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

Percentage Accurate: 97.7% → 97.8%

Time: 8.9s

Alternatives: 12

Speedup: 1.0×

• 25.4% 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: 97.8% 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 98.8%

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

3. Taylor expanded in x around 0 93.5%

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

   1. associate-*r/ 92.2%

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

   2. *-commutative 92.2%

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

   3. associate-/r/ 99.0%

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

5. Simplified 99.0%

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

6. Final simplification 99.0%

   \[\leadsto t + \frac{z - t}{\frac{y}{x}} \]
7. Add Preprocessing

Alternative 2: 53.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))))
   (if (<= x -2.35e+120)
     t_1
     (if (<= x -3.3e-66)
       (/ (* z x) y)
       (if (<= x 8.6e-33) t (if (<= x 1.15e+77) (* x (/ z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if (x <= -2.35e+120) {
		tmp = t_1;
	} else if (x <= -3.3e-66) {
		tmp = (z * x) / y;
	} else if (x <= 8.6e-33) {
		tmp = t;
	} else if (x <= 1.15e+77) {
		tmp = x * (z / y);
	} 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) * -t
    if (x <= (-2.35d+120)) then
        tmp = t_1
    else if (x <= (-3.3d-66)) then
        tmp = (z * x) / y
    else if (x <= 8.6d-33) then
        tmp = t
    else if (x <= 1.15d+77) then
        tmp = x * (z / y)
    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) * -t;
	double tmp;
	if (x <= -2.35e+120) {
		tmp = t_1;
	} else if (x <= -3.3e-66) {
		tmp = (z * x) / y;
	} else if (x <= 8.6e-33) {
		tmp = t;
	} else if (x <= 1.15e+77) {
		tmp = x * (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * -t
	tmp = 0
	if x <= -2.35e+120:
		tmp = t_1
	elif x <= -3.3e-66:
		tmp = (z * x) / y
	elif x <= 8.6e-33:
		tmp = t
	elif x <= 1.15e+77:
		tmp = x * (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (x <= -2.35e+120)
		tmp = t_1;
	elseif (x <= -3.3e-66)
		tmp = Float64(Float64(z * x) / y);
	elseif (x <= 8.6e-33)
		tmp = t;
	elseif (x <= 1.15e+77)
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * -t;
	tmp = 0.0;
	if (x <= -2.35e+120)
		tmp = t_1;
	elseif (x <= -3.3e-66)
		tmp = (z * x) / y;
	elseif (x <= 8.6e-33)
		tmp = t;
	elseif (x <= 1.15e+77)
		tmp = x * (z / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[x, -2.35e+120], t$95$1, If[LessEqual[x, -3.3e-66], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[x, 8.6e-33], t, If[LessEqual[x, 1.15e+77], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.34999999999999997e120 or 1.14999999999999997e77 < x

