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

Percentage Accurate: 97.5% → 97.6%

Time: 7.6s

Alternatives: 14

Speedup: 1.0×

• 25.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% 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, 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 97.6%

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

   1. *-commutative 97.6%

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

   2. clear-num 97.6%

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

   3. un-div-inv 97.7%

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

4. Applied egg-rr 97.7%

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

5. Final simplification 97.7%

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

Alternative 2: 63.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- y)))))
   (if (<= (/ x y) -2e+274)
     (* x (/ z y))
     (if (<= (/ x y) -2e+19)
       t_1
       (if (<= (/ x y) -1e-66)
         (* z (/ x y))
         (if (<= (/ x y) 0.0002) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / -y);
	double tmp;
	if ((x / y) <= -2e+274) {
		tmp = x * (z / y);
	} else if ((x / y) <= -2e+19) {
		tmp = t_1;
	} else if ((x / y) <= -1e-66) {
		tmp = z * (x / y);
	} else if ((x / y) <= 0.0002) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / -y)
    if ((x / y) <= (-2d+274)) then
        tmp = x * (z / y)
    else if ((x / y) <= (-2d+19)) then
        tmp = t_1
    else if ((x / y) <= (-1d-66)) then
        tmp = z * (x / y)
    else if ((x / y) <= 0.0002d0) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / -y);
	double tmp;
	if ((x / y) <= -2e+274) {
		tmp = x * (z / y);
	} else if ((x / y) <= -2e+19) {
		tmp = t_1;
	} else if ((x / y) <= -1e-66) {
		tmp = z * (x / y);
	} else if ((x / y) <= 0.0002) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / -y)
	tmp = 0
	if (x / y) <= -2e+274:
		tmp = x * (z / y)
	elif (x / y) <= -2e+19:
		tmp = t_1
	elif (x / y) <= -1e-66:
		tmp = z * (x / y)
	elif (x / y) <= 0.0002:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(-y)))
	tmp = 0.0
	if (Float64(x / y) <= -2e+274)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= -2e+19)
		tmp = t_1;
	elseif (Float64(x / y) <= -1e-66)
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= 0.0002)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / -y);
	tmp = 0.0;
	if ((x / y) <= -2e+274)
		tmp = x * (z / y);
	elseif ((x / y) <= -2e+19)
		tmp = t_1;
	elseif ((x / y) <= -1e-66)
		tmp = z * (x / y);
	elseif ((x / y) <= 0.0002)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+274], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e+19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1e-66], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0002], t, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -1.99999999999999984e274

   1. Initial program 82.5%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 82.5%

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

   6. Applied egg-rr 82.5%

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

   7. Taylor expanded in z around inf 81.2%

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

      1. associate-/l* 81.3%

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

   9. Simplified 81.3%

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

   if -1.99999999999999984e274 < (/.f64 x y) < -2e19 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 91.7%

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

   4. Taylor expanded in y around 0 91.4%

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

   5. Taylor expanded in z around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. associate-/l* 61.8%

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

      3. *-commutative 61.8%

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

      4. distribute-rgt-neg-in 61.8%

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

   7. Simplified 61.8%

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

   if -2e19 < (/.f64 x y) < -9.9999999999999998e-67

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 91.3%

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

   4. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/l* 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around inf 82.5%

