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

Percentage Accurate: 97.8% → 97.8%

Time: 7.0s

Alternatives: 8

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: 97.8% 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: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.9%

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

2. Final simplification 98.9%

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

Alternative 2: 63.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 100\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+15) (not (<= (/ x y) 100.0))) (* (/ x y) (- t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+15) || !((x / y) <= 100.0)) {
		tmp = (x / y) * -t;
	} 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) <= (-2d+15)) .or. (.not. ((x / y) <= 100.0d0))) then
        tmp = (x / y) * -t
    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) <= -2e+15) || !((x / y) <= 100.0)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+15) or not ((x / y) <= 100.0):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+15) || !(Float64(x / y) <= 100.0))
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+15) || ~(((x / y) <= 100.0)))
		tmp = (x / y) * -t;
	else
		tmp = t;
	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], 100.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e15 or 100 < (/.f64 x y)

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 46.1%

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

      1. mul-1-neg 46.1%

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

      2. associate-/l* 53.3%

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

   4. Simplified 53.3%

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

      1. +-commutative 53.3%

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

      2. unsub-neg 53.3%

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

      3. div-inv 54.0%

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

      4. clear-num 54.0%

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

   6. Applied egg-rr 54.0%

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

   7. Taylor expanded in x around inf 45.8%

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

      1. mul-1-neg 45.8%

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

      2. associate-*l/ 48.7%

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

      3. distribute-rgt-neg-in 48.7%

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

      4. *-commutative 48.7%

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

   9. Simplified 48.7%

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

   10. Taylor expanded in x around 0 45.8%

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

       1. mul-1-neg 45.8%

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

       2. associate-*r/ 53.4%

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

       3. distribute-lft-neg-out 53.4%

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

       4. *-commutative 53.4%

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

   12. Simplified 53.4%

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

   if -2e15 < (/.f64 x y) < 100

   1. Initial program 98.7%

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

      1. remove-double-neg 98.7%

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

      2. unsub-neg 98.7%

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

      3. associate-*l/ 93.5%

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

      4. associate-*r/ 87.2%

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

      5. fma-neg 87.2%

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

      6. remove-double-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in x around 0 70.2%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 100\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-80} \lor \neg \left(z \leq 8.5 \cdot 10^{-27}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-80) (not (<= z 8.5e-27)))
   (+ t (* (/ x y) z))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-80) || !(z <= 8.5e-27)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.95d-80)) .or. (.not. (z <= 8.5d-27))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-80) || !(z <= 8.5e-27)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-80) or not (z <= 8.5e-27):
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e-80) || !(z <= 8.5e-27))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e-80) || ~((z <= 8.5e-27)))
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e-80], N[Not[LessEqual[z, 8.5e-27]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e-80 or 8.50000000000000033e-27 < z

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 87.6%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   if -1.9499999999999999e-80 < z < 8.50000000000000033e-27

   1. Initial program 99.0%

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

      1. remove-double-neg 99.0%

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

      2. unsub-neg 99.0%

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

      3. associate-*l/ 91.7%

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

      4. associate-*r/ 96.1%

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

      5. fma-neg 96.1%

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

      6. remove-double-neg 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. *-rgt-identity 81.8%

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

      3. associate-*r/ 87.7%

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

      4. distribute-rgt-neg-in 87.7%

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

      5. mul-1-neg 87.7%

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

      6. distribute-lft-in 87.6%

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

      7. mul-1-neg 87.6%

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

      8. unsub-neg 87.6%

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

   6. Simplified 87.6%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-80} \lor \neg \left(z \leq 8.5 \cdot 10^{-27}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-80} \lor \neg \left(z \leq 4.8 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-80) (not (<= z 4.8e-22)))
   (+ t (* (/ x y) z))
   (- t (* (/ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-80) || !(z <= 4.8e-22)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.6d-80)) .or. (.not. (z <= 4.8d-22))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t - ((x / y) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-80) || !(z <= 4.8e-22)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - ((x / y) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-80) or not (z <= 4.8e-22):
		tmp = t + ((x / y) * z)
	else:
		tmp = t - ((x / y) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-80) || !(z <= 4.8e-22))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t - Float64(Float64(x / y) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-80) || ~((z <= 4.8e-22)))
		tmp = t + ((x / y) * z);
	else
		tmp = t - ((x / y) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-80], N[Not[LessEqual[z, 4.8e-22]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5999999999999999e-80 or 4.80000000000000005e-22 < z

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 87.6%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   if -1.5999999999999999e-80 < z < 4.80000000000000005e-22

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. associate-/l* 87.7%

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

   4. Simplified 87.7%

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

      1. +-commutative 87.7%

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

      2. unsub-neg 87.7%

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

      3. div-inv 87.6%

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

      4. clear-num 87.7%

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

   6. Applied egg-rr 87.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-80} \lor \neg \left(z \leq 4.8 \cdot 10^{-22}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]

