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

Percentage Accurate: 97.6% → 97.7%

Time: 6.5s

Alternatives: 10

Speedup: 1.0×

• 25.2% 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 98.0%

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

3. Taylor expanded in x around 0 91.6%

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

   1. *-commutative 91.6%

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

   2. associate-/l* 98.3%

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

5. Simplified 98.3%

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

6. Final simplification 98.3%

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

Alternative 2: 93.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 10^{-85}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+15) (not (<= (/ x y) 1e-85)))
   (+ t (* x (/ (- z t) y)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+15) || !((x / y) <= 1e-85)) {
		tmp = t + (x * ((z - t) / 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 (((x / y) <= (-2d+15)) .or. (.not. ((x / y) <= 1d-85))) then
        tmp = t + (x * ((z - t) / 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 (((x / y) <= -2e+15) || !((x / y) <= 1e-85)) {
		tmp = t + (x * ((z - t) / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+15) or not ((x / y) <= 1e-85):
		tmp = t + (x * ((z - t) / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+15) || !(Float64(x / y) <= 1e-85))
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / 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 (((x / y) <= -2e+15) || ~(((x / y) <= 1e-85)))
		tmp = t + (x * ((z - t) / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+15], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-85]], $MachinePrecision]], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e15 or 9.9999999999999998e-86 < (/.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in x around 0 87.4%

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

      1. associate-*r/ 95.5%

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

   5. Simplified 95.5%

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

   if -2e15 < (/.f64 x y) < 9.9999999999999998e-86

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

   5. Simplified 94.6%

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

      1. *-commutative 94.6%

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

      2. associate-/r/ 99.2%

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

   7. Applied egg-rr 99.2%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 10^{-85}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-78}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;t + \frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e-78)
   (+ t (/ z (/ y x)))
   (if (<= z 1.25e-43) (+ t (/ t (/ (- y) x))) (+ t (* z (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e-78) {
		tmp = t + (z / (y / x));
	} else if (z <= 1.25e-43) {
		tmp = t + (t / (-y / x));
	} 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 <= (-2d-78)) then
        tmp = t + (z / (y / x))
    else if (z <= 1.25d-43) then
        tmp = t + (t / (-y / x))
    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 <= -2e-78) {
		tmp = t + (z / (y / x));
	} else if (z <= 1.25e-43) {
		tmp = t + (t / (-y / x));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2e-78:
		tmp = t + (z / (y / x))
	elif z <= 1.25e-43:
		tmp = t + (t / (-y / x))
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e-78)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (z <= 1.25e-43)
		tmp = Float64(t + Float64(t / Float64(Float64(-y) / x)));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2e-78)
		tmp = t + (z / (y / x));
	elseif (z <= 1.25e-43)
		tmp = t + (t / (-y / x));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2e-78], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e-43], N[(t + N[(t / N[((-y) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e-78

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

   5. Simplified 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/r/ 88.2%

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

   7. Applied egg-rr 88.2%

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

   if -2e-78 < z < 1.25000000000000005e-43

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*l/ 88.6%

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

      4. distribute-rgt-neg-out 88.6%

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

   5. Simplified 88.6%

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

      1. add-sqr-sqrt 44.6%

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

      2. sqrt-unprod 51.1%

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

      3. sqr-neg 51.1%

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

      4. sqrt-unprod 22.6%

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

      5. add-sqr-sqrt 45.4%

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

      6. clear-num 45.4%

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

      7. associate-*l/ 45.4%

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

      8. *-un-lft-identity 45.4%

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

      9. frac-2neg 45.4%

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

      10. add-sqr-sqrt 22.8%

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

      11. sqrt-unprod 52.4%

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

      12. sqr-neg 52.4%

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

      13. sqrt-unprod 43.8%

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

      14. add-sqr-sqrt 89.3%

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

      15. distribute-neg-frac 89.3%

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

   7. Applied egg-rr 89.3%

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

   if 1.25000000000000005e-43 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 84.9%

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

      1. associate-*l/ 92.8%

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

      2. *-commutative 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-78}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-43}:\\ \;\;\;\;t + \frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-167} \lor \neg \left(z \leq 3.2 \cdot 10^{-49}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.6e-167) (not (<= z 3.2e-49)))
   (+ t (* z (/ x y)))
   (- t (/ (* t x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.6e-167) || !(z <= 3.2e-49)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t - ((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 ((z <= (-5.6d-167)) .or. (.not. (z <= 3.2d-49))) then
        tmp = t + (z * (x / y))
    else
        tmp = t - ((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 ((z <= -5.6e-167) || !(z <= 3.2e-49)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t - ((t * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.6e-167) or not (z <= 3.2e-49):
		tmp = t + (z * (x / y))
	else:
		tmp = t - ((t * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.6e-167) || !(z <= 3.2e-49))
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(t - Float64(Float64(t * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.6e-167) || ~((z <= 3.2e-49)))
		tmp = t + (z * (x / y));
	else
		tmp = t - ((t * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.6e-167], N[Not[LessEqual[z, 3.2e-49]], $MachinePrecision]], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.59999999999999971e-167 or 3.20000000000000002e-49 < z

