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

Percentage Accurate: 97.9% → 97.9%

Time: 5.3s

Alternatives: 11

Speedup: 1.0×

• 25.4% 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: 97.9% 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: 97.9% 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 97.7%

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

2. Final simplification 97.7%

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

Alternative 2: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2000.0) (not (<= (/ x y) 2e-6))) (/ (- t) (/ y x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2000.0) || !((x / y) <= 2e-6)) {
		tmp = -t / (y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2000.0d0)) .or. (.not. ((x / y) <= 2d-6))) then
        tmp = -t / (y / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2000.0) || !((x / y) <= 2e-6)) {
		tmp = -t / (y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2000.0) or not ((x / y) <= 2e-6):
		tmp = -t / (y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2000.0) || !(Float64(x / y) <= 2e-6))
		tmp = Float64(Float64(-t) / Float64(y / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2000.0) || ~(((x / y) <= 2e-6)))
		tmp = -t / (y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-6]], $MachinePrecision]], N[((-t) / N[(y / x), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e3 or 1.99999999999999991e-6 < (/.f64 x y)

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. unsub-neg 45.9%

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

      3. associate-*r/ 54.3%

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

   4. Simplified 54.3%

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

   5. Taylor expanded in t around 0 54.3%

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

   6. Taylor expanded in x around inf 45.9%

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

      1. associate-*r/ 45.9%

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

      2. neg-mul-1 45.9%

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

      3. distribute-rgt-neg-out 45.9%

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

      4. associate-*r/ 53.3%

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

   8. Simplified 53.3%

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

      1. distribute-frac-neg 53.3%

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

      2. distribute-rgt-neg-out 53.3%

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

      3. add-sqr-sqrt 25.9%

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

      4. sqrt-unprod 27.4%

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

      5. sqr-neg 27.4%

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

      6. sqrt-unprod 4.2%

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

      7. add-sqr-sqrt 9.9%

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

      8. clear-num 9.9%

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

      9. un-div-inv 9.9%

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

      10. add-sqr-sqrt 4.3%

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

      11. sqrt-unprod 27.4%

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

      12. sqr-neg 27.4%

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

      13. sqrt-unprod 25.9%

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

      14. add-sqr-sqrt 52.6%

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

   10. Applied egg-rr 52.6%

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

   if -2e3 < (/.f64 x y) < 1.99999999999999991e-6

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 82.5%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2000.0)
   (* t (/ (- x) y))
   (if (<= (/ x y) 2e-6) t (/ (- t) (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2000.0) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 2e-6) {
		tmp = t;
	} else {
		tmp = -t / (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) <= (-2000.0d0)) then
        tmp = t * (-x / y)
    else if ((x / y) <= 2d-6) then
        tmp = t
    else
        tmp = -t / (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) <= -2000.0) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 2e-6) {
		tmp = t;
	} else {
		tmp = -t / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2000.0:
		tmp = t * (-x / y)
	elif (x / y) <= 2e-6:
		tmp = t
	else:
		tmp = -t / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2000.0)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (Float64(x / y) <= 2e-6)
		tmp = t;
	else
		tmp = Float64(Float64(-t) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2000.0)
		tmp = t * (-x / y);
	elseif ((x / y) <= 2e-6)
		tmp = t;
	else
		tmp = -t / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2000.0], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-6], t, N[((-t) / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e3

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. unsub-neg 46.2%

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

      3. associate-*r/ 52.4%

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

   4. Simplified 52.4%

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

   5. Taylor expanded in t around 0 52.4%

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

   6. Taylor expanded in x around inf 46.1%

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

      1. associate-*r/ 46.1%

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

      2. neg-mul-1 46.1%

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

      3. distribute-rgt-neg-out 46.1%

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

      4. associate-*r/ 51.5%

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

   8. Simplified 51.5%

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

   if -2e3 < (/.f64 x y) < 1.99999999999999991e-6

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 82.5%

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

   if 1.99999999999999991e-6 < (/.f64 x y)

