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

Percentage Accurate: 97.6% → 97.7%

Time: 6.7s

Alternatives: 8

Speedup: 1.0×

• 24.9% 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 98.7%

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

   1. *-commutative 98.7%

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

   2. clear-num 98.7%

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

   3. un-div-inv 98.8%

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

3. Applied egg-rr 98.8%

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

4. Final simplification 98.8%

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

Alternative 2: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10000000000.0) (not (<= (/ x y) 5e-5)))
   (* (- x) (/ t y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000000000.0) || !((x / y) <= 5e-5)) {
		tmp = -x * (t / 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) <= (-10000000000.0d0)) .or. (.not. ((x / y) <= 5d-5))) then
        tmp = -x * (t / 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) <= -10000000000.0) || !((x / y) <= 5e-5)) {
		tmp = -x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -10000000000.0) or not ((x / y) <= 5e-5):
		tmp = -x * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10000000000.0) || !(Float64(x / y) <= 5e-5))
		tmp = Float64(Float64(-x) * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -10000000000.0) || ~(((x / y) <= 5e-5)))
		tmp = -x * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -10000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-5]], $MachinePrecision]], N[((-x) * N[(t / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e10 or 5.00000000000000024e-5 < (/.f64 x y)

   1. Initial program 99.1%

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

      1. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. unsub-neg 48.9%

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

      3. *-rgt-identity 48.9%

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

      4. associate-*r/ 54.0%

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

      5. distribute-lft-out-- 54.0%

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

   6. Simplified 54.0%

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

   7. Taylor expanded in x around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. distribute-frac-neg 53.9%

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

   9. Simplified 53.9%

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

       1. associate-*r/ 48.9%

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

       2. distribute-rgt-neg-in 48.9%

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

       3. distribute-frac-neg 48.9%

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

       4. add-sqr-sqrt 25.0%

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

       5. sqrt-unprod 24.0%

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

       6. sqr-neg 24.0%

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

       7. sqrt-unprod 4.6%

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

       8. add-sqr-sqrt 5.4%

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

       9. associate-/l* 5.5%

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

       10. associate-/r/ 4.8%

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

       11. add-sqr-sqrt 3.9%

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

       12. sqrt-unprod 23.5%

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

       13. sqr-neg 23.5%

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

       14. sqrt-unprod 24.9%

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

       15. add-sqr-sqrt 47.4%

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

   11. Applied egg-rr 47.4%

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

   if -1e10 < (/.f64 x y) < 5.00000000000000024e-5

   1. Initial program 98.4%

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

      1. fma-def 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 80.4%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 63.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -10000000000.0) (not (<= (/ x y) 5e-5)))
   (* t (/ (- x) y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -10000000000.0) || !((x / y) <= 5e-5)) {
		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) <= (-10000000000.0d0)) .or. (.not. ((x / y) <= 5d-5))) 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) <= -10000000000.0) || !((x / y) <= 5e-5)) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -10000000000.0) or not ((x / y) <= 5e-5):
		tmp = t * (-x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -10000000000.0) || !(Float64(x / y) <= 5e-5))
		tmp = Float64(t * Float64(Float64(-x) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -10000000000.0) || ~(((x / y) <= 5e-5)))
		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], -10000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-5]], $MachinePrecision]], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e10 or 5.00000000000000024e-5 < (/.f64 x y)

