmp = (x / y) * z
    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) * -t;
	double tmp;
	if ((x / y) <= -1e+20) {
		tmp = t_1;
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else if (((x / y) <= 2e+114) || !((x / y) <= 2e+193)) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * -t
	tmp = 0
	if (x / y) <= -1e+20:
		tmp = t_1
	elif (x / y) <= 1e-7:
		tmp = t
	elif ((x / y) <= 2e+114) or not ((x / y) <= 2e+193):
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (Float64(x / y) <= -1e+20)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-7)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+114) || !(Float64(x / y) <= 2e+193))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * -t;
	tmp = 0.0;
	if ((x / y) <= -1e+20)
		tmp = t_1;
	elseif ((x / y) <= 1e-7)
		tmp = t;
	elseif (((x / y) <= 2e+114) || ~(((x / y) <= 2e+193)))
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+20], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-7], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+114], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+193]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1e20 or 2e114 < (/.f64 x y) < 2.00000000000000013e193

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 98.6%

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

   3. Taylor expanded in x around -inf 98.6%

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

   4. Taylor expanded in z around 0 63.9%

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

      1. mul-1-neg 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-*l/ 65.3%

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

      4. distribute-rgt-neg-out 65.3%

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

   6. Simplified 65.3%

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

   if -1e20 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 77.6%

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

   if 9.9999999999999995e-8 < (/.f64 x y) < 2e114 or 2.00000000000000013e193 < (/.f64 x y)

   1. Initial program 91.9%

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

   2. Taylor expanded in x around 0 87.9%

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

   3. Taylor expanded in x around -inf 87.6%

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

   4. Taylor expanded in z around inf 57.0%

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

      1. *-commutative 57.0%

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

      2. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

      1. associate-/r/ 66.9%

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

   8. Applied egg-rr 66.9%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 3: 64.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+20)
   (/ t (/ (- y) x))
   (if (<= (/ x y) 1e-7)
     t
     (if (or (<= (/ x y) 2e+114) (not (<= (/ x y) 2e+193)))
       (* (/ x y) z)
       (* (/ x y) (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+20) {
		tmp = t / (-y / x);
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else if (((x / y) <= 2e+114) || !((x / y) <= 2e+193)) {
		tmp = (x / y) * z;
	} else {
		tmp = (x / y) * -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 ((x / y) <= (-1d+20)) then
        tmp = t / (-y / x)
    else if ((x / y) <= 1d-7) then
        tmp = t
    else if (((x / y) <= 2d+114) .or. (.not. ((x / y) <= 2d+193))) then
        tmp = (x / y) * z
    else
        tmp = (x / y) * -t
    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+20) {
		tmp = t / (-y / x);
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else if (((x / y) <= 2e+114) || !((x / y) <= 2e+193)) {
		tmp = (x / y) * z;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+20:
		tmp = t / (-y / x)
	elif (x / y) <= 1e-7:
		tmp = t
	elif ((x / y) <= 2e+114) or not ((x / y) <= 2e+193):
		tmp = (x / y) * z
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+20)
		tmp = Float64(t / Float64(Float64(-y) / x));
	elseif (Float64(x / y) <= 1e-7)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+114) || !(Float64(x / y) <= 2e+193))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e+20)
		tmp = t / (-y / x);
	elseif ((x / y) <= 1e-7)
		tmp = t;
	elseif (((x / y) <= 2e+114) || ~(((x / y) <= 2e+193)))
		tmp = (x / y) * z;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+20], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-7], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+114], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+193]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -1e20

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 98.2%

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

   3. Taylor expanded in x around -inf 98.2%

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

   4. Taylor expanded in z around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. associate-*l/ 63.2%

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

      4. distribute-rgt-neg-out 63.2%

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

   6. Simplified 63.2%

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

      1. associate-*l/ 59.8%

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

      2. distribute-rgt-neg-out 59.8%

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

      3. distribute-lft-neg-out 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-/l* 63.3%

