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

Percentage Accurate: 97.7% → 98.6%

Time: 9.0s

Alternatives: 9

Speedup: 1.0×

• 25.5% 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: 97.7% 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: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 4 \cdot 10^{+279}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) 4e+279) (+ t (* (- z t) (/ x y))) (+ t (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 4e+279) {
		tmp = t + ((z - t) * (x / y));
	} else {
		tmp = t + (x * ((z - 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 ((x / y) <= 4d+279) then
        tmp = t + ((z - t) * (x / y))
    else
        tmp = t + (x * ((z - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 4e+279) {
		tmp = t + ((z - t) * (x / y));
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 4e+279:
		tmp = t + ((z - t) * (x / y))
	else:
		tmp = t + (x * ((z - t) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 4e+279)
		tmp = Float64(t + Float64(Float64(z - t) * Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= 4e+279)
		tmp = t + ((z - t) * (x / y));
	else
		tmp = t + (x * ((z - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 4e+279], N[(t + N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 4.00000000000000023e279

   1. Initial program 97.8%

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

   if 4.00000000000000023e279 < (/.f64 x y)

   1. Initial program 81.7%

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

      1. associate-*l/ 99.9%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 100.0%

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

   6. Applied egg-rr 100.0%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 4 \cdot 10^{+279}:\\ \;\;\;\;t + \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+27} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+27) (not (<= (/ x y) 4e-6))) (* t (/ x (- y))) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+27) || !((x / y) <= 4e-6)) {
		tmp = t * (x / -y);
	} 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) <= (-5d+27)) .or. (.not. ((x / y) <= 4d-6))) then
        tmp = t * (x / -y)
    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) <= -5e+27) || !((x / y) <= 4e-6)) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+27) or not ((x / y) <= 4e-6):
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+27) || !(Float64(x / y) <= 4e-6))
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+27) || ~(((x / y) <= 4e-6)))
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+27], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-6]], $MachinePrecision]], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999979e27 or 3.99999999999999982e-6 < (/.f64 x y)

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-*l/ 61.6%

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

      3. neg-mul-1 61.6%

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

      4. *-lft-identity 61.6%

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

      5. distribute-lft-neg-in 61.6%

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

      6. mul-1-neg 61.6%

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

      7. distribute-rgt-in 61.7%

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

      8. mul-1-neg 61.7%

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

      9. unsub-neg 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in x around inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-frac-neg2 61.1%

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

   8. Simplified 61.1%

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

   if -4.99999999999999979e27 < (/.f64 x y) < 3.99999999999999982e-6

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 72.4%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+27} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+27)
   (* t (/ x (- y)))
   (if (<= (/ x y) 4e-6) t (/ (* t (- x)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+27) {
		tmp = t * (x / -y);
	} else if ((x / y) <= 4e-6) {
		tmp = t;
	} else {
		tmp = (t * -x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+27)) then
        tmp = t * (x / -y)
    else if ((x / y) <= 4d-6) then
        tmp = t
    else
        tmp = (t * -x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+27) {
		tmp = t * (x / -y);
	} else if ((x / y) <= 4e-6) {
		tmp = t;
	} else {
		tmp = (t * -x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+27:
		tmp = t * (x / -y)
	elif (x / y) <= 4e-6:
		tmp = t
	else:
		tmp = (t * -x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+27)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (Float64(x / y) <= 4e-6)
		tmp = t;
	else
		tmp = Float64(Float64(t * Float64(-x)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+27)
		tmp = t * (x / -y);
	elseif ((x / y) <= 4e-6)
		tmp = t;
	else
		tmp = (t * -x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+27], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e-6], t, N[(N[(t * (-x)), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.99999999999999979e27

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0 60.0%

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

      1. *-commutative 60.0%

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

      2. associate-*l/ 65.2%

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

      3. neg-mul-1 65.2%

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

      4. *-lft-identity 65.2%

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

      5. distribute-lft-neg-in 65.2%

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

      6. mul-1-neg 65.2%

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

      7. distribute-rgt-in 65.2%

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

      8. mul-1-neg 65.2%

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

      9. unsub-neg 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in x around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-frac-neg2 65.2%

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

   8. Simplified 65.2%

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

   if -4.99999999999999979e27 < (/.f64 x y) < 3.99999999999999982e-6

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 72.4%

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

   if 3.99999999999999982e-6 < (/.f64 x y)

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 60.1%

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

      1. *-commutative 60.1%

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

      2. associate-*l/ 58.9%

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

      3. neg-mul-1 58.9%

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

      4. *-lft-identity 58.9%

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

      5. distribute-lft-neg-in 58.9%

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

      6. mul-1-neg 58.9%

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

      7. distribute-rgt-in 58.9%

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

      8. mul-1-neg 58.9%

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

      9. unsub-neg 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in x around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. distribute-frac-neg2 57.9%