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 45.6%

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

      1. mul-1-neg 45.6%

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

      2. unsub-neg 45.6%

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

      3. associate-*r/ 56.4%

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

   4. Simplified 56.4%

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

   5. Taylor expanded in t around 0 56.4%

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

   6. Taylor expanded in x around inf 45.7%

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

      1. associate-*r/ 45.7%

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

      2. neg-mul-1 45.7%

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

      3. distribute-rgt-neg-out 45.7%

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

      4. associate-*r/ 55.2%

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

   8. Simplified 55.2%

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

      1. distribute-frac-neg 55.2%

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

      2. distribute-rgt-neg-out 55.2%

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

      3. add-sqr-sqrt 29.4%

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

      4. sqrt-unprod 35.0%

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

      5. sqr-neg 35.0%

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

      6. sqrt-unprod 5.3%

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

      7. add-sqr-sqrt 11.6%

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

      8. clear-num 11.6%

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

      9. un-div-inv 11.6%

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

      10. add-sqr-sqrt 5.3%

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

      11. sqrt-unprod 35.0%

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

      12. sqr-neg 35.0%

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

      13. sqrt-unprod 29.4%

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

      14. add-sqr-sqrt 55.2%

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

   10. Applied egg-rr 55.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \end{array} \]

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-64} \lor \neg \left(z \leq 1.1 \cdot 10^{-19}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.6e-64) (not (<= z 1.1e-19)))
   (+ t (* (/ x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e-64) || !(z <= 1.1e-19)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (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 ((z <= (-6.6d-64)) .or. (.not. (z <= 1.1d-19))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.6e-64) || !(z <= 1.1e-19)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.6e-64) or not (z <= 1.1e-19):
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.6e-64) || !(z <= 1.1e-19))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.6e-64) || ~((z <= 1.1e-19)))
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.6e-64], N[Not[LessEqual[z, 1.1e-19]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5999999999999999e-64 or 1.0999999999999999e-19 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 86.9%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   4. Simplified 88.8%

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

   if -6.5999999999999999e-64 < z < 1.0999999999999999e-19

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

      3. associate-*r/ 88.9%

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

   4. Simplified 88.9%

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

   5. Taylor expanded in t around 0 88.9%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-64} \lor \neg \left(z \leq 1.1 \cdot 10^{-19}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-52} \lor \neg \left(z \leq 1.2 \cdot 10^{-19}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e-52) (not (<= z 1.2e-19)))
   (+ t (/ z (/ y x)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-52) || !(z <= 1.2e-19)) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t * (1.0 - (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 ((z <= (-8.8d-52)) .or. (.not. (z <= 1.2d-19))) then
        tmp = t + (z / (y / x))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-52) || !(z <= 1.2e-19)) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-52) or not (z <= 1.2e-19):
		tmp = t + (z / (y / x))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-52) || !(z <= 1.2e-19))
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.8e-52) || ~((z <= 1.2e-19)))
		tmp = t + (z / (y / x));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e-52], N[Not[LessEqual[z, 1.2e-19]], $MachinePrecision]], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000036e-52 or 1.20000000000000011e-19 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 87.2%

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

      1. *-commutative 87.2%

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

      2. associate-/l* 89.3%

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

   4. Simplified 89.3%

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

   if -8.80000000000000036e-52 < z < 1.20000000000000011e-19

   1. Initial program 96.6%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-*r/ 88.5%

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

   4. Simplified 88.5%

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

   5. Taylor expanded in t around 0 88.5%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-52} \lor \neg \left(z \leq 1.2 \cdot 10^{-19}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 6: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-64} \lor \neg \left(z \leq 2.02 \cdot 10^{-19}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e-64) (not (<= z 2.02e-19)))
   (+ t (/ z (/ y x)))
   (- t (* (/ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-64) || !(z <= 2.02e-19)) {
		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 ((z <= (-5.8d-64)) .or. (.not. (z <= 2.02d-19))) 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 ((z <= -5.8e-64) || !(z <= 2.02e-19)) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e-64) or not (z <= 2.02e-19):
		tmp = t + (z / (y / x))
	else:
		tmp = t - ((x / y) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e-64) || !(z <= 2.02e-19))
		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 ((z <= -5.8e-64) || ~((z <= 2.02e-19)))
		tmp = t + (z / (y / x));
	else
		tmp = t - ((x / y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e-64], N[Not[LessEqual[z, 2.02e-19]], $MachinePrecision]], 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 2 regimes

2. if z < -5.7999999999999998e-64 or 2.01999999999999989e-19 < z

   1. Initial program 98.6%

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

   2. Taylor expanded in z around inf 86.9%

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

      1. *-commutative 86.9%

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

      2. associate-/l* 88.9%

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

   4. Simplified 88.9%

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

   if -5.7999999999999998e-64 < z < 2.01999999999999989e-19

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. unsub-neg 81.4%

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

      3. associate-*r/ 88.9%

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

   4. Simplified 88.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-64} \lor \neg \left(z \leq 2.02 \cdot 10^{-19}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]

