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

Percentage Accurate: 97.6% → 97.6%

Time: 8.7s

Alternatives: 12

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% 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: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Taylor expanded in x around 0 93.1%

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

   1. associate-*r/ 93.2%

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

   2. *-commutative 93.2%

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

   3. associate-/r/ 98.5%

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

5. Simplified 98.5%

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

6. Final simplification 98.5%

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

Alternative 2: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+62} \lor \neg \left(t \leq 7.2 \cdot 10^{+50}\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.2e+62) (not (<= t 7.2e+50)))
   (- t (/ t (/ y x)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+62) || !(t <= 7.2e+50)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.2d+62)) .or. (.not. (t <= 7.2d+50))) then
        tmp = t - (t / (y / x))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+62) || !(t <= 7.2e+50)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.2e+62) or not (t <= 7.2e+50):
		tmp = t - (t / (y / x))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.2e+62) || !(t <= 7.2e+50))
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.2e+62) || ~((t <= 7.2e+50)))
		tmp = t - (t / (y / x));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.2e+62], N[Not[LessEqual[t, 7.2e+50]], $MachinePrecision]], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e62 or 7.19999999999999972e50 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.2%

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

      1. associate-*r/ 91.4%

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

      2. *-commutative 91.4%

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

      3. associate-/r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. associate-*r/ 94.6%

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

      3. sub-neg 94.6%

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

   8. Simplified 94.6%

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

      1. clear-num 94.6%

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

      2. div-inv 94.6%

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

   10. Applied egg-rr 94.6%

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

   if -1.2e62 < t < 7.19999999999999972e50

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/r/ 85.7%

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

   7. Applied egg-rr 85.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+62} \lor \neg \left(t \leq 7.2 \cdot 10^{+50}\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+62} \lor \neg \left(t \leq 6.8 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.4e+62) (not (<= t 6.8e+50)))
   (* t (- 1.0 (/ x y)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.4e+62) || !(t <= 6.8e+50)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-5.4d+62)) .or. (.not. (t <= 6.8d+50))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.4e+62) || !(t <= 6.8e+50)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.4e+62) or not (t <= 6.8e+50):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.4e+62) || !(t <= 6.8e+50))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.4e+62) || ~((t <= 6.8e+50)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.4e+62], N[Not[LessEqual[t, 6.8e+50]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4e62 or 6.7999999999999997e50 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. *-rgt-identity 85.8%

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

      3. associate-/l* 94.6%

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

      4. distribute-rgt-neg-in 94.6%

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

      5. mul-1-neg 94.6%

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

      6. distribute-lft-in 94.6%

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

      7. mul-1-neg 94.6%

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

      8. unsub-neg 94.6%

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

   5. Simplified 94.6%

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

   if -5.4e62 < t < 6.7999999999999997e50

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/r/ 85.7%

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

   7. Applied egg-rr 85.7%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+62} \lor \neg \left(t \leq 6.8 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+62} \lor \neg \left(t \leq 5.4 \cdot 10^{+51}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.8e+62) (not (<= t 5.4e+51)))
   (* t (- 1.0 (/ x y)))
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.8e+62) || !(t <= 5.4e+51)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.8d+62)) .or. (.not. (t <= 5.4d+51))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.8e+62) || !(t <= 5.4e+51)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.8e+62) or not (t <= 5.4e+51):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.8e+62) || !(t <= 5.4e+51))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.8e+62) || ~((t <= 5.4e+51)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.8e+62], N[Not[LessEqual[t, 5.4e+51]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e62 or 5.39999999999999983e51 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. *-rgt-identity 85.8%

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

      3. associate-/l* 94.6%

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

      4. distribute-rgt-neg-in 94.6%

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

      5. mul-1-neg 94.6%

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

      6. distribute-lft-in 94.6%

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

      7. mul-1-neg 94.6%

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

      8. unsub-neg 94.6%

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

   5. Simplified 94.6%

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

   if -1.8e62 < t < 5.39999999999999983e51

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 84.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+62} \lor \neg \left(t \leq 5.4 \cdot 10^{+51}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+62} \lor \neg \left(t \leq 5.8 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.1e+62) (not (<= t 5.8e+50)))
   (* t (- 1.0 (/ x y)))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.1e+62) || !(t <= 5.8e+50)) {
		tmp = t * (1.0 - (x / 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 ((t <= (-1.1d+62)) .or. (.not. (t <= 5.8d+50))) then
        tmp = t * (1.0d0 - (x / 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 ((t <= -1.1e+62) || !(t <= 5.8e+50)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.1e+62) or not (t <= 5.8e+50):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.1e+62) || !(t <= 5.8e+50))
		tmp = Float64(t * Float64(1.0 - Float64(x / 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 ((t <= -1.1e+62) || ~((t <= 5.8e+50)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.1e+62], N[Not[LessEqual[t, 5.8e+50]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.10000000000000007e62 or 5.8e50 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. *-rgt-identity 85.8%