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 82.1%

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

      1. associate-*l/ 87.9%

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

      2. *-commutative 87.9%

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

   5. Simplified 87.9%

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

   if -5.59999999999999971e-167 < z < 3.20000000000000002e-49

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 87.1%

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

      1. mul-1-neg 87.1%

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

      2. *-commutative 87.1%

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

   5. Simplified 87.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-167} \lor \neg \left(z \leq 3.2 \cdot 10^{-49}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-165} \lor \neg \left(z \leq 1.32 \cdot 10^{-48}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.1e-165) (not (<= z 1.32e-48)))
   (+ t (* z (/ x y)))
   (- t (* x (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e-165) || !(z <= 1.32e-48)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t - (x * (t / 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 <= (-5.1d-165)) .or. (.not. (z <= 1.32d-48))) then
        tmp = t + (z * (x / y))
    else
        tmp = t - (x * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e-165) || !(z <= 1.32e-48)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t - (x * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.1e-165) or not (z <= 1.32e-48):
		tmp = t + (z * (x / y))
	else:
		tmp = t - (x * (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.1e-165) || !(z <= 1.32e-48))
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(t - Float64(x * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.1e-165) || ~((z <= 1.32e-48)))
		tmp = t + (z * (x / y));
	else
		tmp = t - (x * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.1e-165], N[Not[LessEqual[z, 1.32e-48]], $MachinePrecision]], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1e-165 or 1.32e-48 < z

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 82.6%

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

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

   5. Simplified 88.3%

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

   if -5.1e-165 < z < 1.32e-48

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-/l* 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in z around 0 86.2%

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

      1. mul-1-neg 86.2%

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

      2. associate-*l/ 88.4%

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

      3. distribute-rgt-neg-in 88.4%

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

   8. Simplified 88.4%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-165} \lor \neg \left(z \leq 1.32 \cdot 10^{-48}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-77}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-44}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e-77)
   (+ t (/ z (/ y x)))
   (if (<= z 7.4e-44) (- t (* t (/ x y))) (+ t (* z (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e-77) {
		tmp = t + (z / (y / x));
	} else if (z <= 7.4e-44) {
		tmp = t - (t * (x / 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 <= (-1d-77)) then
        tmp = t + (z / (y / x))
    else if (z <= 7.4d-44) then
        tmp = t - (t * (x / 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 <= -1e-77) {
		tmp = t + (z / (y / x));
	} else if (z <= 7.4e-44) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e-77:
		tmp = t + (z / (y / x))
	elif z <= 7.4e-44:
		tmp = t - (t * (x / y))
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e-77)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (z <= 7.4e-44)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1e-77)
		tmp = t + (z / (y / x));
	elseif (z <= 7.4e-44)
		tmp = t - (t * (x / y));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e-77], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-44], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999993e-78

   1. Initial program 98.5%

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

   3. Taylor expanded in z around inf 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-*l/ 84.4%

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

      3. *-commutative 84.4%

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

   5. Simplified 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-/r/ 88.2%

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

   7. Applied egg-rr 88.2%

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

   if -9.9999999999999993e-78 < z < 7.4e-44

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 83.2%

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

      1. mul-1-neg 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*l/ 88.6%

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

      4. distribute-rgt-neg-out 88.6%

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

   5. Simplified 88.6%

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

   if 7.4e-44 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 84.9%

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

      1. associate-*l/ 92.8%

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

      2. *-commutative 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-77}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-44}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 98.0%

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

3. Final simplification 98.0%

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

Alternative 8: 72.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in z around inf 72.2%

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

   1. *-commutative 72.2%

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

   2. associate-*l/ 72.9%

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

   3. *-commutative 72.9%

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

5. Simplified 72.9%

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

6. Final simplification 72.9%

   \[\leadsto t + x \cdot \frac{z}{y} \]
7. Add Preprocessing

Alternative 9: 76.2% 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 98.0%

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

3. Taylor expanded in z around inf 72.2%

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

   1. associate-*l/ 76.2%

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

   2. *-commutative 76.2%

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

5. Simplified 76.2%

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

6. Final simplification 76.2%

   \[\leadsto t + z \cdot \frac{x}{y} \]
7. Add Preprocessing

Alternative 10: 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 98.0%

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

3. Taylor expanded in z around inf 72.2%

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

   1. *-commutative 72.2%

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

   2. associate-*l/ 72.9%

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

   3. *-commutative 72.9%

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

5. Simplified 72.9%

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

6. Taylor expanded in x around 0 38.8%

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

7. Final simplification 38.8%

   \[\leadsto t \]
8. Add Preprocessing

Developer target: 97.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024031 
(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))