   1. Initial program 99.1%

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

      1. fma-def 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 48.9%

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

      1. mul-1-neg 48.9%

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

      2. unsub-neg 48.9%

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

      3. *-rgt-identity 48.9%

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

      4. associate-*r/ 54.0%

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

      5. distribute-lft-out-- 54.0%

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

   6. Simplified 54.0%

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

   7. Taylor expanded in x around inf 53.9%

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

      1. mul-1-neg 53.9%

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

      2. distribute-frac-neg 53.9%

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

   9. Simplified 53.9%

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

   if -1e10 < (/.f64 x y) < 5.00000000000000024e-5

   1. Initial program 98.4%

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

      1. fma-def 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around 0 80.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -10000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -440000000 \lor \neg \left(t \leq 1.25 \cdot 10^{+15}\right):\\ \;\;\;\;t + \frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -440000000.0) (not (<= t 1.25e+15)))
   (+ t (/ t (/ (- y) x)))
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -440000000.0) || !(t <= 1.25e+15)) {
		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 ((t <= (-440000000.0d0)) .or. (.not. (t <= 1.25d+15))) 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 ((t <= -440000000.0) || !(t <= 1.25e+15)) {
		tmp = t + (t / (-y / x));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -440000000.0) or not (t <= 1.25e+15):
		tmp = t + (t / (-y / x))
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -440000000.0) || !(t <= 1.25e+15))
		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 ((t <= -440000000.0) || ~((t <= 1.25e+15)))
		tmp = t + (t / (-y / x));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -440000000.0], N[Not[LessEqual[t, 1.25e+15]], $MachinePrecision]], 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 2 regimes

2. if t < -4.4e8 or 1.25e15 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. mul-1-neg 84.5%

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

      3. *-commutative 84.5%

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

      4. distribute-rgt-neg-out 84.5%

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

      5. associate-*r/ 85.4%

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

   4. Simplified 85.4%

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

      1. *-commutative 85.4%

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

      2. div-inv 85.4%

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

      3. associate-*l* 91.4%

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

      4. add-sqr-sqrt 47.1%

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

      5. sqrt-unprod 41.9%

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

      6. sqr-neg 41.9%

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

      7. sqrt-unprod 27.1%

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

      8. add-sqr-sqrt 55.9%

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

      9. associate-/r/ 55.9%

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

      10. div-inv 55.9%

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

      11. frac-2neg 55.9%

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

      12. add-sqr-sqrt 28.7%

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

      13. sqrt-unprod 40.5%

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

      14. sqr-neg 40.5%

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

      15. sqrt-unprod 44.3%

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

      16. add-sqr-sqrt 91.5%

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

      17. distribute-neg-frac 91.5%

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

   6. Applied egg-rr 91.5%

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

   if -4.4e8 < t < 1.25e15

   1. Initial program 97.4%

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

   2. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 85.4%

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

      2. associate-/r/ 90.1%

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

   4. Applied egg-rr 90.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -440000000 \lor \neg \left(t \leq 1.25 \cdot 10^{+15}\right):\\ \;\;\;\;t + \frac{t}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-18} \lor \neg \left(t \leq 3.1 \cdot 10^{+15}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.75e-18) (not (<= t 3.1e+15)))
   (* t (- 1.0 (/ x y)))
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.75e-18) || !(t <= 3.1e+15)) {
		tmp = t * (1.0 - (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 ((t <= (-2.75d-18)) .or. (.not. (t <= 3.1d+15))) then
        tmp = t * (1.0d0 - (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 ((t <= -2.75e-18) || !(t <= 3.1e+15)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.75e-18) or not (t <= 3.1e+15):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.75e-18) || !(t <= 3.1e+15))
		tmp = Float64(t * Float64(1.0 - 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 ((t <= -2.75e-18) || ~((t <= 3.1e+15)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.75e-18], N[Not[LessEqual[t, 3.1e+15]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.75e-18 or 3.1e15 < t

   1. Initial program 99.9%

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

      1. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

      3. *-rgt-identity 83.3%

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

      4. associate-*r/ 90.5%

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

      5. distribute-lft-out-- 90.5%

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

   6. Simplified 90.5%

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

   if -2.75e-18 < t < 3.1e15

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 87.0%

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

      1. associate-/l* 87.1%

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

      2. associate-/r/ 91.3%

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

   4. Applied egg-rr 91.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-18} \lor \neg \left(t \leq 3.1 \cdot 10^{+15}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 6: 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 98.7%

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

2. Final simplification 98.7%

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

Alternative 7: 65.1% 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 98.7%

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

   1. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Taylor expanded in z around 0 61.5%

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

   1. mul-1-neg 61.5%

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

   2. unsub-neg 61.5%

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

   3. *-rgt-identity 61.5%

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

   4. associate-*r/ 67.5%

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

   5. distribute-lft-out-- 67.4%

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

6. Simplified 67.4%

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

7. Final simplification 67.4%

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

Alternative 8: 38.2% 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 98.7%

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

   1. fma-def 98.8%

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

3. Simplified 98.8%

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

4. Taylor expanded in x around 0 41.8%

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

5. Final simplification 41.8%

   \[\leadsto t \]

Developer target: 97.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023321 
(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))