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

Percentage Accurate: 97.7% → 97.7%

Time: 7.8s

Alternatives: 9

Speedup: 1.0×

• 24.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-5}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -1e+60)
     t_1
     (if (<= (/ x y) -2000000000000.0)
       (* t (- 1.0 (/ x y)))
       (if (<= (/ x y) 1e-5) (+ t (* (/ x y) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e+60) {
		tmp = t_1;
	} else if ((x / y) <= -2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 1e-5) {
		tmp = t + ((x / y) * z);
	} 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 * ((z - t) / y)
    if ((x / y) <= (-1d+60)) then
        tmp = t_1
    else if ((x / y) <= (-2000000000000.0d0)) then
        tmp = t * (1.0d0 - (x / y))
    else if ((x / y) <= 1d-5) then
        tmp = t + ((x / y) * z)
    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 * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e+60) {
		tmp = t_1;
	} else if ((x / y) <= -2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 1e-5) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -1e+60:
		tmp = t_1
	elif (x / y) <= -2000000000000.0:
		tmp = t * (1.0 - (x / y))
	elif (x / y) <= 1e-5:
		tmp = t + ((x / y) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e+60)
		tmp = t_1;
	elseif (Float64(x / y) <= -2000000000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (Float64(x / y) <= 1e-5)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -1e+60)
		tmp = t_1;
	elseif ((x / y) <= -2000000000000.0)
		tmp = t * (1.0 - (x / y));
	elseif ((x / y) <= 1e-5)
		tmp = t + ((x / y) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+60], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2000000000000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-5], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999995e59 or 1.00000000000000008e-5 < (/.f64 x y)

   1. Initial program 96.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 95.6%

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

   3. Simplified 95.6%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 94.9%

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

   7. Simplified 94.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 93.3%

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

   9. Applied egg-rr 93.3%

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

   if -9.9999999999999995e59 < (/.f64 x y) < -2e12

   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 81.6%

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

   3. Simplified 81.6%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 85.2%

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

   7. Simplified 85.2%

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

   if -2e12 < (/.f64 x y) < 1.00000000000000008e-5

   1. Initial program 98.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.2%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-5}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-5}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- z t)) y)))
   (if (<= (/ x y) -2000000000000.0)
     t_1
     (if (<= (/ x y) 1e-5) (+ t (* (/ x y) z)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (z - t)) / y;
	double tmp;
	if ((x / y) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-5) {
		tmp = t + ((x / y) * z);
	} 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 * (z - t)) / y
    if ((x / y) <= (-2000000000000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 1d-5) then
        tmp = t + ((x / y) * z)
    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 * (z - t)) / y;
	double tmp;
	if ((x / y) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-5) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (z - t)) / y
	tmp = 0
	if (x / y) <= -2000000000000.0:
		tmp = t_1
	elif (x / y) <= 1e-5:
		tmp = t + ((x / y) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(z - t)) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2000000000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-5)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (z - t)) / y;
	tmp = 0.0;
	if ((x / y) <= -2000000000000.0)
		tmp = t_1;
	elseif ((x / y) <= 1e-5)
		tmp = t + ((x / y) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2000000000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-5], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e12 or 1.00000000000000008e-5 < (/.f64 x y)

   1. Initial program 96.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 93.7%

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

   7. Simplified 93.7%

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

   if -2e12 < (/.f64 x y) < 1.00000000000000008e-5

   1. Initial program 98.8%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 98.2%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000000:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-5}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- z t) y))))
   (if (<= (/ x y) -1e-40)
     t_1
     (if (<= (/ x y) 4e-84) (* t (- 1.0 (/ x y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4e-84) {
		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 = x * ((z - t) / y)
    if ((x / y) <= (-1d-40)) then
        tmp = t_1
    else if ((x / y) <= 4d-84) 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 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4e-84) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -1e-40:
		tmp = t_1
	elif (x / y) <= 4e-84:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e-40)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-84)
		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 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -1e-40)
		tmp = t_1;
	elseif ((x / y) <= 4e-84)
		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[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-40], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-84], 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) < -9.9999999999999993e-41 or 4.0000000000000001e-84 < (/.f64 x y)

