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

Percentage Accurate: 97.6% → 97.7%

Time: 7.7s

Alternatives: 14

Speedup: 1.0×

• 24.8% 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: 97.6% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. *-commutative 98.3%

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

   2. clear-num 98.2%

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

   3. un-div-inv 98.5%

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

4. Applied egg-rr 98.5%

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

5. Final simplification 98.5%

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

Alternative 2: 55.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;y \leq -0.00035:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ y x))))
   (if (<= y -0.00035)
     t
     (if (<= y 1.55e-241)
       t_1
       (if (<= y 4.3e-153) (* t (/ x (- y))) (if (<= y 2.5e+27) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if (y <= -0.00035) {
		tmp = t;
	} else if (y <= 1.55e-241) {
		tmp = t_1;
	} else if (y <= 4.3e-153) {
		tmp = t * (x / -y);
	} else if (y <= 2.5e+27) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = z / (y / x)
    if (y <= (-0.00035d0)) then
        tmp = t
    else if (y <= 1.55d-241) then
        tmp = t_1
    else if (y <= 4.3d-153) then
        tmp = t * (x / -y)
    else if (y <= 2.5d+27) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if (y <= -0.00035) {
		tmp = t;
	} else if (y <= 1.55e-241) {
		tmp = t_1;
	} else if (y <= 4.3e-153) {
		tmp = t * (x / -y);
	} else if (y <= 2.5e+27) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (y / x)
	tmp = 0
	if y <= -0.00035:
		tmp = t
	elif y <= 1.55e-241:
		tmp = t_1
	elif y <= 4.3e-153:
		tmp = t * (x / -y)
	elif y <= 2.5e+27:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(y / x))
	tmp = 0.0
	if (y <= -0.00035)
		tmp = t;
	elseif (y <= 1.55e-241)
		tmp = t_1;
	elseif (y <= 4.3e-153)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (y <= 2.5e+27)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (y / x);
	tmp = 0.0;
	if (y <= -0.00035)
		tmp = t;
	elseif (y <= 1.55e-241)
		tmp = t_1;
	elseif (y <= 4.3e-153)
		tmp = t * (x / -y);
	elseif (y <= 2.5e+27)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.00035], t, If[LessEqual[y, 1.55e-241], t$95$1, If[LessEqual[y, 4.3e-153], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+27], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.49999999999999996e-4 or 2.4999999999999999e27 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 67.2%

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

   if -3.49999999999999996e-4 < y < 1.55e-241 or 4.3e-153 < y < 2.4999999999999999e27

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf 73.5%

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

   4. Taylor expanded in z around inf 49.9%

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

      1. *-commutative 60.5%

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

      2. associate-/r/ 73.4%

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

   6. Applied egg-rr 61.5%

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

   if 1.55e-241 < y < 4.3e-153

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 63.7%

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

      1. *-commutative 63.7%

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

      2. sub-div 69.9%

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

      3. associate-*l/ 81.9%

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

   5. Applied egg-rr 81.9%

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

   6. Taylor expanded in z around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. distribute-lft-neg-out 63.7%

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

      3. *-commutative 63.7%

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

   8. Simplified 63.7%

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

   9. Taylor expanded in x around 0 63.7%

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

       1. mul-1-neg 63.7%

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

       2. associate-*r/ 69.8%

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

       3. distribute-rgt-neg-in 69.8%

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

       4. distribute-neg-frac2 69.8%

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

   11. Simplified 69.8%

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

Alternative 3: 95.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-20}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000000000.0) (not (<= (/ x y) 1e-20)))
   (/ (- z t) (/ y x))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000000.0) || !((x / y) <= 1e-20)) {
		tmp = (z - t) / (y / x);
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-100000000000.0d0)) .or. (.not. ((x / y) <= 1d-20))) then
        tmp = (z - t) / (y / x)
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000000.0) || !((x / y) <= 1e-20)) {
		tmp = (z - t) / (y / x);
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -100000000000.0) or not ((x / y) <= 1e-20):
		tmp = (z - t) / (y / x)
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -100000000000.0) || !(Float64(x / y) <= 1e-20))
		tmp = Float64(Float64(z - t) / Float64(y / x));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -100000000000.0) || ~(((x / y) <= 1e-20)))
		tmp = (z - t) / (y / x);
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -100000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-20]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e11 or 9.99999999999999945e-21 < (/.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 89.2%