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 86.4%

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

   4. Taylor expanded in x around -inf 78.7%

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

   5. Taylor expanded in z around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. associate-*r/ 63.3%

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

      3. distribute-rgt-neg-out 63.3%

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

      4. distribute-neg-frac2 63.3%

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

   7. Simplified 63.3%

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

   if -2.34999999999999997e120 < x < -3.2999999999999999e-66

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in x around -inf 75.0%

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

   5. Taylor expanded in z around inf 53.5%

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

   if -3.2999999999999999e-66 < x < 8.60000000000000062e-33

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0 63.9%

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

   if 8.60000000000000062e-33 < x < 1.14999999999999997e77

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 96.5%

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

   4. Taylor expanded in x around -inf 81.4%

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

   5. Taylor expanded in z around inf 52.0%

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

      1. associate-*r/ 52.0%

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

   7. Simplified 52.0%

      \[\leadsto \color{blue}{x \cdot \frac{z}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+120}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-66}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+77}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+21} \lor \neg \left(\frac{x}{y} \leq 15000000\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+21) (not (<= (/ x y) 15000000.0)))
   (/ (* (- z t) x) y)
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+21) || !((x / y) <= 15000000.0)) {
		tmp = ((z - t) * 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 (((x / y) <= (-2d+21)) .or. (.not. ((x / y) <= 15000000.0d0))) then
        tmp = ((z - t) * 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 (((x / y) <= -2e+21) || !((x / y) <= 15000000.0)) {
		tmp = ((z - t) * x) / y;
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+21) or not ((x / y) <= 15000000.0):
		tmp = ((z - t) * x) / y
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+21) || !(Float64(x / y) <= 15000000.0))
		tmp = Float64(Float64(Float64(z - t) * 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 (((x / y) <= -2e+21) || ~(((x / y) <= 15000000.0)))
		tmp = ((z - t) * x) / y;
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+21], N[Not[LessEqual[N[(x / y), $MachinePrecision], 15000000.0]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e21 or 1.5e7 < (/.f64 x y)

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 94.6%

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

   4. Taylor expanded in x around -inf 94.2%

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

   if -2e21 < (/.f64 x y) < 1.5e7

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 98.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+21} \lor \neg \left(\frac{x}{y} \leq 15000000\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-85} \lor \neg \left(z \leq 8.4 \cdot 10^{-66}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e-85) (not (<= z 8.4e-66)))
   (+ t (* z (/ x y)))
   (- t (/ t (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-85) || !(z <= 8.4e-66)) {
		tmp = t + (z * (x / y));
	} 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 <= (-8.8d-85)) .or. (.not. (z <= 8.4d-66))) then
        tmp = t + (z * (x / y))
    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 <= -8.8e-85) || !(z <= 8.4e-66)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-85) or not (z <= 8.4e-66):
		tmp = t + (z * (x / y))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-85) || !(z <= 8.4e-66))
		tmp = Float64(t + Float64(z * Float64(x / y)));
	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 <= -8.8e-85) || ~((z <= 8.4e-66)))
		tmp = t + (z * (x / y));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e-85], N[Not[LessEqual[z, 8.4e-66]], $MachinePrecision]], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8e-85 or 8.4000000000000001e-66 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 87.7%

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

   if -8.8e-85 < z < 8.4000000000000001e-66

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 92.8%

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

      1. associate-*r/ 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-/r/ 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in z around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. associate-*r/ 92.5%

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

      3. rem-square-sqrt 54.9%

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

      4. distribute-lft-neg-in 54.9%

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

      5. cancel-sign-sub-inv 54.9%

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

      6. rem-square-sqrt 92.5%

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

   8. Simplified 92.5%

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

      1. clear-num 92.5%

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

      2. div-inv 93.1%

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

   10. Applied egg-rr 93.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-85} \lor \neg \left(z \leq 8.4 \cdot 10^{-66}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-85} \lor \neg \left(z \leq 3.9 \cdot 10^{-66}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-85) (not (<= z 3.9e-66)))
   (+ t (* z (/ x y)))
   (- t (* t (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-85) || !(z <= 3.9e-66)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t - (t * (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 <= (-1.6d-85)) .or. (.not. (z <= 3.9d-66))) then
        tmp = t + (z * (x / y))
    else
        tmp = t - (t * (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 <= -1.6e-85) || !(z <= 3.9e-66)) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-85) or not (z <= 3.9e-66):
		tmp = t + (z * (x / y))
	else:
		tmp = t - (t * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-85) || !(z <= 3.9e-66))
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-85) || ~((z <= 3.9e-66)))
		tmp = t + (z * (x / y));
	else
		tmp = t - (t * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-85], N[Not[LessEqual[z, 3.9e-66]], $MachinePrecision]], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000014e-85 or 3.89999999999999983e-66 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 87.7%

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

   if -1.60000000000000014e-85 < z < 3.89999999999999983e-66

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 92.8%

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

      1. associate-*r/ 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-/r/ 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in z around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. associate-*r/ 92.5%