Alternative 7: 39.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 1.45 \cdot 10^{+108}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) 1.45e+108) t (* (/ x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 1.45e+108) {
		tmp = t;
	} 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) <= 1.45d+108) then
        tmp = t
    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) <= 1.45e+108) {
		tmp = t;
	} else {
		tmp = (x / y) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 1.45e+108:
		tmp = t
	else:
		tmp = (x / y) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 1.45e+108)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= 1.45e+108)
		tmp = t;
	else
		tmp = (x / y) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 1.45e+108], t, N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 1.45000000000000004e108

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 47.7%

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

   if 1.45000000000000004e108 < (/.f64 x y)

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 45.5%

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

      1. mul-1-neg 45.5%

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

      2. unsub-neg 45.5%

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

      3. associate-*r/ 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in t around 0 54.2%

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

   6. Taylor expanded in x around inf 45.5%

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

      1. associate-*r/ 45.5%

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

      2. neg-mul-1 45.5%

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

      3. distribute-rgt-neg-out 45.5%

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

      4. associate-*r/ 54.2%

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

   8. Simplified 54.2%

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

      1. *-commutative 54.2%

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

      2. div-inv 54.2%

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

      3. associate-*l* 42.6%

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

      4. associate-/r/ 41.9%

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

      5. clear-num 42.6%

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

      6. distribute-lft-neg-in 42.6%

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

      7. distribute-rgt-neg-out 42.6%

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

      8. add-log-exp 49.3%

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

      9. *-un-lft-identity 49.3%

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

      10. log-prod 49.3%

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

      11. metadata-eval 49.3%

          \[\leadsto \color{blue}{0} + \log \left(e^{x \cdot \left(-\frac{t}{y}\right)}\right) \]

      12. add-log-exp 42.6%

          \[\leadsto 0 + \color{blue}{x \cdot \left(-\frac{t}{y}\right)} \]

      13. distribute-rgt-neg-out 42.6%

          \[\leadsto 0 + \color{blue}{\left(-x \cdot \frac{t}{y}\right)} \]

      14. distribute-lft-neg-in 42.6%

          \[\leadsto 0 + \color{blue}{\left(-x\right) \cdot \frac{t}{y}} \]

      15. clear-num 41.9%

          \[\leadsto 0 + \left(-x\right) \cdot \color{blue}{\frac{1}{\frac{y}{t}}} \]

      16. associate-/r/ 42.6%

          \[\leadsto 0 + \left(-x\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot t\right)} \]

      17. associate-*l* 54.2%

          \[\leadsto 0 + \color{blue}{\left(\left(-x\right) \cdot \frac{1}{y}\right) \cdot t} \]

      18. div-inv 54.2%

          \[\leadsto 0 + \color{blue}{\frac{-x}{y}} \cdot t \]

      19. clear-num 54.1%

          \[\leadsto 0 + \color{blue}{\frac{1}{\frac{y}{-x}}} \cdot t \]

      20. associate-*l/ 54.2%

          \[\leadsto 0 + \color{blue}{\frac{1 \cdot t}{\frac{y}{-x}}} \]

      21. *-un-lft-identity 54.2%

          \[\leadsto 0 + \frac{\color{blue}{t}}{\frac{y}{-x}} \]

      22. add-sqr-sqrt 28.6%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      23. sqrt-unprod 34.6%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}} \]

      24. sqr-neg 34.6%

          \[\leadsto 0 + \frac{t}{\frac{y}{\sqrt{\color{blue}{x \cdot x}}}} \]

      25. sqrt-unprod 8.0%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      26. add-sqr-sqrt 14.9%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{x}}} \]

   10. Applied egg-rr 14.9%

       \[\leadsto \color{blue}{0 + \frac{t}{\frac{y}{x}}} \]
   11. Step-by-step derivation

       1. +-lft-identity 14.9%

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

       2. associate-/l* 7.6%

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

       3. associate-*r/ 14.8%

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

   12. Simplified 14.8%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 1.45 \cdot 10^{+108}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \]

Alternative 8: 39.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= (/ x y) 5e+97) t (/ t (/ y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 5e+97) {
		tmp = t;
	} else {
		tmp = t / (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) <= 5d+97) then
        tmp = t
    else
        tmp = t / (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) <= 5e+97) {
		tmp = t;
	} else {
		tmp = t / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 5e+97:
		tmp = t
	else:
		tmp = t / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 5e+97)
		tmp = t;
	else
		tmp = Float64(t / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= 5e+97)
		tmp = t;
	else
		tmp = t / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 5e+97], t, N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 4.99999999999999999e97