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

      1. *-commutative 89.2%

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

      2. sub-div 91.7%

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

      3. associate-/r/ 96.2%

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

   5. Applied egg-rr 96.2%

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

   if -1e11 < (/.f64 x y) < 9.99999999999999945e-21

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 95.1%

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

      1. associate-/l* 90.6%

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

   5. Simplified 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/r/ 98.4%

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

   7. Applied egg-rr 98.4%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-20}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.04 \lor \neg \left(\frac{x}{y} \leq 10^{+52}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.04) (not (<= (/ x y) 1e+52)))
   (* x (/ (- z t) y))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.04) || !((x / y) <= 1e+52)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-0.04d0)) .or. (.not. ((x / y) <= 1d+52))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.04) || !((x / y) <= 1e+52)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.04) or not ((x / y) <= 1e+52):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -0.04) || !(Float64(x / y) <= 1e+52))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -0.04) || ~(((x / y) <= 1e+52)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -0.04], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+52]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.0400000000000000008 or 9.9999999999999999e51 < (/.f64 x y)

   1. Initial program 96.5%

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

   3. Taylor expanded in x around inf 91.0%

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

   4. Taylor expanded in y around 0 93.6%

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

   if -0.0400000000000000008 < (/.f64 x y) < 9.9999999999999999e51

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 93.6%

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

      1. associate-/l* 88.1%

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

   5. Simplified 88.1%

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

      1. *-commutative 88.1%

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

      2. associate-/r/ 96.7%

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

   7. Applied egg-rr 96.7%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.04 \lor \neg \left(\frac{x}{y} \leq 10^{+52}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000000000.0) (not (<= (/ x y) 1e-20)))
   (* x (/ (- z t) y))
   (+ t (/ x (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000000.0) || !((x / y) <= 1e-20)) {
		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) <= (-100000000000.0d0)) .or. (.not. ((x / y) <= 1d-20))) 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) <= -100000000000.0) || !((x / y) <= 1e-20)) {
		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) <= -100000000000.0) or not ((x / y) <= 1e-20):
		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) <= -100000000000.0) || !(Float64(x / y) <= 1e-20))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -100000000000.0) || ~(((x / y) <= 1e-20)))
		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], -100000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-20]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e11 or 9.99999999999999945e-21 < (/.f64 x y)

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 89.2%

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

   4. Taylor expanded in y around 0 91.7%

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

   if -1e11 < (/.f64 x y) < 9.99999999999999945e-21

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 95.1%

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

      1. associate-/l* 90.6%

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

   5. Simplified 90.6%

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

      1. clear-num 90.6%

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

      2. un-div-inv 91.0%

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

   7. Applied egg-rr 91.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 10^{-20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 1000\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000000000.0) (not (<= (/ x y) 1000.0)))
   (* x (/ (- z t) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000000.0) || !((x / y) <= 1000.0)) {
		tmp = 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 / y) <= (-100000000000.0d0)) .or. (.not. ((x / y) <= 1000.0d0))) then
        tmp = 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 / y) <= -100000000000.0) || !((x / y) <= 1000.0)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -100000000000.0) or not ((x / y) <= 1000.0):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -100000000000.0) || !(Float64(x / y) <= 1000.0))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -100000000000.0) || ~(((x / y) <= 1000.0)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -100000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1000.0]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e11 or 1e3 < (/.f64 x y)

