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

Percentage Accurate: 97.9% → 94.0%

Time: 8.4s

Alternatives: 11

Speedup: 1.0×

• 24.8% 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: 97.9% 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: 94.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.0) (not (<= (/ x y) 4e+28)))
   (* x (/ (- z t) y))
   (+ t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.0) || !((x / y) <= 4e+28)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5.0d0)) .or. (.not. ((x / y) <= 4d+28))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + (z * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.0) || !((x / y) <= 4e+28)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + (z * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.0) or not ((x / y) <= 4e+28):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + (z * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5.0) || !(Float64(x / y) <= 4e+28))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	else
		tmp = Float64(t + Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5.0) || ~(((x / y) <= 4e+28)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + (z * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+28]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5 or 3.99999999999999983e28 < (/.f64 x y)

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

      2. clear-num 95.2%

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

      3. un-div-inv 95.6%

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

   4. Applied egg-rr 95.6%

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

   5. Taylor expanded in y around 0 94.5%

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

   6. Taylor expanded in x around -inf 94.1%

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

      1. associate-/l* 98.0%

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

      2. *-commutative 98.0%

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

   8. Applied egg-rr 98.0%

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

   if -5 < (/.f64 x y) < 3.99999999999999983e28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-/l* 96.2%

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

   5. Applied egg-rr 96.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 63.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ t_2 := x \cdot \frac{t}{-y}\\ t_3 := -t \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+295}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))) (t_2 (* x (/ t (- y)))) (t_3 (- (* t (/ x y)))))
   (if (<= (/ x y) -1e+295)
     t_3
     (if (<= (/ x y) -1e+66)
       t_1
       (if (<= (/ x y) -5e+22)
         t_2
         (if (<= (/ x y) -5e-82)
           t_1
           (if (<= (/ x y) 5e-124)
             t
             (if (<= (/ x y) 4e-95)
               t_1
               (if (<= (/ x y) 2e-21)
                 t
                 (if (<= (/ x y) 1e+118)
                   t_1
                   (if (<= (/ x y) 2e+187)
                     t_2
                     (if (<= (/ x y) 5e+289) (* x (/ z y)) t_3))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = x * (t / -y);
	double t_3 = -(t * (x / y));
	double tmp;
	if ((x / y) <= -1e+295) {
		tmp = t_3;
	} else if ((x / y) <= -1e+66) {
		tmp = t_1;
	} else if ((x / y) <= -5e+22) {
		tmp = t_2;
	} else if ((x / y) <= -5e-82) {
		tmp = t_1;
	} else if ((x / y) <= 5e-124) {
		tmp = t;
	} else if ((x / y) <= 4e-95) {
		tmp = t_1;
	} else if ((x / y) <= 2e-21) {
		tmp = t;
	} else if ((x / y) <= 1e+118) {
		tmp = t_1;
	} else if ((x / y) <= 2e+187) {
		tmp = t_2;
	} else if ((x / y) <= 5e+289) {
		tmp = x * (z / y);
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = z * (x / y)
    t_2 = x * (t / -y)
    t_3 = -(t * (x / y))
    if ((x / y) <= (-1d+295)) then
        tmp = t_3
    else if ((x / y) <= (-1d+66)) then
        tmp = t_1
    else if ((x / y) <= (-5d+22)) then
        tmp = t_2
    else if ((x / y) <= (-5d-82)) then
        tmp = t_1
    else if ((x / y) <= 5d-124) then
        tmp = t
    else if ((x / y) <= 4d-95) then
        tmp = t_1
    else if ((x / y) <= 2d-21) then
        tmp = t
    else if ((x / y) <= 1d+118) then
        tmp = t_1
    else if ((x / y) <= 2d+187) then
        tmp = t_2
    else if ((x / y) <= 5d+289) then
        tmp = x * (z / y)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = x * (t / -y);
	double t_3 = -(t * (x / y));
	double tmp;
	if ((x / y) <= -1e+295) {
		tmp = t_3;
	} else if ((x / y) <= -1e+66) {
		tmp = t_1;
	} else if ((x / y) <= -5e+22) {
		tmp = t_2;
	} else if ((x / y) <= -5e-82) {
		tmp = t_1;
	} else if ((x / y) <= 5e-124) {
		tmp = t;
	} else if ((x / y) <= 4e-95) {
		tmp = t_1;
	} else if ((x / y) <= 2e-21) {
		tmp = t;
	} else if ((x / y) <= 1e+118) {
		tmp = t_1;
	} else if ((x / y) <= 2e+187) {
		tmp = t_2;
	} else if ((x / y) <= 5e+289) {
		tmp = x * (z / y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	t_2 = x * (t / -y)
	t_3 = -(t * (x / y))
	tmp = 0
	if (x / y) <= -1e+295:
		tmp = t_3
	elif (x / y) <= -1e+66:
		tmp = t_1
	elif (x / y) <= -5e+22:
		tmp = t_2
	elif (x / y) <= -5e-82:
		tmp = t_1
	elif (x / y) <= 5e-124:
		tmp = t
	elif (x / y) <= 4e-95:
		tmp = t_1
	elif (x / y) <= 2e-21:
		tmp = t
	elif (x / y) <= 1e+118:
		tmp = t_1
	elif (x / y) <= 2e+187:
		tmp = t_2
	elif (x / y) <= 5e+289:
		tmp = x * (z / y)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	t_2 = Float64(x * Float64(t / Float64(-y)))
	t_3 = Float64(-Float64(t * Float64(x / y)))
	tmp = 0.0
	if (Float64(x / y) <= -1e+295)
		tmp = t_3;
	elseif (Float64(x / y) <= -1e+66)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e+22)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e-82)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-124)
		tmp = t;
	elseif (Float64(x / y) <= 4e-95)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-21)
		tmp = t;
	elseif (Float64(x / y) <= 1e+118)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e+187)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e+289)
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	t_2 = x * (t / -y);
	t_3 = -(t * (x / y));
	tmp = 0.0;
	if ((x / y) <= -1e+295)
		tmp = t_3;
	elseif ((x / y) <= -1e+66)
		tmp = t_1;
	elseif ((x / y) <= -5e+22)
		tmp = t_2;
	elseif ((x / y) <= -5e-82)
		tmp = t_1;
	elseif ((x / y) <= 5e-124)
		tmp = t;
	elseif ((x / y) <= 4e-95)
		tmp = t_1;
	elseif ((x / y) <= 2e-21)
		tmp = t;
	elseif ((x / y) <= 1e+118)
		tmp = t_1;
	elseif ((x / y) <= 2e+187)
		tmp = t_2;
	elseif ((x / y) <= 5e+289)
		tmp = x * (z / y);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = (-N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+295], t$95$3, If[LessEqual[N[(x / y), $MachinePrecision], -1e+66], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e+22], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e-82], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-124], t, If[LessEqual[N[(x / y), $MachinePrecision], 4e-95], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-21], t, If[LessEqual[N[(x / y), $MachinePrecision], 1e+118], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e+187], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e+289], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -9.9999999999999998e294 or 5.00000000000000031e289 < (/.f64 x y)

