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

Percentage Accurate: 97.7% → 97.7%

Time: 7.9s

Alternatives: 11

Speedup: 1.0×

• 25.1% 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: 97.7% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{x}{y}, z - t, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.1%

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

   1. fma-define 97.1%

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

3. Simplified 97.1%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 51.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;x \leq -225000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+26} \lor \neg \left(x \leq 5.8 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))))
   (if (<= x -225000000000.0)
     t_1
     (if (<= x 2.8e-114)
       t
       (if (or (<= x 4.5e+26) (not (<= x 5.8e+108))) (* x (/ z y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if (x <= -225000000000.0) {
		tmp = t_1;
	} else if (x <= 2.8e-114) {
		tmp = t;
	} else if ((x <= 4.5e+26) || !(x <= 5.8e+108)) {
		tmp = x * (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * -t
    if (x <= (-225000000000.0d0)) then
        tmp = t_1
    else if (x <= 2.8d-114) then
        tmp = t
    else if ((x <= 4.5d+26) .or. (.not. (x <= 5.8d+108))) then
        tmp = x * (z / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if (x <= -225000000000.0) {
		tmp = t_1;
	} else if (x <= 2.8e-114) {
		tmp = t;
	} else if ((x <= 4.5e+26) || !(x <= 5.8e+108)) {
		tmp = x * (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * -t
	tmp = 0
	if x <= -225000000000.0:
		tmp = t_1
	elif x <= 2.8e-114:
		tmp = t
	elif (x <= 4.5e+26) or not (x <= 5.8e+108):
		tmp = x * (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (x <= -225000000000.0)
		tmp = t_1;
	elseif (x <= 2.8e-114)
		tmp = t;
	elseif ((x <= 4.5e+26) || !(x <= 5.8e+108))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * -t;
	tmp = 0.0;
	if (x <= -225000000000.0)
		tmp = t_1;
	elseif (x <= 2.8e-114)
		tmp = t;
	elseif ((x <= 4.5e+26) || ~((x <= 5.8e+108)))
		tmp = x * (z / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[x, -225000000000.0], t$95$1, If[LessEqual[x, 2.8e-114], t, If[Or[LessEqual[x, 4.5e+26], N[Not[LessEqual[x, 5.8e+108]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25e11 or 4.49999999999999978e26 < x < 5.80000000000000015e108

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*l/ 74.9%

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

      4. *-lft-identity 74.9%

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

      5. distribute-lft-neg-in 74.9%

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

      6. mul-1-neg 74.9%

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

      7. distribute-rgt-in 75.0%

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

      8. mul-1-neg 75.0%

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

      9. unsub-neg 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around inf 58.6%

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

      1. associate-*r/ 58.6%

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

      2. neg-mul-1 58.6%

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

   8. Simplified 58.6%

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

   if -2.25e11 < x < 2.8000000000000001e-114

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 65.8%

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

   if 2.8000000000000001e-114 < x < 4.49999999999999978e26 or 5.80000000000000015e108 < x

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 94.7%

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

      1. associate--l+ 94.7%

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

      2. div-sub 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in t around 0 58.8%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -225000000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+26} \lor \neg \left(x \leq 5.8 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{t}{-y}\\ \mathbf{if}\;x \leq -250000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+26} \lor \neg \left(x \leq 3.8 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ t (- y)))))
   (if (<= x -250000000.0)
     t_1
     (if (<= x 2.8e-114)
       t
       (if (or (<= x 2.55e+26) (not (<= x 3.8e+108))) (* x (/ z y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (t / -y);
	double tmp;
	if (x <= -250000000.0) {
		tmp = t_1;
	} else if (x <= 2.8e-114) {
		tmp = t;
	} else if ((x <= 2.55e+26) || !(x <= 3.8e+108)) {
		tmp = x * (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (t / -y)
    if (x <= (-250000000.0d0)) then
        tmp = t_1
    else if (x <= 2.8d-114) then
        tmp = t
    else if ((x <= 2.55d+26) .or. (.not. (x <= 3.8d+108))) then
        tmp = x * (z / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (t / -y);
	double tmp;
	if (x <= -250000000.0) {
		tmp = t_1;
	} else if (x <= 2.8e-114) {
		tmp = t;
	} else if ((x <= 2.55e+26) || !(x <= 3.8e+108)) {
		tmp = x * (z / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (t / -y)
	tmp = 0
	if x <= -250000000.0:
		tmp = t_1
	elif x <= 2.8e-114:
		tmp = t
	elif (x <= 2.55e+26) or not (x <= 3.8e+108):
		tmp = x * (z / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(t / Float64(-y)))
	tmp = 0.0
	if (x <= -250000000.0)
		tmp = t_1;
	elseif (x <= 2.8e-114)
		tmp = t;
	elseif ((x <= 2.55e+26) || !(x <= 3.8e+108))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (t / -y);
	tmp = 0.0;
	if (x <= -250000000.0)
		tmp = t_1;
	elseif (x <= 2.8e-114)
		tmp = t;
	elseif ((x <= 2.55e+26) || ~((x <= 3.8e+108)))
		tmp = x * (z / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -250000000.0], t$95$1, If[LessEqual[x, 2.8e-114], t, If[Or[LessEqual[x, 2.55e+26], N[Not[LessEqual[x, 3.8e+108]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5e8 or 2.5499999999999999e26 < x < 3.80000000000000008e108

