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

Percentage Accurate: 97.6% → 97.6%

Time: 6.4s

Alternatives: 12

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 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 97.0%

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

   1. fma-define 97.0%

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

3. Simplified 97.0%

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

Alternative 2: 61.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{y}{-x}}\\ t_2 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+243}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ y (- x)))) (t_2 (* (/ x y) z)))
   (if (<= (/ x y) -5e+193)
     t_1
     (if (<= (/ x y) -2e+103)
       (* x (/ z y))
       (if (<= (/ x y) -100.0)
         t_1
         (if (<= (/ x y) 2e-99)
           t
           (if (<= (/ x y) 5e+84)
             t_2
             (if (<= (/ x y) 5e+169)
               (* (/ x y) (- t))
               (if (<= (/ x y) 2e+243) t_2 (* (/ t y) (- x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (y / -x);
	double t_2 = (x / y) * z;
	double tmp;
	if ((x / y) <= -5e+193) {
		tmp = t_1;
	} else if ((x / y) <= -2e+103) {
		tmp = x * (z / y);
	} else if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-99) {
		tmp = t;
	} else if ((x / y) <= 5e+84) {
		tmp = t_2;
	} else if ((x / y) <= 5e+169) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 2e+243) {
		tmp = t_2;
	} else {
		tmp = (t / y) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (y / -x)
    t_2 = (x / y) * z
    if ((x / y) <= (-5d+193)) then
        tmp = t_1
    else if ((x / y) <= (-2d+103)) then
        tmp = x * (z / y)
    else if ((x / y) <= (-100.0d0)) then
        tmp = t_1
    else if ((x / y) <= 2d-99) then
        tmp = t
    else if ((x / y) <= 5d+84) then
        tmp = t_2
    else if ((x / y) <= 5d+169) then
        tmp = (x / y) * -t
    else if ((x / y) <= 2d+243) then
        tmp = t_2
    else
        tmp = (t / y) * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (y / -x);
	double t_2 = (x / y) * z;
	double tmp;
	if ((x / y) <= -5e+193) {
		tmp = t_1;
	} else if ((x / y) <= -2e+103) {
		tmp = x * (z / y);
	} else if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-99) {
		tmp = t;
	} else if ((x / y) <= 5e+84) {
		tmp = t_2;
	} else if ((x / y) <= 5e+169) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= 2e+243) {
		tmp = t_2;
	} else {
		tmp = (t / y) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (y / -x)
	t_2 = (x / y) * z
	tmp = 0
	if (x / y) <= -5e+193:
		tmp = t_1
	elif (x / y) <= -2e+103:
		tmp = x * (z / y)
	elif (x / y) <= -100.0:
		tmp = t_1
	elif (x / y) <= 2e-99:
		tmp = t
	elif (x / y) <= 5e+84:
		tmp = t_2
	elif (x / y) <= 5e+169:
		tmp = (x / y) * -t
	elif (x / y) <= 2e+243:
		tmp = t_2
	else:
		tmp = (t / y) * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(y / Float64(-x)))
	t_2 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -5e+193)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e+103)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= -100.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-99)
		tmp = t;
	elseif (Float64(x / y) <= 5e+84)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e+169)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= 2e+243)
		tmp = t_2;
	else
		tmp = Float64(Float64(t / y) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (y / -x);
	t_2 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -5e+193)
		tmp = t_1;
	elseif ((x / y) <= -2e+103)
		tmp = x * (z / y);
	elseif ((x / y) <= -100.0)
		tmp = t_1;
	elseif ((x / y) <= 2e-99)
		tmp = t;
	elseif ((x / y) <= 5e+84)
		tmp = t_2;
	elseif ((x / y) <= 5e+169)
		tmp = (x / y) * -t;
	elseif ((x / y) <= 2e+243)
		tmp = t_2;
	else
		tmp = (t / y) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+193], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e+103], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -100.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-99], t, If[LessEqual[N[(x / y), $MachinePrecision], 5e+84], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e+169], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+243], t$95$2, N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 x y) < -4.99999999999999972e193 or -2e103 < (/.f64 x y) < -100