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

      3. associate-/l* 94.6%

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

      4. distribute-rgt-neg-in 94.6%

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

      5. mul-1-neg 94.6%

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

      6. distribute-lft-in 94.6%

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

      7. mul-1-neg 94.6%

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

      8. unsub-neg 94.6%

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

   5. Simplified 94.6%

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

   if -1.10000000000000007e62 < t < 5.8e50

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+62} \lor \neg \left(t \leq 5.8 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+62}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.6e+62)
   (- t (* t (/ x y)))
   (if (<= t 1.45e+52) (+ t (/ z (/ y x))) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.6e+62) {
		tmp = t - (t * (x / y));
	} else if (t <= 1.45e+52) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8.6d+62)) then
        tmp = t - (t * (x / y))
    else if (t <= 1.45d+52) then
        tmp = t + (z / (y / x))
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.6e+62) {
		tmp = t - (t * (x / y));
	} else if (t <= 1.45e+52) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.6e+62:
		tmp = t - (t * (x / y))
	elif t <= 1.45e+52:
		tmp = t + (z / (y / x))
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.6e+62)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (t <= 1.45e+52)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.6e+62)
		tmp = t - (t * (x / y));
	elseif (t <= 1.45e+52)
		tmp = t + (z / (y / x));
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.6e+62], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+52], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.5999999999999994e62

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.9%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-/r/ 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 92.7%

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

      1. mul-1-neg 92.7%

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

      2. associate-*r/ 99.9%

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

      3. sub-neg 99.9%

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

   8. Simplified 99.9%

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

   if -8.5999999999999994e62 < t < 1.45e52

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 83.5%

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

   5. Simplified 83.5%

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

      1. *-commutative 83.5%

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

      2. associate-/r/ 85.7%

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

   7. Applied egg-rr 85.7%

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

   if 1.45e52 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. *-rgt-identity 79.1%

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

      3. associate-/l* 89.4%

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

      4. distribute-rgt-neg-in 89.4%

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

      5. mul-1-neg 89.4%

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

      6. distribute-lft-in 89.4%

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

      7. mul-1-neg 89.4%

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

      8. unsub-neg 89.4%

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

   5. Simplified 89.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+62}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+52}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+41}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.4e+15) t (if (<= y 9e+41) (/ (- t) (/ y x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e+15) {
		tmp = t;
	} else if (y <= 9e+41) {
		tmp = -t / (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 <= (-5.4d+15)) then
        tmp = t
    else if (y <= 9d+41) then
        tmp = -t / (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 <= -5.4e+15) {
		tmp = t;
	} else if (y <= 9e+41) {
		tmp = -t / (y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.4e+15:
		tmp = t
	elif y <= 9e+41:
		tmp = -t / (y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.4e+15)
		tmp = t;
	elseif (y <= 9e+41)
		tmp = Float64(Float64(-t) / Float64(y / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.4e+15)
		tmp = t;
	elseif (y <= 9e+41)
		tmp = -t / (y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.4e+15], t, If[LessEqual[y, 9e+41], N[((-t) / N[(y / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4e15 or 9.0000000000000002e41 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 64.8%

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

   if -5.4e15 < y < 9.0000000000000002e41

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 97.7%

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

      1. associate-*r/ 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-/r/ 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. associate-*r/ 59.5%