   1. Initial program 96.6%

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

   3. Taylor expanded in x around inf 89.8%

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

   4. Taylor expanded in y around 0 92.3%

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

   if -1e11 < (/.f64 x y) < 1e3

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 94.5%

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

      1. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 1000\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-48} \lor \neg \left(\frac{x}{y} \leq 10^{-20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e-48) (not (<= (/ x y) 1e-20)))
   (* x (/ (- z t) y))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e-48) || !((x / y) <= 1e-20)) {
		tmp = x * ((z - t) / 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 (((x / y) <= (-4d-48)) .or. (.not. ((x / y) <= 1d-20))) then
        tmp = x * ((z - t) / 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 (((x / y) <= -4e-48) || !((x / y) <= 1e-20)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e-48) or not ((x / y) <= 1e-20):
		tmp = x * ((z - t) / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e-48) || !(Float64(x / y) <= 1e-20))
		tmp = Float64(x * Float64(Float64(z - t) / 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 (((x / y) <= -4e-48) || ~(((x / y) <= 1e-20)))
		tmp = x * ((z - t) / y);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e-48], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-20]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.9999999999999999e-48 or 9.99999999999999945e-21 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around inf 85.5%

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

   4. Taylor expanded in y around 0 87.7%

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

   if -3.9999999999999999e-48 < (/.f64 x y) < 9.99999999999999945e-21

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. unsub-neg 70.7%

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

      3. *-rgt-identity 70.7%

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

      4. associate-/l* 77.1%

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

      5. distribute-lft-out-- 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-48} \lor \neg \left(\frac{x}{y} \leq 10^{-20}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.04:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-20}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -0.04)
   (* x (/ (- z t) y))
   (if (<= (/ x y) 1e-20) (+ t (/ z (/ y x))) (/ (* (- z t) x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.04) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 1e-20) {
		tmp = t + (z / (y / x));
	} else {
		tmp = ((z - 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 ((x / y) <= (-0.04d0)) then
        tmp = x * ((z - t) / y)
    else if ((x / y) <= 1d-20) then
        tmp = t + (z / (y / x))
    else
        tmp = ((z - 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 ((x / y) <= -0.04) {
		tmp = x * ((z - t) / y);
	} else if ((x / y) <= 1e-20) {
		tmp = t + (z / (y / x));
	} else {
		tmp = ((z - t) * x) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -0.04:
		tmp = x * ((z - t) / y)
	elif (x / y) <= 1e-20:
		tmp = t + (z / (y / x))
	else:
		tmp = ((z - t) * x) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -0.04)
		tmp = Float64(x * Float64(Float64(z - t) / y));
	elseif (Float64(x / y) <= 1e-20)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(Float64(Float64(z - t) * x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -0.04)
		tmp = x * ((z - t) / y);
	elseif ((x / y) <= 1e-20)
		tmp = t + (z / (y / x));
	else
		tmp = ((z - t) * x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -0.04], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-20], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.0400000000000000008

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 91.8%

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

   4. Taylor expanded in y around 0 93.7%

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

   if -0.0400000000000000008 < (/.f64 x y) < 9.99999999999999945e-21

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 95.1%

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

      1. associate-/l* 90.5%

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

   5. Simplified 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-/r/ 98.4%

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

   7. Applied egg-rr 98.4%

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

   if 9.99999999999999945e-21 < (/.f64 x y)

   1. Initial program 98.3%

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

   3. Taylor expanded in x around inf 87.4%

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

      1. *-commutative 87.4%

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

      2. sub-div 90.2%

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

      3. associate-*l/ 95.9%

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

   5. Applied egg-rr 95.9%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.04:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-20}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-149} \lor \neg \left(t \leq 1.55 \cdot 10^{-137}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.55e-149) (not (<= t 1.55e-137)))
   (* t (- 1.0 (/ x y)))
   (/ z (/ y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e-149) || !(t <= 1.55e-137)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.55d-149)) .or. (.not. (t <= 1.55d-137))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e-149) || !(t <= 1.55e-137)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.55e-149) or not (t <= 1.55e-137):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.55e-149) || !(t <= 1.55e-137))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.55e-149) || ~((t <= 1.55e-137)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.55e-149], N[Not[LessEqual[t, 1.55e-137]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.54999999999999994e-149 or 1.54999999999999989e-137 < t