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

      1. associate-*l/ 90.8%

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

   9. Simplified 90.8%

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

   if -9.9999999999999998e-67 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 80.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- t) (/ y x))))
   (if (<= (/ x y) -2e+274)
     (* x (/ z y))
     (if (<= (/ x y) -2e+19)
       t_1
       (if (<= (/ x y) -1e-66)
         (* z (/ x y))
         (if (<= (/ x y) 0.0002) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -t / (y / x);
	double tmp;
	if ((x / y) <= -2e+274) {
		tmp = x * (z / y);
	} else if ((x / y) <= -2e+19) {
		tmp = t_1;
	} else if ((x / y) <= -1e-66) {
		tmp = z * (x / y);
	} else if ((x / y) <= 0.0002) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -t / (y / x)
    if ((x / y) <= (-2d+274)) then
        tmp = x * (z / y)
    else if ((x / y) <= (-2d+19)) then
        tmp = t_1
    else if ((x / y) <= (-1d-66)) then
        tmp = z * (x / y)
    else if ((x / y) <= 0.0002d0) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -t / (y / x);
	double tmp;
	if ((x / y) <= -2e+274) {
		tmp = x * (z / y);
	} else if ((x / y) <= -2e+19) {
		tmp = t_1;
	} else if ((x / y) <= -1e-66) {
		tmp = z * (x / y);
	} else if ((x / y) <= 0.0002) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -t / (y / x)
	tmp = 0
	if (x / y) <= -2e+274:
		tmp = x * (z / y)
	elif (x / y) <= -2e+19:
		tmp = t_1
	elif (x / y) <= -1e-66:
		tmp = z * (x / y)
	elif (x / y) <= 0.0002:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-t) / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -2e+274)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= -2e+19)
		tmp = t_1;
	elseif (Float64(x / y) <= -1e-66)
		tmp = Float64(z * Float64(x / y));
	elseif (Float64(x / y) <= 0.0002)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -t / (y / x);
	tmp = 0.0;
	if ((x / y) <= -2e+274)
		tmp = x * (z / y);
	elseif ((x / y) <= -2e+19)
		tmp = t_1;
	elseif ((x / y) <= -1e-66)
		tmp = z * (x / y);
	elseif ((x / y) <= 0.0002)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-t) / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+274], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2e+19], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1e-66], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0002], t, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -1.99999999999999984e274

   1. Initial program 82.5%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 82.5%

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

   6. Applied egg-rr 82.5%

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

   7. Taylor expanded in z around inf 81.2%

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

      1. associate-/l* 81.3%

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

   9. Simplified 81.3%

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

   if -1.99999999999999984e274 < (/.f64 x y) < -2e19 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 91.7%

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

   4. Taylor expanded in y around 0 91.4%

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

   5. Taylor expanded in z around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. associate-/l* 61.8%

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

      3. *-commutative 61.8%

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

      4. distribute-rgt-neg-in 61.8%

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

   7. Simplified 61.8%

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

      1. clear-num 61.8%

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

      2. associate-/r/ 61.9%

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

      3. clear-num 61.9%

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

      4. frac-2neg 61.9%

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

      5. remove-double-neg 61.9%

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

      6. distribute-neg-frac2 61.9%

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

   9. Applied egg-rr 61.9%

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

   if -2e19 < (/.f64 x y) < -9.9999999999999998e-67

   1. Initial program 99.6%

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

   3. Taylor expanded in y around 0 91.3%

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

   4. Taylor expanded in y around 0 85.7%

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

      1. *-commutative 85.7%

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

      2. associate-/l* 93.9%

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

   6. Applied egg-rr 93.9%

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

   7. Taylor expanded in z around inf 82.5%

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

      1. associate-*l/ 90.8%

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

   9. Simplified 90.8%

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

   if -9.9999999999999998e-67 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 80.8%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+274}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+19}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-163}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-150} \lor \neg \left(t \leq 2.2 \cdot 10^{-95}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -2.5e-194)
     t_1
     (if (<= t 2.9e-163)
       (/ (* z x) y)
       (if (or (<= t 2.8e-150) (not (<= t 2.2e-95))) t_1 (* z (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -2.5e-194) {
		tmp = t_1;
	} else if (t <= 2.9e-163) {
		tmp = (z * x) / y;
	} else if ((t <= 2.8e-150) || !(t <= 2.2e-95)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (t <= (-2.5d-194)) then
        tmp = t_1
    else if (t <= 2.9d-163) then
        tmp = (z * x) / y
    else if ((t <= 2.8d-150) .or. (.not. (t <= 2.2d-95))) then
        tmp = t_1
    else
        tmp = z * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -2.5e-194) {
		tmp = t_1;
	} else if (t <= 2.9e-163) {
		tmp = (z * x) / y;
	} else if ((t <= 2.8e-150) || !(t <= 2.2e-95)) {
		tmp = t_1;
	} else {
		tmp = z * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -2.5e-194:
		tmp = t_1
	elif t <= 2.9e-163:
		tmp = (z * x) / y
	elif (t <= 2.8e-150) or not (t <= 2.2e-95):
		tmp = t_1
	else:
		tmp = z * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -2.5e-194)
		tmp = t_1;
	elseif (t <= 2.9e-163)
		tmp = Float64(Float64(z * x) / y);
	elseif ((t <= 2.8e-150) || !(t <= 2.2e-95))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -2.5e-194)
		tmp = t_1;
	elseif (t <= 2.9e-163)
		tmp = (z * x) / y;
	elseif ((t <= 2.8e-150) || ~((t <= 2.2e-95)))
		tmp = t_1;
	else
		tmp = z * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e-194], t$95$1, If[LessEqual[t, 2.9e-163], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[t, 2.8e-150], N[Not[LessEqual[t, 2.2e-95]], $MachinePrecision]], t$95$1, N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5000000000000001e-194 or 2.9000000000000001e-163 < t < 2.79999999999999996e-150 or 2.1999999999999999e-95 < t