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

      3. rem-square-sqrt 54.9%

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

      4. distribute-lft-neg-in 54.9%

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

      5. cancel-sign-sub-inv 54.9%

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

      6. rem-square-sqrt 92.5%

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

   8. Simplified 92.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-85} \lor \neg \left(z \leq 3.9 \cdot 10^{-66}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-84} \lor \neg \left(z \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e-84) (not (<= z 2.3e-65)))
   (+ t (* z (/ x y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e-84) || !(z <= 2.3e-65)) {
		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 <= (-1.02d-84)) .or. (.not. (z <= 2.3d-65))) 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 <= -1.02e-84) || !(z <= 2.3e-65)) {
		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 <= -1.02e-84) or not (z <= 2.3e-65):
		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 <= -1.02e-84) || !(z <= 2.3e-65))
		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 <= -1.02e-84) || ~((z <= 2.3e-65)))
		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, -1.02e-84], N[Not[LessEqual[z, 2.3e-65]], $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 < -1.02000000000000004e-84 or 2.3e-65 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 87.7%

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

   if -1.02000000000000004e-84 < z < 2.3e-65

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 92.5%

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

      3. neg-mul-1 92.5%

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

      4. *-lft-identity 92.5%

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

      5. distribute-lft-neg-in 92.5%

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

      6. mul-1-neg 92.5%

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

      7. distribute-rgt-in 92.5%

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

      8. mul-1-neg 92.5%

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

      9. unsub-neg 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-84} \lor \neg \left(z \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-84} \lor \neg \left(z \leq 3.6 \cdot 10^{-65}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.02e-84) (not (<= z 3.6e-65)))
   (+ t (* x (/ z y)))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.02e-84) || !(z <= 3.6e-65)) {
		tmp = t + (x * (z / 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 <= (-1.02d-84)) .or. (.not. (z <= 3.6d-65))) then
        tmp = t + (x * (z / 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 <= -1.02e-84) || !(z <= 3.6e-65)) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.02e-84) or not (z <= 3.6e-65):
		tmp = t + (x * (z / y))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.02e-84) || !(z <= 3.6e-65))
		tmp = Float64(t + Float64(x * Float64(z / 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 <= -1.02e-84) || ~((z <= 3.6e-65)))
		tmp = t + (x * (z / y));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.02e-84], N[Not[LessEqual[z, 3.6e-65]], $MachinePrecision]], N[(t + N[(x * N[(z / 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 < -1.02000000000000004e-84 or 3.5999999999999998e-65 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 83.9%

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

      1. associate-/l* 82.5%

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

   5. Simplified 82.5%

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

   if -1.02000000000000004e-84 < z < 3.5999999999999998e-65

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l/ 92.5%

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

      3. neg-mul-1 92.5%

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

      4. *-lft-identity 92.5%

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

      5. distribute-lft-neg-in 92.5%

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

      6. mul-1-neg 92.5%

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

      7. distribute-rgt-in 92.5%

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

      8. mul-1-neg 92.5%

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

      9. unsub-neg 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{-84} \lor \neg \left(z \leq 3.6 \cdot 10^{-65}\right):\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.4e+67)
   (* x (/ z y))
   (if (<= z 2.9e+191) (* t (- 1.0 (/ x y))) (/ (* z x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.4e+67) {
		tmp = x * (z / y);
	} else if (z <= 2.9e+191) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (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 <= (-7.4d+67)) then
        tmp = x * (z / y)
    else if (z <= 2.9d+191) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (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 <= -7.4e+67) {
		tmp = x * (z / y);
	} else if (z <= 2.9e+191) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.4e+67:
		tmp = x * (z / y)
	elif z <= 2.9e+191:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (z * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.4e+67)
		tmp = Float64(x * Float64(z / y));
	elseif (z <= 2.9e+191)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(z * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.4e+67)
		tmp = x * (z / y);
	elseif (z <= 2.9e+191)
		tmp = t * (1.0 - (x / y));
	else
		tmp = (z * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.4e+67], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+191], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.3999999999999995e67