   1. Initial program 86.2%

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

      1. *-commutative 86.2%

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

      2. clear-num 86.2%

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

      3. un-div-inv 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in z around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. associate-*l/ 65.0%

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

      3. distribute-rgt-neg-in 65.0%

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

   7. Simplified 65.0%

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

      1. +-commutative 65.0%

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

      2. distribute-rgt-neg-out 65.0%

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

      3. unsub-neg 65.0%

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

      4. *-commutative 65.0%

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

   9. Applied egg-rr 65.0%

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

   10. Taylor expanded in x around inf 65.0%

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

       1. mul-1-neg 65.0%

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

       2. associate-*l/ 65.0%

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

       3. distribute-rgt-neg-in 65.0%

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

       4. associate-*l/ 65.0%

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

       5. associate-*r/ 71.6%

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

   12. Simplified 71.6%

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

   if -9.9999999999999998e294 < (/.f64 x y) < -9.99999999999999945e65 or -4.9999999999999996e22 < (/.f64 x y) < -4.9999999999999998e-82 or 5.0000000000000003e-124 < (/.f64 x y) < 3.99999999999999996e-95 or 1.99999999999999982e-21 < (/.f64 x y) < 9.99999999999999967e117

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in y around 0 83.7%

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

   6. Taylor expanded in x around -inf 77.9%

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

   7. Taylor expanded in z around inf 59.4%

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

      1. associate-*l/ 67.6%

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

      2. *-commutative 67.6%

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

   9. Simplified 67.6%

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

   if -9.99999999999999945e65 < (/.f64 x y) < -4.9999999999999996e22 or 9.99999999999999967e117 < (/.f64 x y) < 1.99999999999999981e187