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. *-rgt-identity 74.1%

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

      4. associate-/l* 80.4%

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

      5. distribute-lft-out-- 80.4%

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

   5. Simplified 80.4%

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

   if -1.54999999999999994e-149 < t < 1.54999999999999989e-137

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 72.8%

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

   4. Taylor expanded in z around inf 67.4%

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

      1. *-commutative 83.8%

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

      2. associate-/r/ 93.6%

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

   6. Applied egg-rr 77.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-149} \lor \neg \left(t \leq 1.55 \cdot 10^{-137}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{-8}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+29}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.7e-8) t (if (<= y 3.6e+29) (/ z (/ y x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.7e-8) {
		tmp = t;
	} else if (y <= 3.6e+29) {
		tmp = z / (y / x);
	} 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 <= (-5.7d-8)) then
        tmp = t
    else if (y <= 3.6d+29) then
        tmp = z / (y / x)
    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 <= -5.7e-8) {
		tmp = t;
	} else if (y <= 3.6e+29) {
		tmp = z / (y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.7e-8:
		tmp = t
	elif y <= 3.6e+29:
		tmp = z / (y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.7e-8)
		tmp = t;
	elseif (y <= 3.6e+29)
		tmp = Float64(z / Float64(y / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.7e-8)
		tmp = t;
	elseif (y <= 3.6e+29)
		tmp = z / (y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.7e-8], t, If[LessEqual[y, 3.6e+29], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.70000000000000009e-8 or 3.59999999999999976e29 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 67.2%

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

   if -5.70000000000000009e-8 < y < 3.59999999999999976e29

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 72.3%

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

   4. Taylor expanded in z around inf 47.2%

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

      1. *-commutative 57.8%

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

      2. associate-/r/ 71.1%

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

   6. Applied egg-rr 58.8%

      \[\leadsto \color{blue}{\frac{z}{\frac{y}{x}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00033:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.00033) t (if (<= y 5.6e+27) (/ x (/ y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.00033) {
		tmp = t;
	} else if (y <= 5.6e+27) {
		tmp = x / (y / z);
	} 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 <= (-0.00033d0)) then
        tmp = t
    else if (y <= 5.6d+27) then
        tmp = x / (y / z)
    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 <= -0.00033) {
		tmp = t;
	} else if (y <= 5.6e+27) {
		tmp = x / (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.00033:
		tmp = t
	elif y <= 5.6e+27:
		tmp = x / (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.00033)
		tmp = t;
	elseif (y <= 5.6e+27)
		tmp = Float64(x / Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.00033)
		tmp = t;
	elseif (y <= 5.6e+27)
		tmp = x / (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.00033], t, If[LessEqual[y, 5.6e+27], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e-4 or 5.5999999999999999e27 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 67.2%

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

   if -3.3e-4 < y < 5.5999999999999999e27

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 72.3%

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

   4. Taylor expanded in z around inf 47.2%

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

      1. clear-num 57.7%

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

      2. un-div-inv 58.1%

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

   6. Applied egg-rr 47.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{z}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-11}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{+30}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e-11) t (if (<= y 1.92e+30) (* x (/ z y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e-11) {
		tmp = t;
	} else if (y <= 1.92e+30) {
		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 (y <= (-2.05d-11)) then
        tmp = t
    else if (y <= 1.92d+30) 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 (y <= -2.05e-11) {
		tmp = t;
	} else if (y <= 1.92e+30) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.05e-11:
		tmp = t
	elif y <= 1.92e+30:
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e-11)
		tmp = t;
	elseif (y <= 1.92e+30)
		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 (y <= -2.05e-11)
		tmp = t;
	elseif (y <= 1.92e+30)
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e-11], t, If[LessEqual[y, 1.92e+30], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e-11 or 1.9200000000000001e30 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 67.2%

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

   if -2.05e-11 < y < 1.9200000000000001e30

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf 72.3%

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

   4. Taylor expanded in z around inf 47.2%

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

Alternative 13: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 14: 38.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around 0 39.1%

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

Developer target: 97.1% 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 2024091 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (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))