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 94.0%

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

   4. Taylor expanded in x around -inf 79.3%

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

   5. Taylor expanded in z around inf 74.2%

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

      1. associate-*r/ 77.9%

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

   7. Simplified 77.9%

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

   if -7.3999999999999995e67 < z < 2.9000000000000001e191

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l/ 80.3%

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

      3. neg-mul-1 80.3%

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

      4. *-lft-identity 80.3%

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

      5. distribute-lft-neg-in 80.3%

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

      6. mul-1-neg 80.3%

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

      7. distribute-rgt-in 80.3%

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

      8. mul-1-neg 80.3%

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

      9. unsub-neg 80.3%

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

   5. Simplified 80.3%

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

   if 2.9000000000000001e191 < z

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0 90.6%

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

   4. Taylor expanded in x around -inf 61.1%

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

   5. Taylor expanded in z around inf 61.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+191}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-15} \lor \neg \left(z \leq 7.5 \cdot 10^{-68}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.2e-15) (not (<= z 7.5e-68))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.2e-15) || !(z <= 7.5e-68)) {
		tmp = x * (z / 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 ((z <= (-7.2d-15)) .or. (.not. (z <= 7.5d-68))) then
        tmp = x * (z / 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 ((z <= -7.2e-15) || !(z <= 7.5e-68)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.2e-15) or not (z <= 7.5e-68):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.2e-15) || !(z <= 7.5e-68))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.2e-15) || ~((z <= 7.5e-68)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.2e-15], N[Not[LessEqual[z, 7.5e-68]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000002e-15 or 7.50000000000000081e-68 < z

   1. Initial program 99.3%

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

   3. Taylor expanded in x around 0 93.7%

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

   4. Taylor expanded in x around -inf 70.4%

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

   5. Taylor expanded in z around inf 59.0%

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

      1. associate-*r/ 57.6%

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

   7. Simplified 57.6%

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

   if -7.2000000000000002e-15 < z < 7.50000000000000081e-68

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 50.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-15} \lor \neg \left(z \leq 7.5 \cdot 10^{-68}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.6e-14) (* x (/ z y)) (if (<= z 6.8e-68) t (/ (* z x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.6e-14) {
		tmp = x * (z / y);
	} else if (z <= 6.8e-68) {
		tmp = t;
	} else {
		tmp = (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 <= (-2.6d-14)) then
        tmp = x * (z / y)
    else if (z <= 6.8d-68) then
        tmp = t
    else
        tmp = (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 <= -2.6e-14) {
		tmp = x * (z / y);
	} else if (z <= 6.8e-68) {
		tmp = t;
	} else {
		tmp = (z * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.6e-14:
		tmp = x * (z / y)
	elif z <= 6.8e-68:
		tmp = t
	else:
		tmp = (z * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.6e-14)
		tmp = Float64(x * Float64(z / y));
	elseif (z <= 6.8e-68)
		tmp = t;
	else
		tmp = Float64(Float64(z * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.6e-14)
		tmp = x * (z / y);
	elseif (z <= 6.8e-68)
		tmp = t;
	else
		tmp = (z * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.6e-14], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-68], t, N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999997e-14

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.4%

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

   4. Taylor expanded in x around -inf 74.9%

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

   5. Taylor expanded in z around inf 68.0%

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

      1. associate-*r/ 69.4%

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

   7. Simplified 69.4%

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

   if -2.59999999999999997e-14 < z < 6.80000000000000037e-68

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 50.5%

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

   if 6.80000000000000037e-68 < z

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 92.2%

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

   4. Taylor expanded in x around -inf 66.6%

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

   5. Taylor expanded in z around inf 51.2%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% 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 98.8%

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

3. Final simplification 98.8%

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

Alternative 12: 38.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 t)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t):
	return t

Julia

function code(x, y, z, t)
	return t
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 98.8%

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

3. Taylor expanded in x around 0 37.4%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Developer Target 1: 97.4% accurate, 0.5× 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 2024136 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

  (+ (* (/ x y) (- z t)) t))