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

Percentage Accurate: 97.6% → 97.7%

Time: 8.8s

Alternatives: 11

Speedup: 1.0×

• 24.1% 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 98.7%

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

   3. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

   6. --lowering--.f64 93.5%

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

3. Simplified 93.5%

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

   1. associate-*l/ N/A

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

   2. +-commutative N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y} \cdot \left(z - t\right)\right), \color{blue}{t}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{x}{y}\right), t\right) \]

   5. clear-num N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{y}{x}}\right), t\right) \]

   6. un-div-inv N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{y}{x}}\right), t\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{y}{x}\right)\right), t\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{y}{x}\right)\right), t\right) \]

   9. /-lowering-/.f64 98.8%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, x\right)\right), t\right) \]

6. Applied egg-rr 98.8%

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

7. Final simplification 98.8%

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

Alternative 2: 95.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.02:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -0.02)
   (* (- z t) (/ x y))
   (if (<= (/ x y) 0.005) (+ t (/ z (/ y x))) (/ x (/ y (- z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.02) {
		tmp = (z - t) * (x / y);
	} else if ((x / y) <= 0.005) {
		tmp = t + (z / (y / x));
	} else {
		tmp = x / (y / (z - 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 ((x / y) <= (-0.02d0)) then
        tmp = (z - t) * (x / y)
    else if ((x / y) <= 0.005d0) then
        tmp = t + (z / (y / x))
    else
        tmp = x / (y / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -0.02) {
		tmp = (z - t) * (x / y);
	} else if ((x / y) <= 0.005) {
		tmp = t + (z / (y / x));
	} else {
		tmp = x / (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -0.02:
		tmp = (z - t) * (x / y)
	elif (x / y) <= 0.005:
		tmp = t + (z / (y / x))
	else:
		tmp = x / (y / (z - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -0.02)
		tmp = Float64(Float64(z - t) * Float64(x / y));
	elseif (Float64(x / y) <= 0.005)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(x / Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -0.02)
		tmp = (z - t) * (x / y);
	elseif ((x / y) <= 0.005)
		tmp = t + (z / (y / x));
	else
		tmp = x / (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -0.02], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.005], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.0200000000000000004

   1. Initial program 99.8%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.1%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 93.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 93.0%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(z - t\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 96.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 96.9%

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

   if -0.0200000000000000004 < (/.f64 x y) < 0.0050000000000000001

   1. Initial program 99.2%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.1%

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

      1. associate-*l/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y} \cdot \left(z - t\right)\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{x}{y}\right), t\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{y}{x}}\right), t\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{y}{x}}\right), t\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{y}{x}\right)\right), t\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{y}{x}\right)\right), t\right) \]

      9. /-lowering-/.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, x\right)\right), t\right) \]

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(y, x\right)\right), t\right) \]
   8. Step-by-step derivation

   9. Simplified 97.9%

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

   if 0.0050000000000000001 < (/.f64 x y)

   1. Initial program 96.4%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 87.8%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 87.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 87.4%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{y}{z - t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(z - t\right)}\right)\right) \]

      5. --lowering--.f64 96.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right)\right) \]

   9. Applied egg-rr 96.5%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.02:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -0.02:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ x y))))
   (if (<= (/ x y) -0.02)
     t_1
     (if (<= (/ x y) 0.005) (+ t (/ z (/ y x))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -0.02) {
		tmp = t_1;
	} else if ((x / y) <= 0.005) {
		tmp = t + (z / (y / x));
	} 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 = (z - t) * (x / y)
    if ((x / y) <= (-0.02d0)) then
        tmp = t_1
    else if ((x / y) <= 0.005d0) then
        tmp = t + (z / (y / x))
    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 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -0.02) {
		tmp = t_1;
	} else if ((x / y) <= 0.005) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z - t) * (x / y)
	tmp = 0
	if (x / y) <= -0.02:
		tmp = t_1
	elif (x / y) <= 0.005:
		tmp = t + (z / (y / x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z - t) * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -0.02)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.005)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z - t) * (x / y);
	tmp = 0.0;
	if ((x / y) <= -0.02)
		tmp = t_1;
	elseif ((x / y) <= 0.005)
		tmp = t + (z / (y / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.02], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.005], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -0.0200000000000000004 or 0.0050000000000000001 < (/.f64 x y)

   1. Initial program 98.2%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 91.6%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 91.6%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 90.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 90.4%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(z - t\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 96.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 96.0%

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

   if -0.0200000000000000004 < (/.f64 x y) < 0.0050000000000000001

   1. Initial program 99.2%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 95.1%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 95.1%

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

      1. associate-*l/ N/A

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

      2. +-commutative N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{x}{y} \cdot \left(z - t\right)\right), \color{blue}{t}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{x}{y}\right), t\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z - t\right) \cdot \frac{1}{\frac{y}{x}}\right), t\right) \]