   1. Initial program 97.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 90.4%

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

   3. Simplified 90.4%

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

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

      2. *-commutative N/A

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

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

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

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

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

      5. --lowering--.f64 84.4%

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

   9. Applied egg-rr 84.4%

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

   if -9.9999999999999993e-41 < (/.f64 x y) < 4.0000000000000001e-84

   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 96.4%

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

   3. Simplified 96.4%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 80.1%

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

   7. Simplified 80.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ y x))))
   (if (<= (/ x y) -1e-40) t_1 (if (<= (/ x y) 4e-84) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if ((x / y) <= -1e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4e-84) {
		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 / (y / x)
    if ((x / y) <= (-1d-40)) then
        tmp = t_1
    else if ((x / y) <= 4d-84) 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 / (y / x);
	double tmp;
	if ((x / y) <= -1e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4e-84) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (y / x)
	tmp = 0
	if (x / y) <= -1e-40:
		tmp = t_1
	elif (x / y) <= 4e-84:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -1e-40)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-84)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (y / x);
	tmp = 0.0;
	if ((x / y) <= -1e-40)
		tmp = t_1;
	elseif ((x / y) <= 4e-84)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-40], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-84], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999993e-41 or 4.0000000000000001e-84 < (/.f64 x y)

   1. Initial program 97.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 90.4%

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

   3. Simplified 90.4%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 51.9%

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

   7. Simplified 51.9%

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

      1. associate-/l* N/A

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

      2. *-commutative 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 57.2%

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

   9. Applied egg-rr 57.2%

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

   if -9.9999999999999993e-41 < (/.f64 x y) < 4.0000000000000001e-84

   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 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 80.1%

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

Alternative 6: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)))
   (if (<= (/ x y) -1e-40) t_1 (if (<= (/ x y) 4e-84) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double tmp;
	if ((x / y) <= -1e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4e-84) {
		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 = (x / y) * z
    if ((x / y) <= (-1d-40)) then
        tmp = t_1
    else if ((x / y) <= 4d-84) 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 = (x / y) * z;
	double tmp;
	if ((x / y) <= -1e-40) {
		tmp = t_1;
	} else if ((x / y) <= 4e-84) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	tmp = 0
	if (x / y) <= -1e-40:
		tmp = t_1
	elif (x / y) <= 4e-84:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -1e-40)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-84)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -1e-40)
		tmp = t_1;
	elseif ((x / y) <= 4e-84)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-40], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-84], t, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999993e-41 or 4.0000000000000001e-84 < (/.f64 x y)

   1. Initial program 97.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 90.4%

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

   3. Simplified 90.4%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 51.9%

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

   7. Simplified 51.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   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 57.1%

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

   9. Applied egg-rr 57.1%

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

   if -9.9999999999999993e-41 < (/.f64 x y) < 4.0000000000000001e-84

   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 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 80.1%

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

Alternative 7: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 25.5:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -1.8e-126) t_1 (if (<= t 25.5) (* (/ x y) z) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1.8e-126) {
		tmp = t_1;
	} else if (t <= 25.5) {
		tmp = (x / y) * z;
	} 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 = t * (1.0d0 - (x / y))
    if (t <= (-1.8d-126)) then
        tmp = t_1
    else if (t <= 25.5d0) then
        tmp = (x / y) * z
    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 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -1.8e-126) {
		tmp = t_1;
	} else if (t <= 25.5) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -1.8e-126:
		tmp = t_1
	elif t <= 25.5:
		tmp = (x / y) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -1.8e-126)
		tmp = t_1;
	elseif (t <= 25.5)
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -1.8e-126)
		tmp = t_1;
	elseif (t <= 25.5)
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e-126], t$95$1, If[LessEqual[t, 25.5], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e-126 or 25.5 < t

   1. Initial program 99.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 93.1%

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

   3. Simplified 93.1%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 86.8%

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

   7. Simplified 86.8%

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

   if -1.8e-126 < t < 25.5

   1. Initial program 95.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 92.8%

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

   3. Simplified 92.8%

      \[\leadsto \color{blue}{t + \frac{x \cdot \left(z - t\right)}{y}} \]
   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 68.0%

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

   7. Simplified 68.0%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   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 73.2%

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

   9. Applied egg-rr 73.2%

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

Alternative 8: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+125}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+125) (+ t (* (/ x y) z)) (+ t (/ (* x (- z t)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+125) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t + ((x * (z - t)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4d+125)) then
        tmp = t + ((x / y) * z)
    else
        tmp = t + ((x * (z - t)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+125) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t + ((x * (z - t)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e+125:
		tmp = t + ((x / y) * z)
	else:
		tmp = t + ((x * (z - t)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e+125)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t + Float64(Float64(x * Float64(z - t)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4e+125)
		tmp = t + ((x / y) * z);
	else
		tmp = t + ((x * (z - t)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e+125], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999997e125

   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 94.7%

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

   if -3.9999999999999997e125 < y

   1. Initial program 97.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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 95.3%

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

   3. Simplified 95.3%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+125}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.6% 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. 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 93.0%

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

3. Simplified 93.0%

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

5. Taylor expanded in x around 0

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

7. Simplified 38.1%

   \[\leadsto \color{blue}{t} \]
8. 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 2024161 
(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))