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

Percentage Accurate: 97.7% → 97.9%

Time: 5.7s

Alternatives: 8

Speedup: 0.8×

• 25.6% 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: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.6 \cdot 10^{-79}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x 6.6e-79) (+ t (* (/ x y) (- z t))) (+ t (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 6.6e-79) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 6.6d-79) then
        tmp = t + ((x / y) * (z - t))
    else
        tmp = t + (x * ((z - t) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 6.6e-79) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (x * ((z - t) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 6.6e-79:
		tmp = t + ((x / y) * (z - t))
	else:
		tmp = t + (x * ((z - t) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 6.6e-79)
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	else
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 6.6e-79)
		tmp = t + ((x / y) * (z - t));
	else
		tmp = t + (x * ((z - t) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 6.6e-79], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.5999999999999996e-79

   1. Initial program 98.7%

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

   if 6.5999999999999996e-79 < x

   1. Initial program 94.2%

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

      1. remove-double-neg 94.2%

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

      2. unsub-neg 94.2%

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

      3. associate-*l/ 89.3%

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

      4. associate-*r/ 99.9%

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

      5. fma-neg 99.9%

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

      6. remove-double-neg 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.6 \cdot 10^{-79}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 2: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+30} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+30) (not (<= (/ x y) 2e-34)))
   (/ (* x (- z t)) y)
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+30) || !((x / y) <= 2e-34)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d+30)) .or. (.not. ((x / y) <= 2d-34))) then
        tmp = (x * (z - t)) / y
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+30) || !((x / y) <= 2e-34)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+30) or not ((x / y) <= 2e-34):
		tmp = (x * (z - t)) / y
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+30) || !(Float64(x / y) <= 2e-34))
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+30) || ~(((x / y) <= 2e-34)))
		tmp = (x * (z - t)) / y;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+30], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-34]], $MachinePrecision]], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999998e30 or 1.99999999999999986e-34 < (/.f64 x y)

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 93.4%

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

   3. Taylor expanded in x around -inf 92.9%

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

   if -4.9999999999999998e30 < (/.f64 x y) < 1.99999999999999986e-34

   1. Initial program 98.5%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate-*l/ 96.9%

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

      2. *-commutative 96.9%

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

   4. Simplified 96.9%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+30} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 3: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+49} \lor \neg \left(t \leq 1.25 \cdot 10^{-84}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.85e+49) (not (<= t 1.25e-84)))
   (* t (- 1.0 (/ x y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.85e+49) || !(t <= 1.25e-84)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	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 <= (-1.85d+49)) .or. (.not. (t <= 1.25d-84))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.85e+49) || !(t <= 1.25e-84)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.85e+49) or not (t <= 1.25e-84):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.85e+49) || !(t <= 1.25e-84))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.85e+49) || ~((t <= 1.25e-84)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.85e+49], N[Not[LessEqual[t, 1.25e-84]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85000000000000009e49 or 1.25e-84 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. unsub-neg 81.3%

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

      3. *-commutative 81.3%

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

      4. associate-*l/ 88.8%

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

      5. cancel-sign-sub-inv 88.8%

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

      6. *-lft-identity 88.8%

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

      7. mul-1-neg 88.8%

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

      8. distribute-rgt-in 88.8%

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

      9. mul-1-neg 88.8%

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

      10. unsub-neg 88.8%

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

   4. Simplified 88.8%

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

   if -1.85000000000000009e49 < t < 1.25e-84

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf 83.7%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

   4. Simplified 86.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+49} \lor \neg \left(t \leq 1.25 \cdot 10^{-84}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+49}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-84}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e+49)
   (- t (* (/ x y) t))
   (if (<= t 1.25e-84) (+ t (* (/ x y) z)) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+49) {
		tmp = t - ((x / y) * t);
	} else if (t <= 1.25e-84) {
		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 (t <= (-5d+49)) then
        tmp = t - ((x / y) * t)
    else if (t <= 1.25d-84) 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 (t <= -5e+49) {
		tmp = t - ((x / y) * t);
	} else if (t <= 1.25e-84) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5e+49:
		tmp = t - ((x / y) * t)
	elif t <= 1.25e-84:
		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 (t <= -5e+49)
		tmp = Float64(t - Float64(Float64(x / y) * t));
	elseif (t <= 1.25e-84)
		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 (t <= -5e+49)
		tmp = t - ((x / y) * t);
	elseif (t <= 1.25e-84)
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e+49], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-84], 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 3 regimes

