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

Percentage Accurate: 97.8% → 94.4%

Time: 9.0s

Alternatives: 10

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: 97.8% 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: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -50000000.0) (not (<= (/ x y) 5e-17)))
   (* (- z t) (/ x y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -50000000.0) || !((x / y) <= 5e-17)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-50000000.0d0)) .or. (.not. ((x / y) <= 5d-17))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -50000000.0) || !((x / y) <= 5e-17)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -50000000.0) or not ((x / y) <= 5e-17):
		tmp = (z - t) * (x / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -50000000.0) || !(Float64(x / y) <= 5e-17))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -50000000.0) || ~(((x / y) <= 5e-17)))
		tmp = (z - t) * (x / 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], -50000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-17]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / 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) < -5e7 or 4.9999999999999999e-17 < (/.f64 x y)

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 91.2%

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

      1. associate-*r/ 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-/r/ 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0 91.2%

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

   7. Taylor expanded in x around -inf 90.9%

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

      1. *-commutative 90.9%

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

      2. associate-/l* 97.9%

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

   9. Applied egg-rr 97.9%

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

   if -5e7 < (/.f64 x y) < 4.9999999999999999e-17

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 93.1%

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

      1. associate-/l* 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-17}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{y}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-106}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z y))))
   (if (<= x -2.8e+144)
     (* t (/ x (- y)))
     (if (<= x -1.05e-79)
       t_1
       (if (<= x 3e-106) t (if (<= x 1.75e+170) t_1 (* x (/ t (- y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / y);
	double tmp;
	if (x <= -2.8e+144) {
		tmp = t * (x / -y);
	} else if (x <= -1.05e-79) {
		tmp = t_1;
	} else if (x <= 3e-106) {
		tmp = t;
	} else if (x <= 1.75e+170) {
		tmp = t_1;
	} else {
		tmp = x * (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) :: t_1
    real(8) :: tmp
    t_1 = x * (z / y)
    if (x <= (-2.8d+144)) then
        tmp = t * (x / -y)
    else if (x <= (-1.05d-79)) then
        tmp = t_1
    else if (x <= 3d-106) then
        tmp = t
    else if (x <= 1.75d+170) then
        tmp = t_1
    else
        tmp = x * (t / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / y);
	double tmp;
	if (x <= -2.8e+144) {
		tmp = t * (x / -y);
	} else if (x <= -1.05e-79) {
		tmp = t_1;
	} else if (x <= 3e-106) {
		tmp = t;
	} else if (x <= 1.75e+170) {
		tmp = t_1;
	} else {
		tmp = x * (t / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / y)
	tmp = 0
	if x <= -2.8e+144:
		tmp = t * (x / -y)
	elif x <= -1.05e-79:
		tmp = t_1
	elif x <= 3e-106:
		tmp = t
	elif x <= 1.75e+170:
		tmp = t_1
	else:
		tmp = x * (t / -y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / y))
	tmp = 0.0
	if (x <= -2.8e+144)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif (x <= -1.05e-79)
		tmp = t_1;
	elseif (x <= 3e-106)
		tmp = t;
	elseif (x <= 1.75e+170)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / y);
	tmp = 0.0;
	if (x <= -2.8e+144)
		tmp = t * (x / -y);
	elseif (x <= -1.05e-79)
		tmp = t_1;
	elseif (x <= 3e-106)
		tmp = t;
	elseif (x <= 1.75e+170)
		tmp = t_1;
	else
		tmp = x * (t / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+144], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.05e-79], t$95$1, If[LessEqual[x, 3e-106], t, If[LessEqual[x, 1.75e+170], t$95$1, N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.80000000000000007e144

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 75.0%

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

      1. associate-*r/ 96.2%

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

      2. *-commutative 96.2%

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

      3. associate-/r/ 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in y around 0 75.0%

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

   7. Taylor expanded in x around -inf 68.8%

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

   8. Taylor expanded in z around 0 46.0%

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

      1. associate-*r/ 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-*r* 61.8%

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

      4. *-commutative 61.8%

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

      5. associate-*r/ 61.8%

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

      6. mul-1-neg 61.8%

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

   10. Simplified 61.8%

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

   if -2.80000000000000007e144 < x < -1.05e-79 or 3.00000000000000019e-106 < x < 1.75000000000000003e170

   1. Initial program 98.8%

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

   3. Taylor expanded in x around 0 90.4%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/r/ 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in y around 0 90.4%

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

   7. Taylor expanded in x around -inf 69.3%

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

   8. Taylor expanded in z around inf 51.0%

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

      1. associate-*r/ 55.6%

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

   10. Simplified 55.6%

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

   if -1.05e-79 < x < 3.00000000000000019e-106

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 72.1%

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

   if 1.75000000000000003e170 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. associate-*r/ 94.3%

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

      2. *-commutative 94.3%

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

      3. associate-/r/ 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in z around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. associate-*r/ 62.7%