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. associate-*l/ 76.1%

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

      3. distribute-rgt-neg-in 76.1%

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

   7. Simplified 76.1%

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

      1. +-commutative 76.1%

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

      2. distribute-rgt-neg-out 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

   9. Applied egg-rr 76.1%

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

   10. Taylor expanded in x around inf 65.1%

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

       1. mul-1-neg 65.1%

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

       2. associate-*l/ 76.1%

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

       3. distribute-rgt-neg-in 76.1%

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

   12. Simplified 76.1%

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

   if -4.9999999999999998e-82 < (/.f64 x y) < 5.0000000000000003e-124 or 3.99999999999999996e-95 < (/.f64 x y) < 1.99999999999999982e-21

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 82.7%

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

   if 1.99999999999999981e187 < (/.f64 x y) < 5.00000000000000031e289

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 99.9%

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

   6. Taylor expanded in x around -inf 99.9%

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

   7. Taylor expanded in z around inf 87.7%

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

      1. associate-*r/ 87.8%

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

   9. Simplified 87.8%

      \[\leadsto \color{blue}{x \cdot \frac{z}{y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+295}:\\ \;\;\;\;-t \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+118}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;-t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ t_2 := -t \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+295}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+22}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))) (t_2 (- (* t (/ x y)))))
   (if (<= (/ x y) -1e+295)
     t_2
     (if (<= (/ x y) -1e+66)
       t_1
       (if (<= (/ x y) -5e+22)
         t_2
         (if (<= (/ x y) -5e-82)
           t_1
           (if (<= (/ x y) 5e-124)
             t
             (if (<= (/ x y) 4e-95)
               t_1
               (if (<= (/ x y) 2e-21)
                 t
                 (if (<= (/ x y) 5e+289) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double t_2 = -(t * (x / y));
	double tmp;
	if ((x / y) <= -1e+295) {
		tmp = t_2;
	} else if ((x / y) <= -1e+66) {
		tmp = t_1;
	} else if ((x / y) <= -5e+22) {
		tmp = t_2;
	} else if ((x / y) <= -5e-82) {
		tmp = t_1;
	} else if ((x / y) <= 5e-124) {
		tmp = t;
	} else if ((x / y) <= 4e-95) {
		tmp = t_1;
	} else if ((x / y) <= 2e-21) {
		tmp = t;
	} else if ((x / y) <= 5e+289) {
		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 = z * (x / y)
    t_2 = -(t * (x / y))
    if ((x / y) <= (-1d+295)) then
        tmp = t_2
    else if ((x / y) <= (-1d+66)) then
        tmp = t_1
    else if ((x / y) <= (-5d+22)) then
        tmp = t_2
    else if ((x / y) <= (-5d-82)) then
        tmp = t_1
    else if ((x / y) <= 5d-124) then
        tmp = t
    else if ((x / y) <= 4d-95) then
        tmp = t_1
    else if ((x / y) <= 2d-21) then
        tmp = t
    else if ((x / y) <= 5d+289) 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 = z * (x / y);
	double t_2 = -(t * (x / y));
	double tmp;
	if ((x / y) <= -1e+295) {
		tmp = t_2;
	} else if ((x / y) <= -1e+66) {
		tmp = t_1;
	} else if ((x / y) <= -5e+22) {
		tmp = t_2;
	} else if ((x / y) <= -5e-82) {
		tmp = t_1;
	} else if ((x / y) <= 5e-124) {
		tmp = t;
	} else if ((x / y) <= 4e-95) {
		tmp = t_1;
	} else if ((x / y) <= 2e-21) {
		tmp = t;
	} else if ((x / y) <= 5e+289) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	t_2 = -(t * (x / y))
	tmp = 0
	if (x / y) <= -1e+295:
		tmp = t_2
	elif (x / y) <= -1e+66:
		tmp = t_1
	elif (x / y) <= -5e+22:
		tmp = t_2
	elif (x / y) <= -5e-82:
		tmp = t_1
	elif (x / y) <= 5e-124:
		tmp = t
	elif (x / y) <= 4e-95:
		tmp = t_1
	elif (x / y) <= 2e-21:
		tmp = t
	elif (x / y) <= 5e+289:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	t_2 = Float64(-Float64(t * Float64(x / y)))
	tmp = 0.0
	if (Float64(x / y) <= -1e+295)
		tmp = t_2;
	elseif (Float64(x / y) <= -1e+66)
		tmp = t_1;
	elseif (Float64(x / y) <= -5e+22)
		tmp = t_2;
	elseif (Float64(x / y) <= -5e-82)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-124)
		tmp = t;
	elseif (Float64(x / y) <= 4e-95)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-21)
		tmp = t;
	elseif (Float64(x / y) <= 5e+289)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	t_2 = -(t * (x / y));
	tmp = 0.0;
	if ((x / y) <= -1e+295)
		tmp = t_2;
	elseif ((x / y) <= -1e+66)
		tmp = t_1;
	elseif ((x / y) <= -5e+22)
		tmp = t_2;
	elseif ((x / y) <= -5e-82)
		tmp = t_1;
	elseif ((x / y) <= 5e-124)
		tmp = t;
	elseif ((x / y) <= 4e-95)
		tmp = t_1;
	elseif ((x / y) <= 2e-21)
		tmp = t;
	elseif ((x / y) <= 5e+289)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+295], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -1e+66], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5e+22], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -5e-82], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-124], t, If[LessEqual[N[(x / y), $MachinePrecision], 4e-95], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-21], t, If[LessEqual[N[(x / y), $MachinePrecision], 5e+289], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999998e294 or -9.99999999999999945e65 < (/.f64 x y) < -4.9999999999999996e22 or 5.00000000000000031e289 < (/.f64 x y)