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

   8. Simplified 57.9%

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

      1. distribute-frac-neg2 57.9%

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

      2. distribute-frac-neg 57.9%

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

      3. associate-*r/ 59.2%

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

      4. associate-*l/ 56.6%

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

      5. *-commutative 56.6%

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

      6. frac-2neg 56.6%

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

      7. associate-*r/ 59.2%

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

      8. add-sqr-sqrt 23.0%

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

      9. sqrt-unprod 21.9%

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

      10. sqr-neg 21.9%

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

      11. sqrt-unprod 0.7%

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

      12. add-sqr-sqrt 1.5%

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

      13. add-sqr-sqrt 0.8%

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

      14. sqrt-unprod 32.6%

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

      15. sqr-neg 32.6%

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

      16. sqrt-unprod 36.1%

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

      17. add-sqr-sqrt 59.2%

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

   10. Applied egg-rr 59.2%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+73} \lor \neg \left(z \leq 6.95 \cdot 10^{+34}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e+73) (not (<= z 6.95e+34)))
   (+ t (* x (/ z y)))
   (- t (/ (* t x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e+73) || !(z <= 6.95e+34)) {
		tmp = t + (x * (z / 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 <= (-1.5d+73)) .or. (.not. (z <= 6.95d+34))) then
        tmp = t + (x * (z / 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 <= -1.5e+73) || !(z <= 6.95e+34)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t - ((t * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5e+73) or not (z <= 6.95e+34):
		tmp = t + (x * (z / y))
	else:
		tmp = t - ((t * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5e+73) || !(z <= 6.95e+34))
		tmp = Float64(t + Float64(x * Float64(z / 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 <= -1.5e+73) || ~((z <= 6.95e+34)))
		tmp = t + (x * (z / y));
	else
		tmp = t - ((t * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5e+73], N[Not[LessEqual[z, 6.95e+34]], $MachinePrecision]], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000005e73 or 6.9500000000000002e34 < z

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

   if -1.50000000000000005e73 < z < 6.9500000000000002e34

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 82.5%

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

      1. associate-*r/ 82.5%

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

      2. mul-1-neg 82.5%

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

      3. *-commutative 82.5%

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

      4. distribute-rgt-neg-out 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+73} \lor \neg \left(z \leq 6.95 \cdot 10^{+34}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+73} \lor \neg \left(z \leq 6.95 \cdot 10^{+34}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.12e+73) (not (<= z 6.95e+34)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e+73) || !(z <= 6.95e+34)) {
		tmp = t + (x * (z / y));
	} 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 <= (-1.12d+73)) .or. (.not. (z <= 6.95d+34))) then
        tmp = t + (x * (z / y))
    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 <= -1.12e+73) || !(z <= 6.95e+34)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.12e+73) or not (z <= 6.95e+34):
		tmp = t + (x * (z / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.12e+73) || !(z <= 6.95e+34))
		tmp = Float64(t + Float64(x * Float64(z / y)));
	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 <= -1.12e+73) || ~((z <= 6.95e+34)))
		tmp = t + (x * (z / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.12e+73], N[Not[LessEqual[z, 6.95e+34]], $MachinePrecision]], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e73 or 6.9500000000000002e34 < z

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 92.5%

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

   5. Simplified 92.5%

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

   if -1.12e73 < z < 6.9500000000000002e34

   1. Initial program 95.0%

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

   3. Taylor expanded in z around 0 82.5%

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

      1. *-commutative 82.5%

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

      2. associate-*l/ 81.5%

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

      3. neg-mul-1 81.5%

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

      4. *-lft-identity 81.5%

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

      5. distribute-lft-neg-in 81.5%

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

      6. mul-1-neg 81.5%

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

      7. distribute-rgt-in 81.5%

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

      8. mul-1-neg 81.5%

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

      9. unsub-neg 81.5%

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

   5. Simplified 81.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+73} \lor \neg \left(z \leq 6.95 \cdot 10^{+34}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.8% 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 96.2%

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

3. Taylor expanded in x around 0 95.6%

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

   1. associate-*r/ 95.7%

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

   2. *-commutative 95.7%

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

   3. associate-/r/ 96.5%

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

5. Simplified 96.5%

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

6. Final simplification 96.5%

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

Alternative 7: 92.6% 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 96.2%

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

   1. associate-*l/ 95.6%

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

   2. associate-/l* 95.7%

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

   3. fma-define 95.7%

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

3. Simplified 95.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 95.7%

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

6. Applied egg-rr 95.7%

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

7. Final simplification 95.7%

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

Alternative 8: 65.9% 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 96.2%

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

3. Taylor expanded in z around 0 65.3%

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

   1. *-commutative 65.3%

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

   2. associate-*l/ 67.0%

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

   3. neg-mul-1 67.0%

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

   4. *-lft-identity 67.0%

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

   5. distribute-lft-neg-in 67.0%

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

   6. mul-1-neg 67.0%

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

   7. distribute-rgt-in 67.0%

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

   8. mul-1-neg 67.0%

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

   9. unsub-neg 67.0%

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

5. Simplified 67.0%

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

Alternative 9: 38.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in x around 0 34.2%

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

Developer Target 1: 97.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024132 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

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

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