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*l/ 74.9%

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

      4. *-lft-identity 74.9%

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

      5. distribute-lft-neg-in 74.9%

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

      6. mul-1-neg 74.9%

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

      7. distribute-rgt-in 75.0%

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

      8. mul-1-neg 75.0%

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

      9. unsub-neg 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in x around inf 58.6%

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

      1. associate-*r/ 58.6%

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

      2. neg-mul-1 58.6%

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

   8. Simplified 58.6%

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

      1. *-commutative 58.6%

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

      2. distribute-frac-neg 58.6%

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

      3. distribute-lft-neg-out 58.6%

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

      4. add-sqr-sqrt 32.0%

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

      5. sqrt-unprod 32.3%

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

      6. sqr-neg 32.3%

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

      7. sqrt-unprod 2.4%

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

      8. add-sqr-sqrt 4.1%

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

      9. associate-/r/ 2.0%

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

      10. div-inv 2.0%

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

      11. clear-num 2.0%

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

      12. add-sqr-sqrt 1.4%

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

      13. sqrt-unprod 32.3%

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

      14. sqr-neg 32.3%

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

      15. sqrt-unprod 32.0%

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

      16. add-sqr-sqrt 57.5%

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

   10. Applied egg-rr 57.5%

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

   if -2.5e8 < x < 2.8000000000000001e-114

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 65.8%

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

   if 2.8000000000000001e-114 < x < 2.5499999999999999e26 or 3.80000000000000008e108 < x

   1. Initial program 93.2%

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

   3. Taylor expanded in x around inf 94.7%

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

      1. associate--l+ 94.7%

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

      2. div-sub 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in t around 0 58.8%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -250000000:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+26} \lor \neg \left(x \leq 3.8 \cdot 10^{+108}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000 \lor \neg \left(\frac{x}{y} \leq 0.4\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -20000.0) (not (<= (/ x y) 0.4)))
   (* x (/ (- z t) y))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000.0) || !((x / y) <= 0.4)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-20000.0d0)) .or. (.not. ((x / y) <= 0.4d0))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000.0) || !((x / y) <= 0.4)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -20000.0) or not ((x / y) <= 0.4):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -20000.0) || !(Float64(x / y) <= 0.4))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -20000.0) || ~(((x / y) <= 0.4)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -20000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.4]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e4 or 0.40000000000000002 < (/.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 94.5%

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

      1. associate--l+ 94.5%

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

      2. div-sub 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in x around inf 93.2%

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

      1. div-sub 94.6%

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

   8. Simplified 94.6%

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

   if -2e4 < (/.f64 x y) < 0.40000000000000002

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 97.3%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000 \lor \neg \left(\frac{x}{y} \leq 0.4\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000 \lor \neg \left(\frac{x}{y} \leq 0.4\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -20000.0) (not (<= (/ x y) 0.4)))
   (* x (/ (- z t) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000.0) || !((x / y) <= 0.4)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-20000.0d0)) .or. (.not. ((x / y) <= 0.4d0))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000.0) || !((x / y) <= 0.4)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -20000.0) or not ((x / y) <= 0.4):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -20000.0) || !(Float64(x / y) <= 0.4))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -20000.0) || ~(((x / y) <= 0.4)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -20000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.4]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e4 or 0.40000000000000002 < (/.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 94.5%

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

      1. associate--l+ 94.5%

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

      2. div-sub 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in x around inf 93.2%

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

      1. div-sub 94.6%

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

   8. Simplified 94.6%

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

   if -2e4 < (/.f64 x y) < 0.40000000000000002

   1. Initial program 99.5%

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

   3. Taylor expanded in z around inf 94.5%

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

      1. associate-/l* 93.6%

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

   5. Simplified 93.6%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000 \lor \neg \left(\frac{x}{y} \leq 0.4\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000000 \lor \neg \left(\frac{x}{y} \leq 0.4\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1000000.0) (not (<= (/ x y) 0.4)))
   (* x (/ (- z t) y))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1000000.0) || !((x / y) <= 0.4)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1000000.0d0)) .or. (.not. ((x / y) <= 0.4d0))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1000000.0) || !((x / y) <= 0.4)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1000000.0) or not ((x / y) <= 0.4):
		tmp = x * ((z - t) / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1000000.0) || !(Float64(x / y) <= 0.4))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1000000.0) || ~(((x / y) <= 0.4)))
		tmp = x * ((z - t) / y);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.4]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e6 or 0.40000000000000002 < (/.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf 95.1%