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

      3. *-rgt-identity 63.5%

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

      4. associate-/l* 73.0%

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

      5. distribute-lft-out-- 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in x around inf 61.4%

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

      1. mul-1-neg 61.4%

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

      2. associate-*l/ 58.7%

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

      3. associate-/r/ 70.9%

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

      4. distribute-neg-frac2 70.9%

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

      5. distribute-frac-neg 70.9%

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

   8. Simplified 70.9%

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

   if -4.99999999999999972e193 < (/.f64 x y) < -2e103

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.6%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. associate-*r/ 63.0%

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

   6. Simplified 63.0%

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

   if -100 < (/.f64 x y) < 2e-99

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 72.8%

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

   if 2e-99 < (/.f64 x y) < 5.0000000000000001e84 or 5.00000000000000017e169 < (/.f64 x y) < 2.0000000000000001e243

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 74.4%

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

   4. Taylor expanded in z around inf 63.3%

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

      1. associate-*l/ 71.9%

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

      2. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   if 5.0000000000000001e84 < (/.f64 x y) < 5.00000000000000017e169

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   4. Taylor expanded in z around 0 64.3%

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

      1. mul-1-neg 64.3%

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

      2. associate-*r/ 70.2%

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

      3. distribute-rgt-neg-in 70.2%

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

   6. Simplified 70.2%

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

   if 2.0000000000000001e243 < (/.f64 x y)

   1. Initial program 85.7%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

      3. *-rgt-identity 68.1%

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

      4. associate-/l* 66.7%

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

      5. distribute-lft-out-- 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-*l/ 68.1%