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 47.7%

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

   if 4.99999999999999999e97 < (/.f64 x y)

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 45.5%

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

      1. mul-1-neg 45.5%

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

      2. unsub-neg 45.5%

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

      3. associate-*r/ 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in t around 0 54.2%

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

   6. Taylor expanded in x around inf 45.5%

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

      1. associate-*r/ 45.5%

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

      2. neg-mul-1 45.5%

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

      3. distribute-rgt-neg-out 45.5%

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

      4. associate-*r/ 54.2%

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

   8. Simplified 54.2%

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

      1. *-commutative 54.2%

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

      2. div-inv 54.2%

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

      3. associate-*l* 42.6%

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

      4. associate-/r/ 41.9%

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

      5. clear-num 42.6%

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

      6. distribute-lft-neg-in 42.6%

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

      7. distribute-rgt-neg-out 42.6%

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

      8. add-log-exp 49.3%

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

      9. *-un-lft-identity 49.3%

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

      10. log-prod 49.3%

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

      11. metadata-eval 49.3%

          \[\leadsto \color{blue}{0} + \log \left(e^{x \cdot \left(-\frac{t}{y}\right)}\right) \]

      12. add-log-exp 42.6%

          \[\leadsto 0 + \color{blue}{x \cdot \left(-\frac{t}{y}\right)} \]

      13. distribute-rgt-neg-out 42.6%

          \[\leadsto 0 + \color{blue}{\left(-x \cdot \frac{t}{y}\right)} \]

      14. distribute-lft-neg-in 42.6%

          \[\leadsto 0 + \color{blue}{\left(-x\right) \cdot \frac{t}{y}} \]

      15. clear-num 41.9%

          \[\leadsto 0 + \left(-x\right) \cdot \color{blue}{\frac{1}{\frac{y}{t}}} \]

      16. associate-/r/ 42.6%

          \[\leadsto 0 + \left(-x\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot t\right)} \]

      17. associate-*l* 54.2%

          \[\leadsto 0 + \color{blue}{\left(\left(-x\right) \cdot \frac{1}{y}\right) \cdot t} \]

      18. div-inv 54.2%

          \[\leadsto 0 + \color{blue}{\frac{-x}{y}} \cdot t \]

      19. clear-num 54.1%

          \[\leadsto 0 + \color{blue}{\frac{1}{\frac{y}{-x}}} \cdot t \]

      20. associate-*l/ 54.2%

          \[\leadsto 0 + \color{blue}{\frac{1 \cdot t}{\frac{y}{-x}}} \]

      21. *-un-lft-identity 54.2%

          \[\leadsto 0 + \frac{\color{blue}{t}}{\frac{y}{-x}} \]

      22. add-sqr-sqrt 28.6%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      23. sqrt-unprod 34.6%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}} \]

      24. sqr-neg 34.6%

          \[\leadsto 0 + \frac{t}{\frac{y}{\sqrt{\color{blue}{x \cdot x}}}} \]

      25. sqrt-unprod 8.0%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      26. add-sqr-sqrt 14.9%

          \[\leadsto 0 + \frac{t}{\frac{y}{\color{blue}{x}}} \]

   10. Applied egg-rr 14.9%

       \[\leadsto \color{blue}{0 + \frac{t}{\frac{y}{x}}} \]
   11. Step-by-step derivation

       1. +-lft-identity 14.9%

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

   12. Simplified 14.9%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 5 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

2. Taylor expanded in x around 0 92.5%

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

   1. associate-*r/ 94.7%

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

4. Simplified 94.7%

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

5. Final simplification 94.7%

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

Alternative 10: 65.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(1 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 1.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return t * (1.0 - (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 * (1.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Python

def code(x, y, z, t):
	return t * (1.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(t * Float64(1.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (1.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.7%

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

2. Taylor expanded in z around 0 60.0%

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

   1. mul-1-neg 60.0%

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

   2. unsub-neg 60.0%

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

   3. associate-*r/ 67.3%

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

4. Simplified 67.3%

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

5. Taylor expanded in t around 0 67.3%

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

6. Final simplification 67.3%

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

Alternative 11: 38.5% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 97.7%

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

2. Taylor expanded in x around 0 38.3%

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

3. Final simplification 38.3%

   \[\leadsto t \]

Developer target: 97.6% 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 2023290 
(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))