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

      3. rem-square-sqrt 36.7%

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

      4. distribute-lft-neg-in 36.7%

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

      5. cancel-sign-sub-inv 36.7%

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

      6. rem-square-sqrt 62.7%

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

   8. Simplified 62.7%

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

      1. clear-num 62.6%

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

      2. un-div-inv 62.7%

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

   10. Applied egg-rr 62.7%

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

   11. Taylor expanded in y around 0 55.6%

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

       1. mul-1-neg 55.6%

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

       2. associate-*l/ 65.9%

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

       3. distribute-lft-neg-in 65.9%

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

       4. *-commutative 65.9%

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

       5. distribute-frac-neg2 65.9%

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

   13. Simplified 65.9%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-106}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{y}\\ t_2 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+140}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-105}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+208}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z y))) (t_2 (* t (/ x (- y)))))
   (if (<= x -1.6e+140)
     t_2
     (if (<= x -6e-80)
       t_1
       (if (<= x 1.2e-105) t (if (<= x 7e+208) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / y);
	double t_2 = t * (x / -y);
	double tmp;
	if (x <= -1.6e+140) {
		tmp = t_2;
	} else if (x <= -6e-80) {
		tmp = t_1;
	} else if (x <= 1.2e-105) {
		tmp = t;
	} else if (x <= 7e+208) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x * (z / y)
    t_2 = t * (x / -y)
    if (x <= (-1.6d+140)) then
        tmp = t_2
    else if (x <= (-6d-80)) then
        tmp = t_1
    else if (x <= 1.2d-105) then
        tmp = t
    else if (x <= 7d+208) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / y);
	double t_2 = t * (x / -y);
	double tmp;
	if (x <= -1.6e+140) {
		tmp = t_2;
	} else if (x <= -6e-80) {
		tmp = t_1;
	} else if (x <= 1.2e-105) {
		tmp = t;
	} else if (x <= 7e+208) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / y)
	t_2 = t * (x / -y)
	tmp = 0
	if x <= -1.6e+140:
		tmp = t_2
	elif x <= -6e-80:
		tmp = t_1
	elif x <= 1.2e-105:
		tmp = t
	elif x <= 7e+208:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / y))
	t_2 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (x <= -1.6e+140)
		tmp = t_2;
	elseif (x <= -6e-80)
		tmp = t_1;
	elseif (x <= 1.2e-105)
		tmp = t;
	elseif (x <= 7e+208)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / y);
	t_2 = t * (x / -y);
	tmp = 0.0;
	if (x <= -1.6e+140)
		tmp = t_2;
	elseif (x <= -6e-80)
		tmp = t_1;
	elseif (x <= 1.2e-105)
		tmp = t;
	elseif (x <= 7e+208)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+140], t$95$2, If[LessEqual[x, -6e-80], t$95$1, If[LessEqual[x, 1.2e-105], t, If[LessEqual[x, 7e+208], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.60000000000000005e140 or 7.00000000000000033e208 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 78.0%

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

      1. associate-*r/ 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-/r/ 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 78.0%

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

   7. Taylor expanded in x around -inf 74.4%

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

   8. Taylor expanded in z around 0 51.2%

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

      1. associate-*r/ 66.0%

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

      2. *-commutative 66.0%

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

      3. associate-*r* 66.0%

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

      4. *-commutative 66.0%

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

      5. associate-*r/ 66.0%

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

      6. mul-1-neg 66.0%

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

   10. Simplified 66.0%

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

   if -1.60000000000000005e140 < x < -6.00000000000000014e-80 or 1.20000000000000007e-105 < x < 7.00000000000000033e208

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 91.0%

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

      1. associate-*r/ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-/r/ 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in y around 0 91.0%

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

   7. Taylor expanded in x around -inf 71.0%

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

   8. Taylor expanded in z around inf 51.2%

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

      1. associate-*r/ 55.0%

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

   10. Simplified 55.0%

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

   if -6.00000000000000014e-80 < x < 1.20000000000000007e-105

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 72.1%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-105}:\\ \;\;\;\;t\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-64}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000000000.0) (not (<= (/ x y) 5e-64)))
   (* (- z t) (/ x y))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000000.0) || !((x / y) <= 5e-64)) {
		tmp = (z - t) * (x / 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) <= (-100000000000.0d0)) .or. (.not. ((x / y) <= 5d-64))) then
        tmp = (z - t) * (x / 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) <= -100000000000.0) || !((x / y) <= 5e-64)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -100000000000.0) or not ((x / y) <= 5e-64):
		tmp = (z - t) * (x / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -100000000000.0) || !(Float64(x / y) <= 5e-64))
		tmp = Float64(Float64(z - t) * Float64(x / 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) <= -100000000000.0) || ~(((x / y) <= 5e-64)))
		tmp = (z - t) * (x / 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], -100000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-64]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / 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) < -1e11 or 5.00000000000000033e-64 < (/.f64 x y)

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 90.9%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-/r/ 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in y around 0 90.9%