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

      3. distribute-rgt-neg-out 68.1%

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

   8. Simplified 68.1%

      \[\leadsto \color{blue}{\frac{t}{y} \cdot \left(-x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+193}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -100:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+243}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ t_2 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+243}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))) (t_2 (* (/ x y) z)))
   (if (<= (/ x y) -5e+193)
     t_1
     (if (<= (/ x y) -2e+103)
       (* x (/ z y))
       (if (<= (/ x y) -100.0)
         t_1
         (if (<= (/ x y) 2e-99)
           t
           (if (<= (/ x y) 5e+84)
             t_2
             (if (<= (/ x y) 5e+169)
               t_1
               (if (<= (/ x y) 2e+243) t_2 (* (/ t y) (- x)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double t_2 = (x / y) * z;
	double tmp;
	if ((x / y) <= -5e+193) {
		tmp = t_1;
	} else if ((x / y) <= -2e+103) {
		tmp = x * (z / y);
	} else if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-99) {
		tmp = t;
	} else if ((x / y) <= 5e+84) {
		tmp = t_2;
	} else if ((x / y) <= 5e+169) {
		tmp = t_1;
	} else if ((x / y) <= 2e+243) {
		tmp = t_2;
	} else {
		tmp = (t / y) * -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) * -t
    t_2 = (x / y) * z
    if ((x / y) <= (-5d+193)) then
        tmp = t_1
    else if ((x / y) <= (-2d+103)) then
        tmp = x * (z / y)
    else if ((x / y) <= (-100.0d0)) then
        tmp = t_1
    else if ((x / y) <= 2d-99) then
        tmp = t
    else if ((x / y) <= 5d+84) then
        tmp = t_2
    else if ((x / y) <= 5d+169) then
        tmp = t_1
    else if ((x / y) <= 2d+243) then
        tmp = t_2
    else
        tmp = (t / y) * -x
    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 t_2 = (x / y) * z;
	double tmp;
	if ((x / y) <= -5e+193) {
		tmp = t_1;
	} else if ((x / y) <= -2e+103) {
		tmp = x * (z / y);
	} else if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-99) {
		tmp = t;
	} else if ((x / y) <= 5e+84) {
		tmp = t_2;
	} else if ((x / y) <= 5e+169) {
		tmp = t_1;
	} else if ((x / y) <= 2e+243) {
		tmp = t_2;
	} else {
		tmp = (t / y) * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * -t
	t_2 = (x / y) * z
	tmp = 0
	if (x / y) <= -5e+193:
		tmp = t_1
	elif (x / y) <= -2e+103:
		tmp = x * (z / y)
	elif (x / y) <= -100.0:
		tmp = t_1
	elif (x / y) <= 2e-99:
		tmp = t
	elif (x / y) <= 5e+84:
		tmp = t_2
	elif (x / y) <= 5e+169:
		tmp = t_1
	elif (x / y) <= 2e+243:
		tmp = t_2
	else:
		tmp = (t / y) * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(-t))
	t_2 = Float64(Float64(x / y) * z)
	tmp = 0.0
	if (Float64(x / y) <= -5e+193)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e+103)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= -100.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-99)
		tmp = t;
	elseif (Float64(x / y) <= 5e+84)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e+169)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e+243)
		tmp = t_2;
	else
		tmp = Float64(Float64(t / y) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * -t;
	t_2 = (x / y) * z;
	tmp = 0.0;
	if ((x / y) <= -5e+193)
		tmp = t_1;
	elseif ((x / y) <= -2e+103)
		tmp = x * (z / y);
	elseif ((x / y) <= -100.0)
		tmp = t_1;
	elseif ((x / y) <= 2e-99)
		tmp = t;
	elseif ((x / y) <= 5e+84)
		tmp = t_2;
	elseif ((x / y) <= 5e+169)
		tmp = t_1;
	elseif ((x / y) <= 2e+243)
		tmp = t_2;
	else
		tmp = (t / y) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+193], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e+103], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -100.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-99], t, If[LessEqual[N[(x / y), $MachinePrecision], 5e+84], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e+169], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e+243], t$95$2, N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -4.99999999999999972e193 or -2e103 < (/.f64 x y) < -100 or 5.0000000000000001e84 < (/.f64 x y) < 5.00000000000000017e169

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 89.3%

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

   4. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. associate-*r/ 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

   6. Simplified 70.7%

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

   if -4.99999999999999972e193 < (/.f64 x y) < -2e103

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.6%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. associate-*r/ 63.0%

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

   6. Simplified 63.0%

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

   if -100 < (/.f64 x y) < 2e-99

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 72.8%

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

   if 2e-99 < (/.f64 x y) < 5.0000000000000001e84 or 5.00000000000000017e169 < (/.f64 x y) < 2.0000000000000001e243

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 74.4%

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

   4. Taylor expanded in z around inf 63.3%

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

      1. associate-*l/ 71.9%

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

      2. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   if 2.0000000000000001e243 < (/.f64 x y)