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. *-rgt-identity 75.5%

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

      4. associate-/l* 81.8%

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

      5. distribute-lft-out-- 81.8%

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

   5. Simplified 81.8%

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

   if -2.5000000000000001e-194 < t < 2.9000000000000001e-163

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 94.8%

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

   4. Taylor expanded in t around 0 76.0%

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

   if 2.79999999999999996e-150 < t < 2.1999999999999999e-95

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 96.2%

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

   4. Taylor expanded in y around 0 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-/l* 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in z around inf 73.7%

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

      1. associate-*l/ 74.0%

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

   9. Simplified 74.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-194}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-163}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-150} \lor \neg \left(t \leq 2.2 \cdot 10^{-95}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{y}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-48} \lor \neg \left(x \leq 3.1 \cdot 10^{-106}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ z y))))
   (if (<= x -3.6e+91)
     t_1
     (if (<= x -7.2e-30)
       (* y (/ t y))
       (if (or (<= x -4.8e-48) (not (<= x 3.1e-106))) t_1 t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z / y);
	double tmp;
	if (x <= -3.6e+91) {
		tmp = t_1;
	} else if (x <= -7.2e-30) {
		tmp = y * (t / y);
	} else if ((x <= -4.8e-48) || !(x <= 3.1e-106)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (z / y)
    if (x <= (-3.6d+91)) then
        tmp = t_1
    else if (x <= (-7.2d-30)) then
        tmp = y * (t / y)
    else if ((x <= (-4.8d-48)) .or. (.not. (x <= 3.1d-106))) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z / y);
	double tmp;
	if (x <= -3.6e+91) {
		tmp = t_1;
	} else if (x <= -7.2e-30) {
		tmp = y * (t / y);
	} else if ((x <= -4.8e-48) || !(x <= 3.1e-106)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z / y)
	tmp = 0
	if x <= -3.6e+91:
		tmp = t_1
	elif x <= -7.2e-30:
		tmp = y * (t / y)
	elif (x <= -4.8e-48) or not (x <= 3.1e-106):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z / y))
	tmp = 0.0
	if (x <= -3.6e+91)
		tmp = t_1;
	elseif (x <= -7.2e-30)
		tmp = Float64(y * Float64(t / y));
	elseif ((x <= -4.8e-48) || !(x <= 3.1e-106))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z / y);
	tmp = 0.0;
	if (x <= -3.6e+91)
		tmp = t_1;
	elseif (x <= -7.2e-30)
		tmp = y * (t / y);
	elseif ((x <= -4.8e-48) || ~((x <= 3.1e-106)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.6e+91], t$95$1, If[LessEqual[x, -7.2e-30], N[(y * N[(t / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -4.8e-48], N[Not[LessEqual[x, 3.1e-106]], $MachinePrecision]], t$95$1, t]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.6e91 or -7.2000000000000006e-30 < x < -4.8e-48 or 3.09999999999999985e-106 < x