2. if t < -5.0000000000000004e49

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-*l/ 88.0%

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

      5. cancel-sign-sub-inv 88.0%

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

      6. *-lft-identity 88.0%

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

      7. mul-1-neg 88.0%

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

      8. distribute-rgt-in 88.0%

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

      9. mul-1-neg 88.0%

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

      10. unsub-neg 88.0%

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

   4. Simplified 88.0%

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

      1. sub-neg 88.0%

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

      2. distribute-lft-in 88.0%

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

      3. *-commutative 88.0%

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

      4. *-un-lft-identity 88.0%

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

      5. distribute-rgt-neg-in 88.0%

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

      6. clear-num 88.0%

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

      7. div-inv 88.0%

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

      8. unsub-neg 88.0%

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

      9. div-inv 88.0%

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

      10. clear-num 88.0%

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

   6. Applied egg-rr 88.0%

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

   if -5.0000000000000004e49 < t < 1.25e-84

   1. Initial program 94.1%

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

   2. Taylor expanded in z around inf 83.7%

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

      1. associate-*l/ 86.8%

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

      2. *-commutative 86.8%

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

   4. Simplified 86.8%

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

   if 1.25e-84 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 83.1%

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

      1. mul-1-neg 83.1%

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

      2. unsub-neg 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-*l/ 89.5%

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

      5. cancel-sign-sub-inv 89.5%

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

      6. *-lft-identity 89.5%

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

      7. mul-1-neg 89.5%

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

      8. distribute-rgt-in 89.5%

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

      9. mul-1-neg 89.5%

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

      10. unsub-neg 89.5%

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

   4. Simplified 89.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+49}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-84}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 49.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e-66) t (if (<= y 1.42e-101) (* x (/ (- t) y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e-66) {
		tmp = t;
	} else if (y <= 1.42e-101) {
		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 (y <= (-3d-66)) then
        tmp = t
    else if (y <= 1.42d-101) 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 (y <= -3e-66) {
		tmp = t;
	} else if (y <= 1.42e-101) {
		tmp = x * (-t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e-66:
		tmp = t
	elif y <= 1.42e-101:
		tmp = x * (-t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e-66)
		tmp = t;
	elseif (y <= 1.42e-101)
		tmp = Float64(x * Float64(Float64(-t) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e-66)
		tmp = t;
	elseif (y <= 1.42e-101)
		tmp = x * (-t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e-66], t, If[LessEqual[y, 1.42e-101], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0000000000000002e-66 or 1.4200000000000001e-101 < y

   1. Initial program 98.1%

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

   2. Taylor expanded in x around 0 61.4%

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

   if -3.0000000000000002e-66 < y < 1.4200000000000001e-101

   1. Initial program 96.0%

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

   2. Taylor expanded in z around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. unsub-neg 60.3%

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

      3. *-commutative 60.3%

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

      4. associate-*l/ 62.3%

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

      5. cancel-sign-sub-inv 62.3%

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

      6. *-lft-identity 62.3%

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

      7. mul-1-neg 62.3%

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

      8. distribute-rgt-in 62.3%

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

      9. mul-1-neg 62.3%

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

      10. unsub-neg 62.3%

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

   4. Simplified 62.3%

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

      1. sub-neg 62.3%

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

      2. distribute-lft-in 62.3%

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

      3. *-commutative 62.3%

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

      4. *-un-lft-identity 62.3%

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

      5. distribute-rgt-neg-in 62.3%

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

      6. clear-num 62.3%

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

      7. div-inv 62.3%

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

      8. unsub-neg 62.3%

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

      9. div-inv 62.3%

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

      10. clear-num 62.3%

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

   6. Applied egg-rr 62.3%

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

   7. Taylor expanded in x around inf 48.0%

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

      1. mul-1-neg 48.0%

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

      2. associate-*l/ 47.8%

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

      3. distribute-lft-neg-in 47.8%

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

      4. *-commutative 47.8%

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

      5. distribute-neg-frac 47.8%

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

   9. Simplified 47.8%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-66}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. remove-double-neg 97.3%

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

   2. unsub-neg 97.3%

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

   3. associate-*l/ 91.7%

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

   4. associate-*r/ 94.0%

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

   5. fma-neg 94.0%

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

   6. remove-double-neg 94.0%

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

3. Simplified 94.0%

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

   1. fma-udef 94.0%

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

5. Applied egg-rr 94.0%

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

6. Final simplification 94.0%

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

Alternative 7: 65.0% 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 97.3%

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

2. Taylor expanded in z around 0 63.5%

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

   1. mul-1-neg 63.5%

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

   2. unsub-neg 63.5%

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

   3. *-commutative 63.5%

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

   4. associate-*l/ 68.3%

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

   5. cancel-sign-sub-inv 68.3%

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

   6. *-lft-identity 68.3%

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

   7. mul-1-neg 68.3%

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

   8. distribute-rgt-in 68.3%

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

   9. mul-1-neg 68.3%

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

   10. unsub-neg 68.3%

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

4. Simplified 68.3%

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

5. Final simplification 68.3%

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

Alternative 8: 38.4% 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 97.3%

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

2. Taylor expanded in x around 0 43.0%

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

3. Final simplification 43.0%

   \[\leadsto t \]

Developer target: 97.4% 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 2023320 
(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))