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

      2. clear-num 88.7%

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

      3. un-div-inv 89.7%

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

   4. Applied egg-rr 89.7%

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

   5. Taylor expanded in z around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. associate-*l/ 66.0%

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

      3. distribute-rgt-neg-in 66.0%

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

   7. Simplified 66.0%

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

      1. +-commutative 66.0%

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

      2. distribute-rgt-neg-out 66.0%

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

      3. unsub-neg 66.0%

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

      4. *-commutative 66.0%

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

   9. Applied egg-rr 66.0%

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

   10. Taylor expanded in x around inf 65.5%

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

       1. mul-1-neg 65.5%

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

       2. associate-*l/ 66.0%

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

       3. distribute-rgt-neg-in 66.0%

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

       4. associate-*l/ 65.5%

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

       5. associate-*r/ 71.4%

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

   12. Simplified 71.4%

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

   if -9.9999999999999998e294 < (/.f64 x y) < -9.99999999999999945e65 or -4.9999999999999996e22 < (/.f64 x y) < -4.9999999999999998e-82 or 5.0000000000000003e-124 < (/.f64 x y) < 3.99999999999999996e-95 or 1.99999999999999982e-21 < (/.f64 x y) < 5.00000000000000031e289

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around 0 86.8%

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

   6. Taylor expanded in x around -inf 82.3%

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

   7. Taylor expanded in z around inf 61.5%

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

      1. associate-*l/ 67.8%

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

      2. *-commutative 67.8%

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

   9. Simplified 67.8%

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

   if -4.9999999999999998e-82 < (/.f64 x y) < 5.0000000000000003e-124 or 3.99999999999999996e-95 < (/.f64 x y) < 1.99999999999999982e-21

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 82.7%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+295}:\\ \;\;\;\;-t \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+22}:\\ \;\;\;\;-t \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-124}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+289}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))) (t_2 (* x (/ (- z t) y))))
   (if (<= (/ x y) -1e-23)
     t_2
     (if (<= (/ x y) 5e-124)
       t_1
       (if (<= (/ x y) 4e-95)
         (* z (/ x y))
         (if (<= (/ x y) 2e-21) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e-23) {
		tmp = t_2;
	} else if ((x / y) <= 5e-124) {
		tmp = t_1;
	} else if ((x / y) <= 4e-95) {
		tmp = z * (x / y);
	} else if ((x / y) <= 2e-21) {
		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 = t * (1.0d0 - (x / y))
    t_2 = x * ((z - t) / y)
    if ((x / y) <= (-1d-23)) then
        tmp = t_2
    else if ((x / y) <= 5d-124) then
        tmp = t_1
    else if ((x / y) <= 4d-95) then
        tmp = z * (x / y)
    else if ((x / y) <= 2d-21) 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 = t * (1.0 - (x / y));
	double t_2 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -1e-23) {
		tmp = t_2;
	} else if ((x / y) <= 5e-124) {
		tmp = t_1;
	} else if ((x / y) <= 4e-95) {
		tmp = z * (x / y);
	} else if ((x / y) <= 2e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	t_2 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -1e-23:
		tmp = t_2
	elif (x / y) <= 5e-124:
		tmp = t_1
	elif (x / y) <= 4e-95:
		tmp = z * (x / y)
	elif (x / y) <= 2e-21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_2 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e-23)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e-124)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-95)
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= 2e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	t_2 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -1e-23)
		tmp = t_2;
	elseif ((x / y) <= 5e-124)
		tmp = t_1;
	elseif ((x / y) <= 4e-95)
		tmp = z * (x / y);
	elseif ((x / y) <= 2e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-23], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e-124], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-95], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-21], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999996e-24 or 1.99999999999999982e-21 < (/.f64 x y)

