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

Percentage Accurate: 97.5% → 97.6%

Time: 8.0s

Alternatives: 9

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: 97.5% 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: 97.6% 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 98.3%

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

   1. *-commutative 98.3%

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

   2. clear-num 98.3%

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

   3. un-div-inv 98.5%

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

3. Applied egg-rr 98.5%

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

4. Final simplification 98.5%

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

Alternative 2: 94.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-150} \lor \neg \left(x \leq 4.2 \cdot 10^{-223}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.02e-150) (not (<= x 4.2e-223)))
   (+ t (* x (/ (- z t) y)))
   (+ t (/ (* z x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-150) || !(x <= 4.2e-223)) {
		tmp = t + (x * ((z - t) / y));
	} else {
		tmp = t + ((z * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.02d-150)) .or. (.not. (x <= 4.2d-223))) then
        tmp = t + (x * ((z - t) / y))
    else
        tmp = t + ((z * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-150) || !(x <= 4.2e-223)) {
		tmp = t + (x * ((z - t) / y));
	} else {
		tmp = t + ((z * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.02e-150) or not (x <= 4.2e-223):
		tmp = t + (x * ((z - t) / y))
	else:
		tmp = t + ((z * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.02e-150) || !(x <= 4.2e-223))
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	else
		tmp = Float64(t + Float64(Float64(z * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.02e-150) || ~((x <= 4.2e-223)))
		tmp = t + (x * ((z - t) / y));
	else
		tmp = t + ((z * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.02e-150], N[Not[LessEqual[x, 4.2e-223]], $MachinePrecision]], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0199999999999999e-150 or 4.19999999999999965e-223 < x

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 95.9%

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

      1. div-sub 96.4%

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

   4. Simplified 96.4%

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

   if -1.0199999999999999e-150 < x < 4.19999999999999965e-223

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 93.7%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-150} \lor \neg \left(x \leq 4.2 \cdot 10^{-223}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \]

Alternative 3: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-71} \lor \neg \left(z \leq 9.2 \cdot 10^{-55}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.35e-71) (not (<= z 9.2e-55)))
   (+ t (* z (/ x y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e-71) || !(z <= 9.2e-55)) {
		tmp = t + (z * (x / 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 <= (-1.35d-71)) .or. (.not. (z <= 9.2d-55))) then
        tmp = t + (z * (x / 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 <= -1.35e-71) || !(z <= 9.2e-55)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.35e-71) or not (z <= 9.2e-55):
		tmp = t + (z * (x / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.35e-71) || !(z <= 9.2e-55))
		tmp = Float64(t + Float64(z * Float64(x / 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 <= -1.35e-71) || ~((z <= 9.2e-55)))
		tmp = t + (z * (x / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.35e-71], N[Not[LessEqual[z, 9.2e-55]], $MachinePrecision]], N[(t + N[(z * N[(x / 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 < -1.3500000000000001e-71 or 9.20000000000000046e-55 < z

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 92.7%

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

      1. associate-/l* 91.7%

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

      2. associate-/r/ 93.9%

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

   4. Applied egg-rr 93.9%

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

   if -1.3500000000000001e-71 < z < 9.20000000000000046e-55

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 78.8%

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

      1. *-lft-identity 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l/ 84.3%

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

      4. associate-*l* 84.3%

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

      5. distribute-rgt-in 84.3%

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

      6. mul-1-neg 84.3%

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

      7. unsub-neg 84.3%

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

   4. Simplified 84.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-71} \lor \neg \left(z \leq 9.2 \cdot 10^{-55}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-70}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e-70)
   (+ t (* x (/ z y)))
   (if (<= z 1.45e-47) (* t (- 1.0 (/ x y))) (+ t (* z (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e-70) {
		tmp = t + (x * (z / y));
	} else if (z <= 1.45e-47) {
		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 (z <= (-1.05d-70)) then
        tmp = t + (x * (z / y))
    else if (z <= 1.45d-47) 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 (z <= -1.05e-70) {
		tmp = t + (x * (z / y));
	} else if (z <= 1.45e-47) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e-70:
		tmp = t + (x * (z / y))
	elif z <= 1.45e-47:
		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 (z <= -1.05e-70)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (z <= 1.45e-47)
		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 (z <= -1.05e-70)
		tmp = t + (x * (z / y));
	elseif (z <= 1.45e-47)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e-70], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-47], 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 3 regimes