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

      6. frac-2neg 63.3%

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

      7. add-sqr-sqrt 32.9%

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

      8. sqrt-unprod 27.9%

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

      9. sqr-neg 27.9%

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

      10. sqrt-unprod 4.4%

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

      11. add-sqr-sqrt 8.8%

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

      12. add-sqr-sqrt 6.2%

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

      13. sqrt-unprod 40.0%

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

      14. sqr-neg 40.0%

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

      15. sqrt-unprod 32.2%

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

      16. add-sqr-sqrt 63.3%

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

   8. Applied egg-rr 63.3%

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

   if -1e20 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 77.6%

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

   if 9.9999999999999995e-8 < (/.f64 x y) < 2e114 or 2.00000000000000013e193 < (/.f64 x y)

   1. Initial program 91.9%

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

   2. Taylor expanded in x around 0 87.9%

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

   3. Taylor expanded in x around -inf 87.6%

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

   4. Taylor expanded in z around inf 57.0%

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

      1. *-commutative 57.0%

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

      2. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

      1. associate-/r/ 66.9%

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

   8. Applied egg-rr 66.9%

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

   if 2e114 < (/.f64 x y) < 2.00000000000000013e193

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in x around -inf 99.9%

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

   4. Taylor expanded in z around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*l/ 71.7%

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

      4. distribute-rgt-neg-out 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 4: 64.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+20)
   (/ t (/ (- y) x))
   (if (<= (/ x y) 1e-7)
     t
     (if (or (<= (/ x y) 2e+114) (not (<= (/ x y) 2e+193)))
       (* (/ x y) z)
       (/ (* t (- x)) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+20) {
		tmp = t / (-y / x);
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else if (((x / y) <= 2e+114) || !((x / y) <= 2e+193)) {
		tmp = (x / y) * z;
	} else {
		tmp = (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 ((x / y) <= (-1d+20)) then
        tmp = t / (-y / x)
    else if ((x / y) <= 1d-7) then
        tmp = t
    else if (((x / y) <= 2d+114) .or. (.not. ((x / y) <= 2d+193))) then
        tmp = (x / y) * z
    else
        tmp = (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 ((x / y) <= -1e+20) {
		tmp = t / (-y / x);
	} else if ((x / y) <= 1e-7) {
		tmp = t;
	} else if (((x / y) <= 2e+114) || !((x / y) <= 2e+193)) {
		tmp = (x / y) * z;
	} else {
		tmp = (t * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+20:
		tmp = t / (-y / x)
	elif (x / y) <= 1e-7:
		tmp = t
	elif ((x / y) <= 2e+114) or not ((x / y) <= 2e+193):
		tmp = (x / y) * z
	else:
		tmp = (t * -x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+20)
		tmp = Float64(t / Float64(Float64(-y) / x));
	elseif (Float64(x / y) <= 1e-7)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+114) || !(Float64(x / y) <= 2e+193))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = Float64(Float64(t * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e+20)
		tmp = t / (-y / x);
	elseif ((x / y) <= 1e-7)
		tmp = t;
	elseif (((x / y) <= 2e+114) || ~(((x / y) <= 2e+193)))
		tmp = (x / y) * z;
	else
		tmp = (t * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+20], N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-7], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+114], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+193]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -1e20

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 98.2%

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

   3. Taylor expanded in x around -inf 98.2%

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

   4. Taylor expanded in z around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. *-commutative 59.8%

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

      3. associate-*l/ 63.2%

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

      4. distribute-rgt-neg-out 63.2%

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

   6. Simplified 63.2%

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

      1. associate-*l/ 59.8%

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

      2. distribute-rgt-neg-out 59.8%

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

      3. distribute-lft-neg-out 59.8%

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

      4. *-commutative 59.8%

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

      5. associate-/l* 63.3%

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

      6. frac-2neg 63.3%

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

      7. add-sqr-sqrt 32.9%

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

      8. sqrt-unprod 27.9%

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

      9. sqr-neg 27.9%

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

      10. sqrt-unprod 4.4%

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

      11. add-sqr-sqrt 8.8%

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

      12. add-sqr-sqrt 6.2%

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

      13. sqrt-unprod 40.0%

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

      14. sqr-neg 40.0%

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

      15. sqrt-unprod 32.2%

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

      16. add-sqr-sqrt 63.3%

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

   8. Applied egg-rr 63.3%

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

   if -1e20 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 77.6%

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

   if 9.9999999999999995e-8 < (/.f64 x y) < 2e114 or 2.00000000000000013e193 < (/.f64 x y)