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.7%

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

      3. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in y around 0 91.8%

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

   6. Taylor expanded in x around -inf 91.1%

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

      1. associate-/l* 94.5%

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

      2. *-commutative 94.5%

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

   8. Applied egg-rr 94.5%

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

   if -9.9999999999999996e-24 < (/.f64 x y) < 5.0000000000000003e-124 or 3.99999999999999996e-95 < (/.f64 x y) < 1.99999999999999982e-21

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 73.9%

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

      1. mul-1-neg 73.9%

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

      2. unsub-neg 73.9%

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

      3. *-rgt-identity 73.9%

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

      4. associate-/l* 77.3%

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

      5. distribute-lft-out-- 77.3%

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

   5. Simplified 77.3%

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

   if 5.0000000000000003e-124 < (/.f64 x y) < 3.99999999999999996e-95

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around 0 99.7%

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

   6. Taylor expanded in x around -inf 98.8%

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

   7. Taylor expanded in z around inf 98.8%

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

      1. associate-*l/ 99.1%

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

      2. *-commutative 99.1%

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

   9. Simplified 99.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-95}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-82} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-124}\right) \land \left(\frac{x}{y} \leq 4 \cdot 10^{-95} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-21}\right)\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-82)
         (and (not (<= (/ x y) 5e-124))
              (or (<= (/ x y) 4e-95) (not (<= (/ x y) 2e-21)))))
   (* z (/ x y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-82) || (!((x / y) <= 5e-124) && (((x / y) <= 4e-95) || !((x / y) <= 2e-21)))) {
		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 (((x / y) <= (-5d-82)) .or. (.not. ((x / y) <= 5d-124)) .and. ((x / y) <= 4d-95) .or. (.not. ((x / y) <= 2d-21))) 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 (((x / y) <= -5e-82) || (!((x / y) <= 5e-124) && (((x / y) <= 4e-95) || !((x / y) <= 2e-21)))) {
		tmp = z * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-82) or (not ((x / y) <= 5e-124) and (((x / y) <= 4e-95) or not ((x / y) <= 2e-21))):
		tmp = z * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-82) || (!(Float64(x / y) <= 5e-124) && ((Float64(x / y) <= 4e-95) || !(Float64(x / y) <= 2e-21))))
		tmp = Float64(z * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-82) || (~(((x / y) <= 5e-124)) && (((x / y) <= 4e-95) || ~(((x / y) <= 2e-21)))))
		tmp = z * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-82], And[N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-124]], $MachinePrecision], Or[LessEqual[N[(x / y), $MachinePrecision], 4e-95], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-21]], $MachinePrecision]]]], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999998e-82 or 5.0000000000000003e-124 < (/.f64 x y) < 3.99999999999999996e-95 or 1.99999999999999982e-21 < (/.f64 x y)

   1. Initial program 96.3%

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

      1. *-commutative 96.3%

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

      2. clear-num 96.2%

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

      3. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in y around 0 90.4%

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

   6. Taylor expanded in x around -inf 87.4%

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

   7. Taylor expanded in z around inf 54.4%

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

      1. associate-*l/ 58.6%

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

      2. *-commutative 58.6%

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

   9. Simplified 58.6%

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

   if -4.9999999999999998e-82 < (/.f64 x y) < 5.0000000000000003e-124 or 3.99999999999999996e-95 < (/.f64 x y) < 1.99999999999999982e-21