      6. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{z - t}{\frac{y}{x}}\right), t\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\left(z - t\right), \left(\frac{y}{x}\right)\right), t\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \left(\frac{y}{x}\right)\right), t\right) \]

      9. /-lowering-/.f64 99.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(z, t\right), \mathsf{/.f64}\left(y, x\right)\right), t\right) \]

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{/.f64}\left(\color{blue}{z}, \mathsf{/.f64}\left(y, x\right)\right), t\right) \]
   8. Step-by-step derivation

   9. Simplified 97.9%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.02:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ x y))))
   (if (<= (/ x y) -200.0)
     t_1
     (if (<= (/ x y) 0.005) (+ t (* z (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -200.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.005) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (x / y)
    if ((x / y) <= (-200.0d0)) then
        tmp = t_1
    else if ((x / y) <= 0.005d0) then
        tmp = t + (z * (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -200.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.005) {
		tmp = t + (z * (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z - t) * (x / y)
	tmp = 0
	if (x / y) <= -200.0:
		tmp = t_1
	elif (x / y) <= 0.005:
		tmp = t + (z * (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z - t) * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -200.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.005)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z - t) * (x / y);
	tmp = 0.0;
	if ((x / y) <= -200.0)
		tmp = t_1;
	elseif ((x / y) <= 0.005)
		tmp = t + (z * (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -200.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.005], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -200 or 0.0050000000000000001 < (/.f64 x y)

   1. Initial program 98.2%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.4%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 91.1%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 91.1%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(z - t\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 96.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 96.0%

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

   if -200 < (/.f64 x y) < 0.0050000000000000001

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 97.8%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.005:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 50000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ x y))))
   (if (<= (/ x y) -5e-83)
     t_1
     (if (<= (/ x y) 50000000.0) (* t (- 1.0 (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -5e-83) {
		tmp = t_1;
	} else if ((x / y) <= 50000000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (x / y)
    if ((x / y) <= (-5d-83)) then
        tmp = t_1
    else if ((x / y) <= 50000000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z - t) * (x / y);
	double tmp;
	if ((x / y) <= -5e-83) {
		tmp = t_1;
	} else if ((x / y) <= 50000000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z - t) * (x / y)
	tmp = 0
	if (x / y) <= -5e-83:
		tmp = t_1
	elif (x / y) <= 50000000.0:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z - t) * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e-83)
		tmp = t_1;
	elseif (Float64(x / y) <= 50000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z - t) * (x / y);
	tmp = 0.0;
	if ((x / y) <= -5e-83)
		tmp = t_1;
	elseif ((x / y) <= 50000000.0)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-83], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 50000000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e-83 or 5e7 < (/.f64 x y)

   1. Initial program 98.4%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 91.0%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 91.0%

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

   5. Taylor expanded in x around inf

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

      1. div-sub N/A

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

      2. associate-/l* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right) \]

      5. --lowering--.f64 86.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right) \]

   7. Simplified 86.3%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(z - t\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{z} - t\right)\right) \]

      4. --lowering--.f64 92.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{\_.f64}\left(z, \color{blue}{t}\right)\right) \]

   9. Applied egg-rr 92.6%

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

   if -5e-83 < (/.f64 x y) < 5e7

   1. Initial program 99.1%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 96.1%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 96.1%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 81.0%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 81.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-83}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 50000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-73)
   (* z (/ x y))
   (if (<= (/ x y) 5e-45) t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-73) {
		tmp = z * (x / y);
	} else if ((x / y) <= 5e-45) {
		tmp = t;
	} 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 ((x / y) <= (-5d-73)) then
        tmp = z * (x / y)
    else if ((x / y) <= 5d-45) then
        tmp = t
    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 ((x / y) <= -5e-73) {
		tmp = z * (x / y);
	} else if ((x / y) <= 5e-45) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-73:
		tmp = z * (x / y)
	elif (x / y) <= 5e-45:
		tmp = t
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-73)
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= 5e-45)
		tmp = t;
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-73)
		tmp = z * (x / y);
	elseif ((x / y) <= 5e-45)
		tmp = t;
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-73], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-45], t, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999998e-73

   1. Initial program 99.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.1%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.1%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 49.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 49.2%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 50.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right) \]

   9. Applied egg-rr 50.5%

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

   if -4.9999999999999998e-73 < (/.f64 x y) < 4.99999999999999976e-45

   1. Initial program 99.1%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 97.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 97.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   6. Step-by-step derivation

   7. Simplified 82.8%

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

   if 4.99999999999999976e-45 < (/.f64 x y)