   1. Initial program 91.9%

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

   2. Taylor expanded in x around 0 87.9%

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

   3. Taylor expanded in x around -inf 87.6%

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

   4. Taylor expanded in z around inf 57.0%

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

      1. *-commutative 57.0%

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

      2. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

      1. associate-/r/ 66.9%

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

   8. Applied egg-rr 66.9%

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

   if 2e114 < (/.f64 x y) < 2.00000000000000013e193

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.9%

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

   3. Taylor expanded in x around -inf 99.9%

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

   4. Taylor expanded in z around 0 76.9%

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

      1. neg-mul-1 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

   6. Simplified 76.9%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;\frac{t}{\frac{-y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+114} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+193}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \end{array} \]

Alternative 5: 94.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+20) (not (<= (/ x y) 5e+18)))
   (/ (* x (- z t)) y)
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+20) || !((x / y) <= 5e+18)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+20)) .or. (.not. ((x / y) <= 5d+18))) then
        tmp = (x * (z - t)) / y
    else
        tmp = t + ((x / y) * z)
    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+20) || !((x / y) <= 5e+18)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+20) or not ((x / y) <= 5e+18):
		tmp = (x * (z - t)) / y
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+20) || !(Float64(x / y) <= 5e+18))
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+20) || ~(((x / y) <= 5e+18)))
		tmp = (x * (z - t)) / y;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+18]], $MachinePrecision]], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e20 or 5e18 < (/.f64 x y)

   1. Initial program 95.7%

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

   2. Taylor expanded in x around 0 97.5%

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

   3. Taylor expanded in x around -inf 97.5%

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

   if -1e20 < (/.f64 x y) < 5e18

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 94.1%

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

      1. associate-*r/ 96.0%

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

   4. Simplified 96.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 6: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{-93} \lor \neg \left(\frac{x}{y} \leq 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6e-93) (not (<= (/ x y) 1e-7))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6e-93) || !((x / y) <= 1e-7)) {
		tmp = (x / y) * 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 (((x / y) <= (-6d-93)) .or. (.not. ((x / y) <= 1d-7))) then
        tmp = (x / y) * 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 (((x / y) <= -6e-93) || !((x / y) <= 1e-7)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6e-93) or not ((x / y) <= 1e-7):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6e-93) || !(Float64(x / y) <= 1e-7))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6e-93) || ~(((x / y) <= 1e-7)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6e-93], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-7]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.0000000000000003e-93 or 9.9999999999999995e-8 < (/.f64 x y)

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 94.2%

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

   3. Taylor expanded in x around -inf 90.5%

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

   4. Taylor expanded in z around inf 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-/l* 51.6%

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

   6. Simplified 51.6%

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

      1. associate-/r/ 57.2%

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

   8. Applied egg-rr 57.2%

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

   if -6.0000000000000003e-93 < (/.f64 x y) < 9.9999999999999995e-8

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 82.1%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{-93} \lor \neg \left(\frac{x}{y} \leq 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+131} \lor \neg \left(t \leq 3.4 \cdot 10^{-46}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.65e+131) (not (<= t 3.4e-46)))
   (- t (* (/ x y) t))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.65e+131) || !(t <= 3.4e-46)) {
		tmp = t - ((x / y) * t);
	} else {
		tmp = t + (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 ((t <= (-1.65d+131)) .or. (.not. (t <= 3.4d-46))) then
        tmp = t - ((x / y) * t)
    else
        tmp = t + (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 ((t <= -1.65e+131) || !(t <= 3.4e-46)) {
		tmp = t - ((x / y) * t);
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.65e+131) or not (t <= 3.4e-46):
		tmp = t - ((x / y) * t)
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.65e+131) || !(t <= 3.4e-46))
		tmp = Float64(t - Float64(Float64(x / y) * t));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.65e+131) || ~((t <= 3.4e-46)))
		tmp = t - ((x / y) * t);
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.65e+131], N[Not[LessEqual[t, 3.4e-46]], $MachinePrecision]], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6499999999999999e131 or 3.39999999999999996e-46 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 89.1%