2. if z < -1.0500000000000001e-70

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-/l* 91.5%

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

      3. associate-/r/ 91.6%

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

   4. Applied egg-rr 91.6%

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

   if -1.0500000000000001e-70 < z < 1.45e-47

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 78.8%

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

      1. *-lft-identity 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l/ 84.3%

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

      4. associate-*l* 84.3%

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

      5. distribute-rgt-in 84.3%

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

      6. mul-1-neg 84.3%

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

      7. unsub-neg 84.3%

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

   4. Simplified 84.3%

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

   if 1.45e-47 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 95.2%

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

      1. associate-/l* 91.9%

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

      2. associate-/r/ 96.3%

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

   4. Applied egg-rr 96.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-70}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-71}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.9e-71)
   (+ t (* x (/ z y)))
   (if (<= z 2.9e-55) (* t (- 1.0 (/ x y))) (+ t (/ z (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e-71) {
		tmp = t + (x * (z / y));
	} else if (z <= 2.9e-55) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.9d-71)) then
        tmp = t + (x * (z / y))
    else if (z <= 2.9d-55) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e-71) {
		tmp = t + (x * (z / y));
	} else if (z <= 2.9e-55) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.9e-71:
		tmp = t + (x * (z / y))
	elif z <= 2.9e-55:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.9e-71)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (z <= 2.9e-55)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.9e-71)
		tmp = t + (x * (z / y));
	elseif (z <= 2.9e-55)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.9e-71], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e-55], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.90000000000000002e-71

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-/l* 91.5%

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

      3. associate-/r/ 91.6%

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

   4. Applied egg-rr 91.6%

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

   if -5.90000000000000002e-71 < z < 2.9e-55

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 78.8%

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

      1. *-lft-identity 78.8%

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

      2. *-commutative 78.8%

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

      3. associate-*l/ 84.3%

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

      4. associate-*l* 84.3%

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

      5. distribute-rgt-in 84.3%

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

      6. mul-1-neg 84.3%

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

      7. unsub-neg 84.3%

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

   4. Simplified 84.3%

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

   if 2.9e-55 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 95.2%

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

      1. associate-/l* 91.9%

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

      2. associate-/r/ 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. clear-num 96.3%

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

      2. associate-*l/ 96.4%

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

      3. *-un-lft-identity 96.4%

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

   6. Applied egg-rr 96.4%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-71}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 6: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-71}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-47}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e-71)
   (+ t (* x (/ z y)))
   (if (<= z 2.5e-47) (- t (/ t (/ y x))) (+ t (/ z (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-71) {
		tmp = t + (x * (z / y));
	} else if (z <= 2.5e-47) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6d-71)) then
        tmp = t + (x * (z / y))
    else if (z <= 2.5d-47) then
        tmp = t - (t / (y / x))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e-71) {
		tmp = t + (x * (z / y));
	} else if (z <= 2.5e-47) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e-71:
		tmp = t + (x * (z / y))
	elif z <= 2.5e-47:
		tmp = t - (t / (y / x))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e-71)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (z <= 2.5e-47)
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6e-71)
		tmp = t + (x * (z / y));
	elseif (z <= 2.5e-47)
		tmp = t - (t / (y / x));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e-71], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-47], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000003e-71

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 90.4%

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

      1. *-commutative 90.4%

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

      2. associate-/l* 91.5%

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

      3. associate-/r/ 91.6%

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

   4. Applied egg-rr 91.6%

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

   if -6.0000000000000003e-71 < z < 2.50000000000000006e-47

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. associate-/l* 84.8%

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

   4. Simplified 84.8%

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

   if 2.50000000000000006e-47 < z

   1. Initial program 97.1%

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

   2. Taylor expanded in z around inf 95.2%

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

      1. associate-/l* 91.9%

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

      2. associate-/r/ 96.3%

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

   4. Applied egg-rr 96.3%

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

      1. clear-num 96.3%

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

      2. associate-*l/ 96.4%

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

      3. *-un-lft-identity 96.4%

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

   6. Applied egg-rr 96.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-71}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-47}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 7: 97.5% 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 98.3%

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

2. Final simplification 98.3%

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

Alternative 8: 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 98.3%

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

2. Taylor expanded in z around 0 59.1%

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

   1. *-lft-identity 59.1%

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

   2. *-commutative 59.1%

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

   3. associate-*l/ 64.3%

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

   4. associate-*l* 64.3%

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

   5. distribute-rgt-in 64.3%

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

   6. mul-1-neg 64.3%

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

   7. unsub-neg 64.3%

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

4. Simplified 64.3%

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

5. Final simplification 64.3%

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

Alternative 9: 39.3% 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 98.3%

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

2. Taylor expanded in x around 0 37.5%

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

3. Final simplification 37.5%

   \[\leadsto t \]

Developer target: 97.3% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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))