   1. Initial program 85.7%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. mul-1-neg 68.1%

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

      2. unsub-neg 68.1%

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

      3. *-rgt-identity 68.1%

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

      4. associate-/l* 66.7%

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

      5. distribute-lft-out-- 66.7%

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

   5. Simplified 66.7%

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

   6. Taylor expanded in x around inf 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-*l/ 68.1%

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

      3. distribute-rgt-neg-out 68.1%

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

   8. Simplified 68.1%

      \[\leadsto \color{blue}{\frac{t}{y} \cdot \left(-x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -100:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+169}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+243}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -100:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+169}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))))
   (if (<= (/ x y) -5e+193)
     t_1
     (if (<= (/ x y) -2e+103)
       (* x (/ z y))
       (if (<= (/ x y) -100.0)
         t_1
         (if (<= (/ x y) 2e-99)
           t
           (if (or (<= (/ x y) 5e+84) (not (<= (/ x y) 5e+169)))
             (* (/ x y) z)
             t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -5e+193) {
		tmp = t_1;
	} else if ((x / y) <= -2e+103) {
		tmp = x * (z / y);
	} else if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-99) {
		tmp = t;
	} else if (((x / y) <= 5e+84) || !((x / y) <= 5e+169)) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * -t
    if ((x / y) <= (-5d+193)) then
        tmp = t_1
    else if ((x / y) <= (-2d+103)) then
        tmp = x * (z / y)
    else if ((x / y) <= (-100.0d0)) then
        tmp = t_1
    else if ((x / y) <= 2d-99) then
        tmp = t
    else if (((x / y) <= 5d+84) .or. (.not. ((x / y) <= 5d+169))) then
        tmp = (x / y) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -5e+193) {
		tmp = t_1;
	} else if ((x / y) <= -2e+103) {
		tmp = x * (z / y);
	} else if ((x / y) <= -100.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-99) {
		tmp = t;
	} else if (((x / y) <= 5e+84) || !((x / y) <= 5e+169)) {
		tmp = (x / y) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * -t
	tmp = 0
	if (x / y) <= -5e+193:
		tmp = t_1
	elif (x / y) <= -2e+103:
		tmp = x * (z / y)
	elif (x / y) <= -100.0:
		tmp = t_1
	elif (x / y) <= 2e-99:
		tmp = t
	elif ((x / y) <= 5e+84) or not ((x / y) <= 5e+169):
		tmp = (x / y) * z
	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 (Float64(x / y) <= -5e+193)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e+103)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= -100.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-99)
		tmp = t;
	elseif ((Float64(x / y) <= 5e+84) || !(Float64(x / y) <= 5e+169))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * -t;
	tmp = 0.0;
	if ((x / y) <= -5e+193)
		tmp = t_1;
	elseif ((x / y) <= -2e+103)
		tmp = x * (z / y);
	elseif ((x / y) <= -100.0)
		tmp = t_1;
	elseif ((x / y) <= 2e-99)
		tmp = t;
	elseif (((x / y) <= 5e+84) || ~(((x / y) <= 5e+169)))
		tmp = (x / y) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+193], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e+103], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -100.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-99], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 5e+84], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+169]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -4.99999999999999972e193 or -2e103 < (/.f64 x y) < -100 or 5.0000000000000001e84 < (/.f64 x y) < 5.00000000000000017e169

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 89.3%

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

   4. Taylor expanded in z around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. associate-*r/ 70.7%

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

      3. distribute-rgt-neg-in 70.7%

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

   6. Simplified 70.7%

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

   if -4.99999999999999972e193 < (/.f64 x y) < -2e103

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 99.6%

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

   4. Taylor expanded in z around inf 63.0%

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

      1. associate-*r/ 63.0%

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

   6. Simplified 63.0%

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

   if -100 < (/.f64 x y) < 2e-99

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 72.8%

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

   if 2e-99 < (/.f64 x y) < 5.0000000000000001e84 or 5.00000000000000017e169 < (/.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in x around inf 82.2%

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

   4. Taylor expanded in z around inf 55.4%

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

      1. associate-*l/ 64.3%

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

      2. *-commutative 64.3%

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

   6. Simplified 64.3%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+193}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -100:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-99}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+84} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+169}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -100000000000.0) (not (<= (/ x y) 2e-6)))
   (* x (/ (- z t) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -100000000000.0) || !((x / y) <= 2e-6)) {
		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) <= (-100000000000.0d0)) .or. (.not. ((x / y) <= 2d-6))) 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) <= -100000000000.0) || !((x / y) <= 2e-6)) {
		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) <= -100000000000.0) or not ((x / y) <= 2e-6):
		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) <= -100000000000.0) || !(Float64(x / y) <= 2e-6))
		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) <= -100000000000.0) || ~(((x / y) <= 2e-6)))
		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], -100000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-6]], $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) < -1e11 or 1.99999999999999991e-6 < (/.f64 x y)