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

      1. mul-1-neg 89.1%

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

      2. unsub-neg 89.1%

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

      3. associate-*r/ 92.9%

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

   4. Simplified 92.9%

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

   if -1.6499999999999999e131 < t < 3.39999999999999996e-46

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 85.0%

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

      1. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+131} \lor \neg \left(t \leq 3.4 \cdot 10^{-46}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+130}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.6e+130)
   (- t (/ t (/ y x)))
   (if (<= t 4.5e-46) (+ t (/ z (/ y x))) (- t (* (/ x y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.6e+130) {
		tmp = t - (t / (y / x));
	} else if (t <= 4.5e-46) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - ((x / y) * 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 (t <= (-2.6d+130)) then
        tmp = t - (t / (y / x))
    else if (t <= 4.5d-46) then
        tmp = t + (z / (y / x))
    else
        tmp = t - ((x / y) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.6e+130) {
		tmp = t - (t / (y / x));
	} else if (t <= 4.5e-46) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.6e+130:
		tmp = t - (t / (y / x))
	elif t <= 4.5e-46:
		tmp = t + (z / (y / x))
	else:
		tmp = t - ((x / y) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.6e+130)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	elseif (t <= 4.5e-46)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(t - Float64(Float64(x / y) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.6e+130)
		tmp = t - (t / (y / x));
	elseif (t <= 4.5e-46)
		tmp = t + (z / (y / x));
	else
		tmp = t - ((x / y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.6e+130], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-46], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5999999999999998e130

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.5%

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

      1. mul-1-neg 97.5%

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

      2. unsub-neg 97.5%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 90.6%

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

   4. Simplified 90.6%

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

      1. associate-*l/ 97.5%

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

      2. associate-/l* 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -2.5999999999999998e130 < t < 4.50000000000000001e-46

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 85.0%

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

      1. associate-/l* 87.1%

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

   4. Simplified 87.1%

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

   if 4.50000000000000001e-46 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. unsub-neg 84.1%

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

      3. associate-*r/ 88.7%

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

   4. Simplified 88.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+130}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-46}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]

Alternative 9: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+150}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.6e+150) (/ (* t (- x)) y) (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e+150) {
		tmp = (t * -x) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.6d+150)) then
        tmp = (t * -x) / y
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.6e+150) {
		tmp = (t * -x) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.6e+150:
		tmp = (t * -x) / y
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.6e+150)
		tmp = Float64(Float64(t * Float64(-x)) / y);
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.6e+150)
		tmp = (t * -x) / y;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.6e+150], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.59999999999999986e150

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around -inf 69.5%

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

   4. Taylor expanded in z around 0 69.5%

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

      1. neg-mul-1 69.5%

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

      2. distribute-rgt-neg-in 69.5%

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

   6. Simplified 69.5%

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

   if -3.59999999999999986e150 < t

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 82.4%

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

      1. associate-*r/ 84.0%

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

   4. Simplified 84.0%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+150}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 10: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e+150) (/ (* t (- x)) y) (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e+150) {
		tmp = (t * -x) / y;
	} else {
		tmp = t + (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 (t <= (-4.8d+150)) then
        tmp = (t * -x) / y
    else
        tmp = t + (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 (t <= -4.8e+150) {
		tmp = (t * -x) / y;
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.8e+150:
		tmp = (t * -x) / y
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.8e+150)
		tmp = Float64(Float64(t * Float64(-x)) / y);
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.8e+150)
		tmp = (t * -x) / y;
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.8e+150], N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.80000000000000005e150

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around -inf 69.5%

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

   4. Taylor expanded in z around 0 69.5%

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

      1. neg-mul-1 69.5%

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

      2. distribute-rgt-neg-in 69.5%

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

   6. Simplified 69.5%

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

   if -4.80000000000000005e150 < t

   1. Initial program 96.5%

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

   2. Taylor expanded in z around inf 82.4%

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

      1. associate-/l* 84.3%

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

   4. Simplified 84.3%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 11: 38.0% 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 97.0%

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

2. Taylor expanded in x around 0 43.5%

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

3. Final simplification 43.5%

   \[\leadsto t \]

Developer target: 97.2% accurate, 0.7× 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 2023173 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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