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

      1. associate--l+ 95.1%

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

      2. div-sub 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in x around inf 94.2%

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

      1. div-sub 95.7%

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

   8. Simplified 95.7%

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

   if -1e6 < (/.f64 x y) < 0.40000000000000002

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*l/ 73.8%

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

      4. *-lft-identity 73.8%

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

      5. distribute-lft-neg-in 73.8%

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

      6. mul-1-neg 73.8%

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

      7. distribute-rgt-in 73.8%

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

      8. mul-1-neg 73.8%

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

      9. unsub-neg 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000000 \lor \neg \left(\frac{x}{y} \leq 0.4\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+162} \lor \neg \left(z \leq 1.52 \cdot 10^{+124}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.2e+162) (not (<= z 1.52e+124)))
   (* x (/ z y))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+162) || !(z <= 1.52e+124)) {
		tmp = x * (z / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.2d+162)) .or. (.not. (z <= 1.52d+124))) then
        tmp = x * (z / y)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.2e+162) || !(z <= 1.52e+124)) {
		tmp = x * (z / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.2e+162) or not (z <= 1.52e+124):
		tmp = x * (z / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.2e+162) || !(z <= 1.52e+124))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.2e+162) || ~((z <= 1.52e+124)))
		tmp = x * (z / y);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.2e+162], N[Not[LessEqual[z, 1.52e+124]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.20000000000000005e162 or 1.51999999999999998e124 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 82.1%

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

      1. associate--l+ 82.1%

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

      2. div-sub 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in t around 0 80.2%

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

   if -1.20000000000000005e162 < z < 1.51999999999999998e124

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-*l/ 77.8%

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

      4. *-lft-identity 77.8%

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

      5. distribute-lft-neg-in 77.8%

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

      6. mul-1-neg 77.8%

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

      7. distribute-rgt-in 77.8%

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

      8. mul-1-neg 77.8%

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

      9. unsub-neg 77.8%

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

   5. Simplified 77.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+162} \lor \neg \left(z \leq 1.52 \cdot 10^{+124}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \lor \neg \left(t \leq 430000000\right):\\ \;\;\;\;\frac{x \cdot t}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.4) (not (<= t 430000000.0))) (/ (* x t) x) (* x (/ z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.4) || !(t <= 430000000.0)) {
		tmp = (x * t) / x;
	} else {
		tmp = x * (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.4d0)) .or. (.not. (t <= 430000000.0d0))) then
        tmp = (x * t) / x
    else
        tmp = x * (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.4) || !(t <= 430000000.0)) {
		tmp = (x * t) / x;
	} else {
		tmp = x * (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.4) or not (t <= 430000000.0):
		tmp = (x * t) / x
	else:
		tmp = x * (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.4) || !(t <= 430000000.0))
		tmp = Float64(Float64(x * t) / x);
	else
		tmp = Float64(x * Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.4) || ~((t <= 430000000.0)))
		tmp = (x * t) / x;
	else
		tmp = x * (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.4], N[Not[LessEqual[t, 430000000.0]], $MachinePrecision]], N[(N[(x * t), $MachinePrecision] / x), $MachinePrecision], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.39999999999999991 or 4.3e8 < t

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. associate--l+ 76.1%

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

      2. div-sub 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in x around 0 20.2%

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

      1. associate-*r/ 50.3%

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

   8. Applied egg-rr 50.3%

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

   if -2.39999999999999991 < t < 4.3e8

   1. Initial program 94.2%

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

   3. Taylor expanded in x around inf 93.8%

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

      1. associate--l+ 93.8%

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

      2. div-sub 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in t around 0 58.4%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \lor \neg \left(t \leq 430000000\right):\\ \;\;\;\;\frac{x \cdot t}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3100000000000 \lor \neg \left(x \leq 2.7 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3100000000000.0) (not (<= x 2.7e-114))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3100000000000.0) || !(x <= 2.7e-114)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3100000000000.0d0)) .or. (.not. (x <= 2.7d-114))) then
        tmp = x * (z / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3100000000000.0) || !(x <= 2.7e-114)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3100000000000.0) or not (x <= 2.7e-114):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3100000000000.0) || !(x <= 2.7e-114))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3100000000000.0) || ~((x <= 2.7e-114)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3100000000000.0], N[Not[LessEqual[x, 2.7e-114]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e12 or 2.7e-114 < x

   1. Initial program 95.7%

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

   3. Taylor expanded in x around inf 97.5%

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

      1. associate--l+ 97.5%

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

      2. div-sub 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in t around 0 46.9%

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

   if -3.1e12 < x < 2.7e-114

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 65.1%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3100000000000 \lor \neg \left(x \leq 2.7 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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 97.1%

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

3. Final simplification 97.1%

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

Alternative 11: 38.4% 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 97.1%

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

3. Taylor expanded in x around 0 34.1%

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

Developer Target 1: 97.2% 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 2024172 
(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))