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

   7. Taylor expanded in x around -inf 88.7%

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

      1. *-commutative 88.7%

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

      2. associate-/l* 96.1%

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

   9. Applied egg-rr 96.1%

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

   if -1e11 < (/.f64 x y) < 5.00000000000000033e-64

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. *-rgt-identity 78.1%

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

      3. associate-/l* 80.5%

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

      4. distribute-rgt-neg-in 80.5%

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

      5. mul-1-neg 80.5%

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

      6. distribute-lft-in 80.5%

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

      7. mul-1-neg 80.5%

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

      8. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-64}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+25)
   (/ (* z x) y)
   (if (<= z 1.3e+114) (* t (- 1.0 (/ x y))) (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+25) {
		tmp = (z * x) / y;
	} else if (z <= 1.3e+114) {
		tmp = t * (1.0 - (x / y));
	} 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 (z <= (-6.8d+25)) then
        tmp = (z * x) / y
    else if (z <= 1.3d+114) then
        tmp = t * (1.0d0 - (x / y))
    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 (z <= -6.8e+25) {
		tmp = (z * x) / y;
	} else if (z <= 1.3e+114) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e+25:
		tmp = (z * x) / y
	elif z <= 1.3e+114:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+25)
		tmp = Float64(Float64(z * x) / y);
	elseif (z <= 1.3e+114)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.8e+25)
		tmp = (z * x) / y;
	elseif (z <= 1.3e+114)
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+25], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.3e+114], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999967e25

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-/r/ 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in y around 0 89.5%

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

   7. Taylor expanded in x around -inf 63.3%

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

   8. Taylor expanded in z around inf 59.6%

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

   if -6.79999999999999967e25 < z < 1.3e114

   1. Initial program 98.7%

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

   3. Taylor expanded in z around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. *-rgt-identity 78.3%

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

      3. associate-/l* 83.5%

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

      4. distribute-rgt-neg-in 83.5%

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

      5. mul-1-neg 83.5%

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

      6. distribute-lft-in 83.5%

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

      7. mul-1-neg 83.5%

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

      8. unsub-neg 83.5%

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

   5. Simplified 83.5%

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

   if 1.3e114 < z

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 83.8%

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

      1. associate-*r/ 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-/r/ 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in y around 0 83.8%

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

   7. Taylor expanded in x around -inf 66.5%

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

   8. Taylor expanded in z around inf 63.1%

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

      1. associate-*r/ 71.2%

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

   10. Simplified 71.2%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+114}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-80} \lor \neg \left(x \leq 2 \cdot 10^{-106}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -8e-80) (not (<= x 2e-106))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -8e-80) || !(x <= 2e-106)) {
		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 <= (-8d-80)) .or. (.not. (x <= 2d-106))) 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 <= -8e-80) || !(x <= 2e-106)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -8e-80) or not (x <= 2e-106):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -8e-80) || !(x <= 2e-106))
		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 <= -8e-80) || ~((x <= 2e-106)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -8e-80], N[Not[LessEqual[x, 2e-106]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -7.99999999999999969e-80 or 1.99999999999999988e-106 < x

   1. Initial program 98.1%

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

   3. Taylor expanded in x around 0 86.8%

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

      1. associate-*r/ 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-/r/ 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in y around 0 86.8%

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

   7. Taylor expanded in x around -inf 72.1%

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

   8. Taylor expanded in z around inf 47.2%

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

      1. associate-*r/ 50.4%

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

   10. Simplified 50.4%

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

   if -7.99999999999999969e-80 < x < 1.99999999999999988e-106

   1. Initial program 97.8%

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

   3. Taylor expanded in x around 0 72.1%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-80} \lor \neg \left(x \leq 2 \cdot 10^{-106}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2900:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2900.0) t (if (<= y 2.25e+52) (/ (* z x) y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2900.0) {
		tmp = t;
	} else if (y <= 2.25e+52) {
		tmp = (z * x) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2900.0d0)) then
        tmp = t
    else if (y <= 2.25d+52) then
        tmp = (z * x) / y
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2900.0) {
		tmp = t;
	} else if (y <= 2.25e+52) {
		tmp = (z * x) / y;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2900.0:
		tmp = t
	elif y <= 2.25e+52:
		tmp = (z * x) / y
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2900.0)
		tmp = t;
	elseif (y <= 2.25e+52)
		tmp = Float64(Float64(z * x) / y);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2900.0)
		tmp = t;
	elseif (y <= 2.25e+52)
		tmp = (z * x) / y;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2900.0], t, If[LessEqual[y, 2.25e+52], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2900 or 2.25e52 < y

   1. Initial program 97.6%

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

   3. Taylor expanded in x around 0 62.7%

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

   if -2900 < y < 2.25e52

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 98.4%

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

      1. associate-*r/ 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-/r/ 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0 98.4%

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

   7. Taylor expanded in x around -inf 84.3%

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

   8. Taylor expanded in z around inf 54.4%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2900:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{+52}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in x around 0 91.4%

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

   1. associate-*r/ 93.9%

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

   2. *-commutative 93.9%

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

   3. associate-/r/ 98.0%

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

5. Simplified 98.0%

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

6. Final simplification 98.0%

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

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Final simplification 98.0%

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

Alternative 10: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Taylor expanded in x around 0 40.6%

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

Developer Target 1: 97.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(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))