   1. Initial program 97.0%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 88.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 88.3%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 43.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 43.9%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/r/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      5. /-lowering-/.f64 48.3%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 48.3%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -5e-73) t_1 (if (<= (/ x y) 5e-45) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -5e-73) {
		tmp = t_1;
	} else if ((x / y) <= 5e-45) {
		tmp = 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 = z * (x / y)
    if ((x / y) <= (-5d-73)) then
        tmp = t_1
    else if ((x / y) <= 5d-45) then
        tmp = 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 = z * (x / y);
	double tmp;
	if ((x / y) <= -5e-73) {
		tmp = t_1;
	} else if ((x / y) <= 5e-45) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -5e-73:
		tmp = t_1
	elif (x / y) <= 5e-45:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -5e-73)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-45)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -5e-73)
		tmp = t_1;
	elseif ((x / y) <= 5e-45)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-73], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-45], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999998e-73 or 4.99999999999999976e-45 < (/.f64 x y)

   1. Initial program 98.5%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 90.3%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 90.3%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 46.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 46.7%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 49.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), z\right) \]

   9. Applied egg-rr 49.4%

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

   if -4.9999999999999998e-73 < (/.f64 x y) < 4.99999999999999976e-45

   1. Initial program 99.1%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 97.4%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 97.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t} \]
   6. Step-by-step derivation

   7. Simplified 82.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-45}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+148}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+92}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1e+148)
   (/ (* z x) y)
   (if (<= z 4.3e+92) (* t (- 1.0 (/ x y))) (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1e+148) {
		tmp = (z * x) / y;
	} else if (z <= 4.3e+92) {
		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 (z <= (-1d+148)) then
        tmp = (z * x) / y
    else if (z <= 4.3d+92) 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 (z <= -1e+148) {
		tmp = (z * x) / y;
	} else if (z <= 4.3e+92) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1e+148:
		tmp = (z * x) / y
	elif z <= 4.3e+92:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1e+148)
		tmp = Float64(Float64(z * x) / y);
	elseif (z <= 4.3e+92)
		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 (z <= -1e+148)
		tmp = (z * x) / y;
	elseif (z <= 4.3e+92)
		tmp = t * (1.0 - (x / y));
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1e+148], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 4.3e+92], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e148

   1. Initial program 96.4%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 79.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 79.8%

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

   if -1e148 < z < 4.2999999999999998e92

   1. Initial program 98.9%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.7%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.7%

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

   5. Taylor expanded in t around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \color{blue}{\left(1 + -1 \cdot \frac{x}{y}\right)}\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(t, \left(1 - \color{blue}{\frac{x}{y}}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right) \]

      5. /-lowering-/.f64 82.5%

         \[\leadsto \mathsf{*.f64}\left(t, \mathsf{\_.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right) \]

   7. Simplified 82.5%

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

   if 4.2999999999999998e92 < z

   1. Initial program 99.7%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 92.7%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 92.7%

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

   5. Taylor expanded in t around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot z\right), \color{blue}{y}\right) \]

      2. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, z\right), y\right) \]

   7. Simplified 72.5%

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-/r/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{\left(\frac{y}{x}\right)}\right) \]

      5. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{/.f64}\left(z, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right) \]

   9. Applied egg-rr 77.2%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+148}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+92}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+153}:\\ \;\;\;\;t + \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.85e+153) (+ t (/ (* (- z t) x) y)) (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.85e+153) {
		tmp = t + (((z - t) * x) / y);
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 1.85d+153) then
        tmp = t + (((z - t) * x) / y)
    else
        tmp = t + (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.85e+153) {
		tmp = t + (((z - t) * x) / y);
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.85e+153:
		tmp = t + (((z - t) * x) / y)
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.85e+153)
		tmp = Float64(t + Float64(Float64(Float64(z - t) * x) / y));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.85e+153)
		tmp = t + (((z - t) * x) / y);
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.85e+153], N[(t + N[(N[(N[(z - t), $MachinePrecision] * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.8500000000000001e153

   1. Initial program 98.6%

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

      3. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

      6. --lowering--.f64 96.8%

         \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

   3. Simplified 96.8%

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

   if 1.8500000000000001e153 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{z}\right), t\right) \]
   4. Step-by-step derivation

   5. Simplified 92.4%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.85 \cdot 10^{+153}:\\ \;\;\;\;t + \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. 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 98.7%

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

3. Final simplification 98.7%

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

Alternative 11: 38.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

   1. +-commutative N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \color{blue}{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}\right) \]

   3. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(t, \left(\frac{x \cdot \left(z - t\right)}{\color{blue}{y}}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\left(x \cdot \left(z - t\right)\right), \color{blue}{y}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(z - t\right)\right), y\right)\right) \]

   6. --lowering--.f64 93.5%

      \[\leadsto \mathsf{+.f64}\left(t, \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), y\right)\right) \]

3. Simplified 93.5%

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

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t} \]
6. Step-by-step derivation

7. Simplified 42.4%

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

Developer Target 1: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024138 
(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))