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 93.6%

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

   4. Taylor expanded in z around 0 82.6%

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

      1. +-commutative 82.6%

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

      2. associate-*r/ 83.6%

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

      3. associate-*l/ 85.7%

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

      4. associate-*r* 85.7%

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

      5. *-commutative 85.7%

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

      6. distribute-lft-out 93.6%

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

      7. mul-1-neg 93.6%

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

      8. sub-neg 93.6%

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

      9. div-sub 95.2%

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

   6. Simplified 95.2%

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

   if -1e11 < (/.f64 x y) < 1.99999999999999991e-6

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 94.0%

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

      1. associate-/l* 95.0%

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

   5. Simplified 95.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+103} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+103) (not (<= (/ x y) 2e-99)))
   (* 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) <= -2e+103) || !((x / y) <= 2e-99)) {
		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) <= (-2d+103)) .or. (.not. ((x / y) <= 2d-99))) 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) <= -2e+103) || !((x / y) <= 2e-99)) {
		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) <= -2e+103) or not ((x / y) <= 2e-99):
		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) <= -2e+103) || !(Float64(x / y) <= 2e-99))
		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) <= -2e+103) || ~(((x / y) <= 2e-99)))
		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], -2e+103], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-99]], $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) < -2e103 or 2e-99 < (/.f64 x y)

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 89.7%

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

   4. Taylor expanded in z around 0 79.2%

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

      1. +-commutative 79.2%

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

      2. associate-*r/ 79.4%

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

      3. associate-*l/ 82.1%

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

      4. associate-*r* 82.1%

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

      5. *-commutative 82.1%

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

      6. distribute-lft-out 89.7%

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

      7. mul-1-neg 89.7%

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

      8. sub-neg 89.7%

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

      9. div-sub 91.2%

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

   6. Simplified 91.2%

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

   if -2e103 < (/.f64 x y) < 2e-99

   1. Initial program 96.2%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. unsub-neg 69.9%

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

      3. *-rgt-identity 69.9%

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

      4. associate-/l* 75.1%

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

      5. distribute-lft-out-- 75.1%

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

   5. Simplified 75.1%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+103} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-99}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-6}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -100.0)
   (/ (* x (- z t)) y)
   (if (<= (/ x y) 2e-6) (+ t (* x (/ z y))) (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -100.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 2e-6) {
		tmp = t + (x * (z / y));
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-100.0d0)) then
        tmp = (x * (z - t)) / y
    else if ((x / y) <= 2d-6) then
        tmp = t + (x * (z / y))
    else
        tmp = x * ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -100.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 2e-6) {
		tmp = t + (x * (z / y));
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -100.0:
		tmp = (x * (z - t)) / y
	elif (x / y) <= 2e-6:
		tmp = t + (x * (z / y))
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -100.0)
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	elseif (Float64(x / y) <= 2e-6)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	else
		tmp = Float64(x * Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -100.0)
		tmp = (x * (z - t)) / y;
	elseif ((x / y) <= 2e-6)
		tmp = t + (x * (z / y));
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -100.0], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-6], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -100

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 89.5%

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

      1. *-commutative 89.5%

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

      2. sub-div 91.0%

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

      3. associate-*l/ 94.0%

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

   5. Applied egg-rr 94.0%

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

   if -100 < (/.f64 x y) < 1.99999999999999991e-6

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 94.6%

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

      1. associate-/l* 95.7%

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

   5. Simplified 95.7%

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

   if 1.99999999999999991e-6 < (/.f64 x y)