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

      3. sub-neg 59.5%

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

   8. Simplified 59.5%

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

   9. Taylor expanded in x around inf 48.8%

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

       1. associate-*l/ 46.1%

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

       2. associate-*r* 46.1%

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

       3. neg-mul-1 46.1%

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

       4. *-commutative 46.1%

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

       5. distribute-neg-frac2 46.1%

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

   11. Simplified 46.1%

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

       1. *-commutative 46.1%

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

       2. distribute-frac-neg2 46.1%

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

       3. distribute-lft-neg-in 46.1%

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

       4. associate-/r/ 48.8%

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

       5. distribute-neg-frac 48.8%

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

   13. Applied egg-rr 48.8%

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

Alternative 8: 49.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{\frac{y}{-t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.7e+15) t (if (<= y 1.85e+40) (/ x (/ y (- t))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.7e+15) {
		tmp = t;
	} else if (y <= 1.85e+40) {
		tmp = x / (y / -t);
	} 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 <= (-3.7d+15)) then
        tmp = t
    else if (y <= 1.85d+40) then
        tmp = x / (y / -t)
    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 <= -3.7e+15) {
		tmp = t;
	} else if (y <= 1.85e+40) {
		tmp = x / (y / -t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.7e+15:
		tmp = t
	elif y <= 1.85e+40:
		tmp = x / (y / -t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.7e+15)
		tmp = t;
	elseif (y <= 1.85e+40)
		tmp = Float64(x / Float64(y / Float64(-t)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.7e+15)
		tmp = t;
	elseif (y <= 1.85e+40)
		tmp = x / (y / -t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.7e+15], t, If[LessEqual[y, 1.85e+40], N[(x / N[(y / (-t)), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e15 or 1.85e40 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 64.8%

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

   if -3.7e15 < y < 1.85e40

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 97.7%

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

      1. associate-*r/ 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-/r/ 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. associate-*r/ 59.5%

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

      3. sub-neg 59.5%

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

   8. Simplified 59.5%

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

   9. Taylor expanded in x around inf 48.8%

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

       1. mul-1-neg 48.8%

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

       2. associate-*r/ 48.8%

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

       3. *-commutative 48.8%

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

       4. associate-/r/ 46.3%

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

       5. distribute-neg-frac2 46.3%

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

   11. Simplified 46.3%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{\frac{y}{-t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.52e+16) t (if (<= y 2.3e+44) (* x (/ t (- y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e+16) {
		tmp = t;
	} else if (y <= 2.3e+44) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.52d+16)) then
        tmp = t
    else if (y <= 2.3d+44) then
        tmp = x * (t / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e+16) {
		tmp = t;
	} else if (y <= 2.3e+44) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.52e+16:
		tmp = t
	elif y <= 2.3e+44:
		tmp = x * (t / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.52e+16)
		tmp = t;
	elseif (y <= 2.3e+44)
		tmp = Float64(x * Float64(t / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.52e+16)
		tmp = t;
	elseif (y <= 2.3e+44)
		tmp = x * (t / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.52e+16], t, If[LessEqual[y, 2.3e+44], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.52e16 or 2.30000000000000004e44 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 64.8%

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

   if -1.52e16 < y < 2.30000000000000004e44

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 97.7%

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

      1. associate-*r/ 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-/r/ 97.5%

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

   5. Simplified 97.5%

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

   6. Taylor expanded in z around 0 59.5%

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

      1. mul-1-neg 59.5%

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

      2. associate-*r/ 59.5%

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

      3. sub-neg 59.5%

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

   8. Simplified 59.5%

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

   9. Taylor expanded in x around inf 48.8%

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

       1. associate-*l/ 46.1%

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

       2. associate-*r* 46.1%

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

       3. neg-mul-1 46.1%

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

       4. *-commutative 46.1%

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

       5. distribute-neg-frac2 46.1%

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

   11. Simplified 46.1%

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

Alternative 10: 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 97.9%

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

3. Final simplification 97.9%

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

Alternative 11: 65.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ t \cdot \left(1 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* t (- 1.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * (1.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (1.0 - (x / y));
}

Python

def code(x, y, z, t):
	return t * (1.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(t * Float64(1.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t * (1.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.9%

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

3. Taylor expanded in z around 0 62.7%

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

   1. mul-1-neg 62.7%

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

   2. *-rgt-identity 62.7%

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

   3. associate-/l* 66.5%

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

   4. distribute-rgt-neg-in 66.5%

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

   5. mul-1-neg 66.5%

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

   6. distribute-lft-in 66.5%

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

   7. mul-1-neg 66.5%

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

   8. unsub-neg 66.5%

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

5. Simplified 66.5%

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

Alternative 12: 38.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Taylor expanded in x around 0 36.8%

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

Developer Target 1: 97.3% 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 2024135 
(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))