   1. Initial program 96.7%

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

   3. Taylor expanded in y around 0 84.5%

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

   4. Taylor expanded in y around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. associate-/l* 84.9%

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

   6. Applied egg-rr 84.9%

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

   7. Taylor expanded in z around inf 47.3%

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

      1. associate-/l* 52.7%

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

   9. Simplified 52.7%

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

   if -3.6e91 < x < -7.2000000000000006e-30

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 83.6%

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

   4. Taylor expanded in y around inf 21.2%

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

      1. *-commutative 21.2%

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

      2. associate-/l* 45.1%

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

   6. Applied egg-rr 45.1%

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

   if -4.8e-48 < x < 3.09999999999999985e-106

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 70.8%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \frac{t}{y}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-48} \lor \neg \left(x \leq 3.1 \cdot 10^{-106}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 20000000\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-66) (not (<= (/ x y) 20000000.0)))
   (* (- z t) (/ x y))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-66) || !((x / y) <= 20000000.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d-66)) .or. (.not. ((x / y) <= 20000000.0d0))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-66) || !((x / y) <= 20000000.0)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-66) or not ((x / y) <= 20000000.0):
		tmp = (z - t) * (x / y)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-66) || !(Float64(x / y) <= 20000000.0))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e-66) || ~(((x / y) <= 20000000.0)))
		tmp = (z - t) * (x / y);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-66], N[Not[LessEqual[N[(x / y), $MachinePrecision], 20000000.0]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999998e-67 or 2e7 < (/.f64 x y)

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 92.6%

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

   4. Taylor expanded in y around 0 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-/l* 96.5%

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

   6. Applied egg-rr 96.5%

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

   if -9.9999999999999998e-67 < (/.f64 x y) < 2e7

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 77.7%

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

      1. mul-1-neg 77.7%

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

      2. unsub-neg 77.7%

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

      3. *-rgt-identity 77.7%

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

      4. associate-/l* 82.1%

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

      5. distribute-lft-out-- 82.1%

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

   5. Simplified 82.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 20000000\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-43) (not (<= (/ x y) 0.0002)))
   (* (- z t) (/ x y))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-43) || !((x / y) <= 0.0002)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d-43)) .or. (.not. ((x / y) <= 0.0002d0))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-43) || !((x / y) <= 0.0002)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-43) or not ((x / y) <= 0.0002):
		tmp = (z - t) * (x / y)
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-43) || !(Float64(x / y) <= 0.0002))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-43) || ~(((x / y) <= 0.0002)))
		tmp = (z - t) * (x / y);
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-43], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000019e-43 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 92.5%

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

   4. Taylor expanded in y around 0 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-/l* 96.1%

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

   6. Applied egg-rr 96.1%

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

   if -5.00000000000000019e-43 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 95.0%

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

      1. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-43) (not (<= (/ x y) 0.0002)))
   (* (- z t) (/ x y))
   (+ t (/ x (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-43) || !((x / y) <= 0.0002)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d-43)) .or. (.not. ((x / y) <= 0.0002d0))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t + (x / (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-43) || !((x / y) <= 0.0002)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (x / (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-43) or not ((x / y) <= 0.0002):
		tmp = (z - t) * (x / y)
	else:
		tmp = t + (x / (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-43) || !(Float64(x / y) <= 0.0002))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t + Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-43) || ~(((x / y) <= 0.0002)))
		tmp = (z - t) * (x / y);
	else
		tmp = t + (x / (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-43], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000019e-43 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 92.5%

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

   4. Taylor expanded in y around 0 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-/l* 96.1%

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

   6. Applied egg-rr 96.1%

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

   if -5.00000000000000019e-43 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 95.0%

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

      1. associate-/l* 93.4%

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

   5. Simplified 93.4%

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

      1. clear-num 93.4%

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

      2. un-div-inv 94.0%

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

   7. Applied egg-rr 94.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-43} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5000.0) (not (<= (/ x y) 0.0002)))
   (* (- z t) (/ x y))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5000.0) || !((x / y) <= 0.0002)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (z / (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) :: tmp
    if (((x / y) <= (-5000.0d0)) .or. (.not. ((x / y) <= 0.0002d0))) then
        tmp = (z - t) * (x / y)
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5000.0) || !((x / y) <= 0.0002)) {
		tmp = (z - t) * (x / y);
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5000.0) or not ((x / y) <= 0.0002):
		tmp = (z - t) * (x / y)
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5000.0) || !(Float64(x / y) <= 0.0002))
		tmp = Float64(Float64(z - t) * Float64(x / y));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5000.0) || ~(((x / y) <= 0.0002)))
		tmp = (z - t) * (x / y);
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e3 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 93.0%