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 96.7%

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

   4. Taylor expanded in z around 0 76.0%

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

      1. +-commutative 76.0%

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

      2. associate-*r/ 80.7%

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

      3. associate-*l/ 85.2%

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

      4. associate-*r* 85.2%

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

      5. *-commutative 85.2%

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

      6. distribute-lft-out 96.7%

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

      7. mul-1-neg 96.7%

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

      8. sub-neg 96.7%

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

      9. div-sub 98.3%

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

   6. Simplified 98.3%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-6}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+49} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+49) (not (<= (/ x y) 2e-99))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+49) || !((x / y) <= 2e-99)) {
		tmp = (x / y) * z;
	} 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 / y) <= (-1d+49)) .or. (.not. ((x / y) <= 2d-99))) then
        tmp = (x / y) * z
    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 / y) <= -1e+49) || !((x / y) <= 2e-99)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+49) or not ((x / y) <= 2e-99):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+49) || !(Float64(x / y) <= 2e-99))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+49) || ~(((x / y) <= 2e-99)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+49], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-99]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999946e48 or 2e-99 < (/.f64 x y)

   1. Initial program 97.8%

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

   3. Taylor expanded in x around inf 88.2%

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

   4. Taylor expanded in z around inf 50.1%

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

      1. associate-*l/ 55.7%

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

      2. *-commutative 55.7%

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

   6. Simplified 55.7%

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

   if -9.99999999999999946e48 < (/.f64 x y) < 2e-99

   1. Initial program 96.0%

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

   3. Taylor expanded in x around 0 68.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+49} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.75e+118)
   (* x (/ z y))
   (if (<= z 1.5e+52) (* t (- 1.0 (/ x y))) (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+118) {
		tmp = x * (z / y);
	} else if (z <= 1.5e+52) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (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 (z <= (-2.75d+118)) then
        tmp = x * (z / y)
    else if (z <= 1.5d+52) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (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 (z <= -2.75e+118) {
		tmp = x * (z / y);
	} else if (z <= 1.5e+52) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.75e+118:
		tmp = x * (z / y)
	elif z <= 1.5e+52:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.75e+118)
		tmp = Float64(x * Float64(z / y));
	elseif (z <= 1.5e+52)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.75e+118)
		tmp = x * (z / y);
	elseif (z <= 1.5e+52)
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.75e+118], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+52], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7500000000000002e118

   1. Initial program 89.1%

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

   3. Taylor expanded in x around inf 74.5%

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

   4. Taylor expanded in z around inf 69.1%

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

      1. associate-*r/ 74.3%

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

   6. Simplified 74.3%

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

   if -2.7500000000000002e118 < z < 1.5e52

   1. Initial program 98.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   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. unsub-neg 74.0%

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

      3. *-rgt-identity 74.0%

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

      4. associate-/l* 79.3%

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

      5. distribute-lft-out-- 79.3%

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

   5. Simplified 79.3%

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

   if 1.5e52 < z

   1. Initial program 98.1%

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

   3. Taylor expanded in x around inf 72.3%

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

   4. Taylor expanded in z around inf 66.9%

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

      1. associate-*l/ 74.5%

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

      2. *-commutative 74.5%

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

   6. Simplified 74.5%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+97}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.42e+97) t (if (<= y 5.8e+37) (* x (/ z y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.42e+97) {
		tmp = t;
	} else if (y <= 5.8e+37) {
		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 (y <= (-1.42d+97)) then
        tmp = t
    else if (y <= 5.8d+37) 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 (y <= -1.42e+97) {
		tmp = t;
	} else if (y <= 5.8e+37) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.42e+97:
		tmp = t
	elif y <= 5.8e+37:
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.42e+97)
		tmp = t;
	elseif (y <= 5.8e+37)
		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 (y <= -1.42e+97)
		tmp = t;
	elseif (y <= 5.8e+37)
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.42e+97], t, If[LessEqual[y, 5.8e+37], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.41999999999999991e97 or 5.79999999999999957e37 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in x around 0 62.0%

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

   if -1.41999999999999991e97 < y < 5.79999999999999957e37

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 78.6%

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

   4. Taylor expanded in z around inf 50.3%

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

      1. associate-*r/ 48.8%

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

   6. Simplified 48.8%

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

Alternative 11: 97.6% 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 97.0%

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

3. Final simplification 97.0%

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

Alternative 12: 38.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

3. Taylor expanded in x around 0 35.1%

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

Developer target: 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 2024086 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))