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

Percentage Accurate: 97.6% → 97.7%

Time: 5.6s

Alternatives: 7

Speedup: 1.0×

• 24.6% 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: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. *-commutative 97.6%

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

   2. clear-num 97.6%

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

   3. un-div-inv 98.0%

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

3. Applied egg-rr 98.0%

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

4. Final simplification 98.0%

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

Alternative 2: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -112000000000 \lor \neg \left(t \leq 68000000\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -112000000000.0) (not (<= t 68000000.0)))
   (- t (/ t (/ y x)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -112000000000.0) || !(t <= 68000000.0)) {
		tmp = t - (t / (y / x));
	} 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 <= (-112000000000.0d0)) .or. (.not. (t <= 68000000.0d0))) then
        tmp = t - (t / (y / x))
    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 <= -112000000000.0) || !(t <= 68000000.0)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -112000000000.0) or not (t <= 68000000.0):
		tmp = t - (t / (y / x))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -112000000000.0) || !(t <= 68000000.0))
		tmp = Float64(t - Float64(t / Float64(y / x)));
	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 <= -112000000000.0) || ~((t <= 68000000.0)))
		tmp = t - (t / (y / x));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -112000000000.0], N[Not[LessEqual[t, 68000000.0]], $MachinePrecision]], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12e11 or 6.8e7 < t

   1. Initial program 99.8%

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

      1. remove-double-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. associate-*l/ 90.3%

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

      4. associate-*r/ 91.5%

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

      5. fma-neg 91.5%

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

      6. remove-double-neg 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in z around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. associate-/l* 91.2%

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

      3. unsub-neg 91.2%

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

      4. associate-/r/ 84.4%

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

      5. *-commutative 84.4%

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

   6. Simplified 84.4%

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

   7. Taylor expanded in x around 0 85.4%

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

      1. associate-/l* 91.2%

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

   9. Simplified 91.2%

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

   if -1.12e11 < t < 6.8e7

   1. Initial program 95.4%

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

   2. Taylor expanded in z around inf 85.2%

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

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

   4. Simplified 87.1%

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

      1. clear-num 87.1%

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

      2. div-inv 87.8%

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

   6. Applied egg-rr 87.8%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -112000000000 \lor \neg \left(t \leq 68000000\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 3: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-18}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.8e-18)
   (+ t (/ z (/ y x)))
   (if (<= z 1.15e+27) (- t (* x (/ t y))) (+ t (/ (* z x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.8e-18) {
		tmp = t + (z / (y / x));
	} else if (z <= 1.15e+27) {
		tmp = t - (x * (t / y));
	} else {
		tmp = t + ((z * 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 <= (-7.8d-18)) then
        tmp = t + (z / (y / x))
    else if (z <= 1.15d+27) then
        tmp = t - (x * (t / y))
    else
        tmp = t + ((z * 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 <= -7.8e-18) {
		tmp = t + (z / (y / x));
	} else if (z <= 1.15e+27) {
		tmp = t - (x * (t / y));
	} else {
		tmp = t + ((z * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.8e-18:
		tmp = t + (z / (y / x))
	elif z <= 1.15e+27:
		tmp = t - (x * (t / y))
	else:
		tmp = t + ((z * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.8e-18)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (z <= 1.15e+27)
		tmp = Float64(t - Float64(x * Float64(t / y)));
	else
		tmp = Float64(t + Float64(Float64(z * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.8e-18)
		tmp = t + (z / (y / x));
	elseif (z <= 1.15e+27)
		tmp = t - (x * (t / y));
	else
		tmp = t + ((z * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.8e-18], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+27], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.8000000000000001e-18

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 77.8%

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

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

      1. clear-num 88.8%

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

      2. div-inv 88.9%

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

   6. Applied egg-rr 88.9%

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

   if -7.8000000000000001e-18 < z < 1.15e27

   1. Initial program 97.0%

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

      1. remove-double-neg 97.0%

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

      2. unsub-neg 97.0%

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

      3. associate-*l/ 92.1%

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

      4. associate-*r/ 94.8%

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

      5. fma-neg 94.8%

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

      6. remove-double-neg 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in z around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. associate-/l* 88.4%

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

      3. unsub-neg 88.4%

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

      4. associate-/r/ 83.4%

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

      5. *-commutative 83.4%

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

   6. Simplified 83.4%

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

   if 1.15e27 < z

   1. Initial program 96.9%

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

   2. Taylor expanded in z around inf 91.8%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-18}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \]

Alternative 4: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 5: 76.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Taylor expanded in z around inf 71.5%

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

   1. associate-*l/ 74.2%

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

   2. *-commutative 74.2%

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

4. Simplified 74.2%

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

5. Final simplification 74.2%

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

Alternative 6: 76.7% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Taylor expanded in z around inf 71.5%

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

   1. associate-*l/ 74.2%

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

   2. *-commutative 74.2%

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

4. Simplified 74.2%

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

   1. clear-num 74.2%

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

   2. div-inv 74.6%

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

6. Applied egg-rr 74.6%

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

7. Final simplification 74.6%

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

Alternative 7: 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 97.6%

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

   1. remove-double-neg 97.6%

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

   2. unsub-neg 97.6%

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

   3. associate-*l/ 92.2%

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

   4. associate-*r/ 92.5%

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

   5. fma-neg 92.5%

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

   6. remove-double-neg 92.5%

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

3. Simplified 92.5%

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

4. Taylor expanded in x around 0 36.6%

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

5. Final simplification 36.6%

   \[\leadsto t \]

Developer target: 97.3% 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 2023297 
(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))