Alternative 5: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-80} \lor \neg \left(z \leq 2.8 \cdot 10^{-25}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.95e-80) (not (<= z 2.8e-25)))
   (+ t (* (/ x y) z))
   (- t (/ t (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-80) || !(z <= 2.8e-25)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.95d-80)) .or. (.not. (z <= 2.8d-25))) then
        tmp = t + ((x / y) * z)
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.95e-80) || !(z <= 2.8e-25)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.95e-80) or not (z <= 2.8e-25):
		tmp = t + ((x / y) * z)
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.95e-80) || !(z <= 2.8e-25))
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.95e-80) || ~((z <= 2.8e-25)))
		tmp = t + ((x / y) * z);
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.95e-80], N[Not[LessEqual[z, 2.8e-25]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e-80 or 2.79999999999999988e-25 < z

   1. Initial program 98.9%

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

   2. Taylor expanded in z around inf 87.6%

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

      1. associate-*l/ 89.7%

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

      2. *-commutative 89.7%

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

   4. Simplified 89.7%

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

   if -1.9499999999999999e-80 < z < 2.79999999999999988e-25

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 81.8%

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

      1. mul-1-neg 81.8%

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

      2. associate-/l* 87.7%

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

   4. Simplified 87.7%

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

      1. +-commutative 87.7%

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

      2. unsub-neg 87.7%

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

      3. div-inv 87.6%

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

      4. clear-num 87.7%

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

   6. Applied egg-rr 87.7%

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

      1. associate-*r/ 81.8%

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

      2. associate-/l* 87.7%

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

   8. Applied egg-rr 87.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-80} \lor \neg \left(z \leq 2.8 \cdot 10^{-25}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 6: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+92} \lor \neg \left(x \leq 3 \cdot 10^{+79}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3e+92) (not (<= x 3e+79))) (* (- x) (/ t y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3e+92) || !(x <= 3e+79)) {
		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 <= (-3d+92)) .or. (.not. (x <= 3d+79))) 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 <= -3e+92) || !(x <= 3e+79)) {
		tmp = -x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3e+92) or not (x <= 3e+79):
		tmp = -x * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3e+92) || !(x <= 3e+79))
		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 <= -3e+92) || ~((x <= 3e+79)))
		tmp = -x * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3e+92], N[Not[LessEqual[x, 3e+79]], $MachinePrecision]], N[((-x) * N[(t / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000013e92 or 2.99999999999999974e79 < x

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 49.6%

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

      1. mul-1-neg 49.6%

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

      2. associate-/l* 61.1%

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

   4. Simplified 61.1%

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

      1. +-commutative 61.1%

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

      2. unsub-neg 61.1%

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

      3. div-inv 62.1%

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

      4. clear-num 62.1%

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

   6. Applied egg-rr 62.1%

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

   7. Taylor expanded in x around inf 44.1%

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

      1. mul-1-neg 44.1%

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

      2. associate-*l/ 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

      4. *-commutative 47.3%

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

   9. Simplified 47.3%

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

   if -3.00000000000000013e92 < x < 2.99999999999999974e79

   1. Initial program 98.9%

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

      1. remove-double-neg 98.9%

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

      2. unsub-neg 98.9%

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

      3. associate-*l/ 95.3%

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

      4. associate-*r/ 85.7%

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

      5. fma-neg 85.7%

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

      6. remove-double-neg 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 52.9%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+92} \lor \neg \left(x \leq 3 \cdot 10^{+79}\right):\\ \;\;\;\;\left(-x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 65.2% 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 98.9%

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

   1. remove-double-neg 98.9%

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

   2. unsub-neg 98.9%

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

   3. associate-*l/ 92.5%

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

   4. associate-*r/ 89.6%

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

   5. fma-neg 89.5%

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

   6. remove-double-neg 89.5%

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

3. Simplified 89.5%

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

4. Taylor expanded in z around 0 57.0%

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

   1. mul-1-neg 57.0%

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

   2. *-rgt-identity 57.0%

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

   3. associate-*r/ 63.0%

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

   4. distribute-rgt-neg-in 63.0%

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

   5. mul-1-neg 63.0%

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

   6. distribute-lft-in 63.0%

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

   7. mul-1-neg 63.0%

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

   8. unsub-neg 63.0%

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

6. Simplified 63.0%

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

7. Final simplification 63.0%

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

Alternative 8: 38.3% 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 98.9%

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

   1. remove-double-neg 98.9%

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

   2. unsub-neg 98.9%

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

   3. associate-*l/ 92.5%

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

   4. associate-*r/ 89.6%

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

   5. fma-neg 89.5%

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

   6. remove-double-neg 89.5%

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

3. Simplified 89.5%

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

4. Taylor expanded in x around 0 38.4%

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

5. Final simplification 38.4%

   \[\leadsto t \]

Developer target: 97.5% 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 2023310 
(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))