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

Percentage Accurate: 97.7% → 97.7%

Time: 5.2s

Alternatives: 4

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% 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 97.5%

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

2. Final simplification 97.5%

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

Alternative 2: 95.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-165} \lor \neg \left(x \leq 4.5 \cdot 10^{-174}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.3e-165) (not (<= x 4.5e-174)))
   (+ t (* x (/ (- z t) y)))
   (+ t (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e-165) || !(x <= 4.5e-174)) {
		tmp = t + (x * ((z - t) / y));
	} else {
		tmp = t + ((x * z) / 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 <= (-4.3d-165)) .or. (.not. (x <= 4.5d-174))) then
        tmp = t + (x * ((z - t) / y))
    else
        tmp = t + ((x * z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.3e-165) || !(x <= 4.5e-174)) {
		tmp = t + (x * ((z - t) / y));
	} else {
		tmp = t + ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.3e-165) or not (x <= 4.5e-174):
		tmp = t + (x * ((z - t) / y))
	else:
		tmp = t + ((x * z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.3e-165) || !(x <= 4.5e-174))
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	else
		tmp = Float64(t + Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.3e-165) || ~((x <= 4.5e-174)))
		tmp = t + (x * ((z - t) / y));
	else
		tmp = t + ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.3e-165], N[Not[LessEqual[x, 4.5e-174]], $MachinePrecision]], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.30000000000000007e-165 or 4.49999999999999964e-174 < x

   1. Initial program 97.2%

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

   2. Taylor expanded in x around 0 88.8%

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

      1. associate-*r/ 95.8%

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

   4. Simplified 95.8%

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

   if -4.30000000000000007e-165 < x < 4.49999999999999964e-174

   1. Initial program 98.8%

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

   2. Taylor expanded in z around inf 98.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-165} \lor \neg \left(x \leq 4.5 \cdot 10^{-174}\right):\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 3: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-88} \lor \neg \left(z \leq 4.4 \cdot 10^{+95}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.8e-88) (not (<= z 4.4e+95)))
   (+ t (* (/ x y) z))
   (- t (/ t (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.8e-88) || !(z <= 4.4e+95)) {
		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 <= (-4.8d-88)) .or. (.not. (z <= 4.4d+95))) 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 <= -4.8e-88) || !(z <= 4.4e+95)) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.8e-88) or not (z <= 4.4e+95):
		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 <= -4.8e-88) || !(z <= 4.4e+95))
		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 <= -4.8e-88) || ~((z <= 4.4e+95)))
		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, -4.8e-88], N[Not[LessEqual[z, 4.4e+95]], $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 < -4.7999999999999999e-88 or 4.3999999999999998e95 < z

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf 84.4%

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

      1. associate-*l/ 91.7%

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

      2. *-commutative 91.7%

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

   4. Simplified 91.7%

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

   if -4.7999999999999999e-88 < z < 4.3999999999999998e95

   1. Initial program 97.1%

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

   2. Taylor expanded in z around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. associate-/l* 88.8%

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

   4. Simplified 88.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-88} \lor \neg \left(z \leq 4.4 \cdot 10^{+95}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 4: 77.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

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)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.5%

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

2. Taylor expanded in z around inf 73.7%

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

   1. associate-*l/ 77.6%

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

   2. *-commutative 77.6%

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

4. Simplified 77.6%

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

5. Final simplification 77.6%

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

Developer target: 97.6% 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 2023275 
(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))