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 82.7%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-82} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-124}\right) \land \left(\frac{x}{y} \leq 4 \cdot 10^{-95} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-21}\right)\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.0) (not (<= (/ x y) 2e-21)))
   (* x (/ (- z t) y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.0) || !((x / y) <= 2e-21)) {
		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) <= (-5.0d0)) .or. (.not. ((x / y) <= 2d-21))) 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) <= -5.0) || !((x / y) <= 2e-21)) {
		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) <= -5.0) or not ((x / y) <= 2e-21):
		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) <= -5.0) || !(Float64(x / y) <= 2e-21))
		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) <= -5.0) || ~(((x / y) <= 2e-21)))
		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], -5.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-21]], $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) < -5 or 1.99999999999999982e-21 < (/.f64 x y)

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

      2. clear-num 95.7%

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

      3. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in y around 0 91.7%

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

   6. Taylor expanded in x around -inf 91.0%

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

      1. associate-/l* 94.4%

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

      2. *-commutative 94.4%

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

   8. Applied egg-rr 94.4%

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

   if -5 < (/.f64 x y) < 1.99999999999999982e-21

   1. Initial program 98.3%

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

   3. Taylor expanded in z around inf 95.1%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+23} \lor \neg \left(z \leq 1.3 \cdot 10^{+149}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e+23) (not (<= z 1.3e+149)))
   (* z (/ x y))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e+23) || !(z <= 1.3e+149)) {
		tmp = z * (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 ((z <= (-8.5d+23)) .or. (.not. (z <= 1.3d+149))) then
        tmp = z * (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 ((z <= -8.5e+23) || !(z <= 1.3e+149)) {
		tmp = z * (x / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e+23) or not (z <= 1.3e+149):
		tmp = z * (x / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e+23) || !(z <= 1.3e+149))
		tmp = Float64(z * 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 ((z <= -8.5e+23) || ~((z <= 1.3e+149)))
		tmp = z * (x / y);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e+23], N[Not[LessEqual[z, 1.3e+149]], $MachinePrecision]], N[(z * 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 z < -8.5000000000000001e23 or 1.29999999999999989e149 < z

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

      2. clear-num 97.7%

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

      3. un-div-inv 97.8%

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

   4. Applied egg-rr 97.8%

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

   5. Taylor expanded in y around 0 90.3%

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

   6. Taylor expanded in x around -inf 72.3%

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

   7. Taylor expanded in z around inf 66.6%

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

      1. associate-*l/ 72.2%

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

      2. *-commutative 72.2%

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

   9. Simplified 72.2%

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

   if -8.5000000000000001e23 < z < 1.29999999999999989e149

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 72.4%

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

      1. mul-1-neg 72.4%

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

      2. unsub-neg 72.4%

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

      3. *-rgt-identity 72.4%

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

      4. associate-/l* 76.7%

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

      5. distribute-lft-out-- 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+23} \lor \neg \left(z \leq 1.3 \cdot 10^{+149}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -430000 \lor \neg \left(x \leq 1.5 \cdot 10^{-162}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -430000.0) (not (<= x 1.5e-162))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -430000.0) || !(x <= 1.5e-162)) {
		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 <= (-430000.0d0)) .or. (.not. (x <= 1.5d-162))) 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 <= -430000.0) || !(x <= 1.5e-162)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -430000.0) or not (x <= 1.5e-162):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -430000.0) || !(x <= 1.5e-162))
		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 <= -430000.0) || ~((x <= 1.5e-162)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -430000.0], N[Not[LessEqual[x, 1.5e-162]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -4.3e5 or 1.49999999999999999e-162 < x

   1. Initial program 96.4%

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

      1. *-commutative 96.4%

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

      2. clear-num 96.3%

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

      3. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in y around 0 87.8%

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

   6. Taylor expanded in x around -inf 76.2%

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

   7. Taylor expanded in z around inf 46.9%

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

      1. associate-*r/ 50.2%

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

   9. Simplified 50.2%

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

   if -4.3e5 < x < 1.49999999999999999e-162

   1. Initial program 97.9%

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

   3. Taylor expanded in x around 0 69.0%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -430000 \lor \neg \left(x \leq 1.5 \cdot 10^{-162}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.0% 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 96.9%

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

   1. *-commutative 96.9%

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

   2. clear-num 96.9%

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

   3. un-div-inv 97.1%

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

4. Applied egg-rr 97.1%

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

5. Final simplification 97.1%

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

Alternative 10: 97.9% 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 96.9%

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

3. Final simplification 96.9%

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

Alternative 11: 39.0% 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 96.9%

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

3. Taylor expanded in x around 0 35.8%

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

4. Final simplification 35.8%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.5% 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 2024096 
(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))