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

   4. Taylor expanded in y around 0 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-/l* 96.0%

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

   6. Applied egg-rr 96.0%

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

   if -5e3 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 94.4%

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

      1. associate-/l* 92.2%

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

   5. Simplified 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-/r/ 97.3%

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

   7. Applied egg-rr 97.3%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e-66) (not (<= (/ x y) 0.0002))) (* z (/ x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e-66) || !((x / y) <= 0.0002)) {
		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) <= (-1d-66)) .or. (.not. ((x / y) <= 0.0002d0))) 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) <= -1e-66) || !((x / y) <= 0.0002)) {
		tmp = z * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e-66) or not ((x / y) <= 0.0002):
		tmp = z * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e-66) || !(Float64(x / y) <= 0.0002))
		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) <= -1e-66) || ~(((x / y) <= 0.0002)))
		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], -1e-66], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.0002]], $MachinePrecision]], N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999998e-67 or 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 92.7%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/l* 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in z around inf 51.8%

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

      1. associate-*l/ 51.8%

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

   9. Simplified 51.8%

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

   if -9.9999999999999998e-67 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 80.8%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-66} \lor \neg \left(\frac{x}{y} \leq 0.0002\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-66}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e-66)
   (/ (* z x) y)
   (if (<= (/ x y) 0.0002) t (* z (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e-66) {
		tmp = (z * x) / y;
	} else if ((x / y) <= 0.0002) {
		tmp = t;
	} else {
		tmp = 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) <= (-1d-66)) then
        tmp = (z * x) / y
    else if ((x / y) <= 0.0002d0) then
        tmp = t
    else
        tmp = 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) <= -1e-66) {
		tmp = (z * x) / y;
	} else if ((x / y) <= 0.0002) {
		tmp = t;
	} else {
		tmp = z * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e-66:
		tmp = (z * x) / y
	elif (x / y) <= 0.0002:
		tmp = t
	else:
		tmp = z * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e-66)
		tmp = Float64(Float64(z * x) / y);
	elseif (Float64(x / y) <= 0.0002)
		tmp = t;
	else
		tmp = Float64(z * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1e-66)
		tmp = (z * x) / y;
	elseif ((x / y) <= 0.0002)
		tmp = t;
	else
		tmp = z * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e-66], N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0002], t, N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999998e-67

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 91.0%

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

   4. Taylor expanded in t around 0 54.3%

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

   if -9.9999999999999998e-67 < (/.f64 x y) < 2.0000000000000001e-4

   1. Initial program 98.3%

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

   3. Taylor expanded in x around 0 80.8%

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

   if 2.0000000000000001e-4 < (/.f64 x y)

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 95.0%

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

   4. Taylor expanded in y around 0 94.3%

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

      1. *-commutative 94.3%

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

      2. associate-/l* 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in z around inf 48.4%

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

      1. associate-*l/ 49.8%

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

   9. Simplified 49.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-66}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0002:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 53.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-53} \lor \neg \left(x \leq 3.2 \cdot 10^{-106}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.8e-53) (not (<= x 3.2e-106))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.8e-53) || !(x <= 3.2e-106)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-7.8d-53)) .or. (.not. (x <= 3.2d-106))) then
        tmp = x * (z / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.8e-53) || !(x <= 3.2e-106)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.8e-53) or not (x <= 3.2e-106):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.8e-53) || !(x <= 3.2e-106))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.8e-53) || ~((x <= 3.2e-106)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.8e-53], N[Not[LessEqual[x, 3.2e-106]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -7.8000000000000004e-53 or 3.2e-106 < x

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 84.3%

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

   4. Taylor expanded in y around 0 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 81.1%

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

   6. Applied egg-rr 81.1%

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

   7. Taylor expanded in z around inf 44.0%

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

      1. associate-/l* 48.3%

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

   9. Simplified 48.3%

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

   if -7.8000000000000004e-53 < x < 3.2e-106

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 70.8%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-53} \lor \neg \left(x \leq 3.2 \cdot 10^{-106}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.5% 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 97.6%

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

3. Final simplification 97.6%

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

Alternative 14: 37.9% 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 97.6%

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

3. Taylor expanded in x around 0 39.5%

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

4. Final simplification 39.5%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 97.4% 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 2024095 
(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))