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

Percentage Accurate: 97.7% → 97.7%

Time: 5.6s

Alternatives: 10

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

2. Final simplification 96.8%

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

Alternative 2: 64.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(-\frac{t}{y}\right)\\ t_2 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+223}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+141}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- (/ t y)))) (t_2 (/ z (/ y x))))
   (if (<= (/ x y) -5e+223)
     (* x (/ z y))
     (if (<= (/ x y) -1e+36)
       t_1
       (if (<= (/ x y) -2e-62)
         t_2
         (if (<= (/ x y) 1e-19) t (if (<= (/ x y) 1e+141) t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * -(t / y);
	double t_2 = z / (y / x);
	double tmp;
	if ((x / y) <= -5e+223) {
		tmp = x * (z / y);
	} else if ((x / y) <= -1e+36) {
		tmp = t_1;
	} else if ((x / y) <= -2e-62) {
		tmp = t_2;
	} else if ((x / y) <= 1e-19) {
		tmp = t;
	} else if ((x / y) <= 1e+141) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x * -(t / y)
    t_2 = z / (y / x)
    if ((x / y) <= (-5d+223)) then
        tmp = x * (z / y)
    else if ((x / y) <= (-1d+36)) then
        tmp = t_1
    else if ((x / y) <= (-2d-62)) then
        tmp = t_2
    else if ((x / y) <= 1d-19) then
        tmp = t
    else if ((x / y) <= 1d+141) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * -(t / y);
	double t_2 = z / (y / x);
	double tmp;
	if ((x / y) <= -5e+223) {
		tmp = x * (z / y);
	} else if ((x / y) <= -1e+36) {
		tmp = t_1;
	} else if ((x / y) <= -2e-62) {
		tmp = t_2;
	} else if ((x / y) <= 1e-19) {
		tmp = t;
	} else if ((x / y) <= 1e+141) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * -(t / y)
	t_2 = z / (y / x)
	tmp = 0
	if (x / y) <= -5e+223:
		tmp = x * (z / y)
	elif (x / y) <= -1e+36:
		tmp = t_1
	elif (x / y) <= -2e-62:
		tmp = t_2
	elif (x / y) <= 1e-19:
		tmp = t
	elif (x / y) <= 1e+141:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(-Float64(t / y)))
	t_2 = Float64(z / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -5e+223)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= -1e+36)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e-62)
		tmp = t_2;
	elseif (Float64(x / y) <= 1e-19)
		tmp = t;
	elseif (Float64(x / y) <= 1e+141)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * -(t / y);
	t_2 = z / (y / x);
	tmp = 0.0;
	if ((x / y) <= -5e+223)
		tmp = x * (z / y);
	elseif ((x / y) <= -1e+36)
		tmp = t_1;
	elseif ((x / y) <= -2e-62)
		tmp = t_2;
	elseif ((x / y) <= 1e-19)
		tmp = t;
	elseif ((x / y) <= 1e+141)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * (-N[(t / y), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+223], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e+36], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e-62], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 1e-19], t, If[LessEqual[N[(x / y), $MachinePrecision], 1e+141], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -4.99999999999999985e223

   1. Initial program 92.3%

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

      1. associate-*l/ 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 83.5%

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

      1. associate-*r/ 83.5%

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

   6. Simplified 83.5%

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

   if -4.99999999999999985e223 < (/.f64 x y) < -1.00000000000000004e36 or 1.00000000000000002e141 < (/.f64 x y)

   1. Initial program 93.9%

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

   2. Taylor expanded in z around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

      3. associate-*r/ 63.5%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 63.1%

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

      2. mul-1-neg 63.1%

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

      3. distribute-rgt-neg-out 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in t around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. associate-*l/ 65.0%

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

      3. *-commutative 65.0%

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

      4. distribute-rgt-neg-in 65.0%

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

   10. Simplified 65.0%

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

   if -1.00000000000000004e36 < (/.f64 x y) < -2.0000000000000001e-62 or 9.9999999999999998e-20 < (/.f64 x y) < 1.00000000000000002e141

   1. Initial program 99.6%

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

      1. associate-*l/ 88.2%

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

      2. div-inv 88.3%

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

      3. fma-def 88.3%

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

   3. Applied egg-rr 88.3%

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

   4. Taylor expanded in z around inf 58.7%

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

      1. associate-*l/ 66.4%

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

   6. Applied egg-rr 66.4%

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

      1. *-commutative 66.4%

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

      2. clear-num 66.4%

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

      3. un-div-inv 66.5%

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

   8. Applied egg-rr 66.5%

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

   if -2.0000000000000001e-62 < (/.f64 x y) < 9.9999999999999998e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 85.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+223}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-19}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+141}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \end{array} \]

Alternative 3: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+223}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-62} \lor \neg \left(\frac{x}{y} \leq 10^{-19}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+223)
   (* x (/ z y))
   (if (<= (/ x y) -1e+36)
     (* t (/ (- x) y))
     (if (or (<= (/ x y) -2e-62) (not (<= (/ x y) 1e-19))) (/ z (/ y x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+223) {
		tmp = x * (z / y);
	} else if ((x / y) <= -1e+36) {
		tmp = t * (-x / y);
	} else if (((x / y) <= -2e-62) || !((x / y) <= 1e-19)) {
		tmp = z / (y / x);
	} 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+223)) then
        tmp = x * (z / y)
    else if ((x / y) <= (-1d+36)) then
        tmp = t * (-x / y)
    else if (((x / y) <= (-2d-62)) .or. (.not. ((x / y) <= 1d-19))) then
        tmp = z / (y / x)
    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+223) {
		tmp = x * (z / y);
	} else if ((x / y) <= -1e+36) {
		tmp = t * (-x / y);
	} else if (((x / y) <= -2e-62) || !((x / y) <= 1e-19)) {
		tmp = z / (y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+223:
		tmp = x * (z / y)
	elif (x / y) <= -1e+36:
		tmp = t * (-x / y)
	elif ((x / y) <= -2e-62) or not ((x / y) <= 1e-19):
		tmp = z / (y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+223)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= -1e+36)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif ((Float64(x / y) <= -2e-62) || !(Float64(x / y) <= 1e-19))
		tmp = Float64(z / Float64(y / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+223)
		tmp = x * (z / y);
	elseif ((x / y) <= -1e+36)
		tmp = t * (-x / y);
	elseif (((x / y) <= -2e-62) || ~(((x / y) <= 1e-19)))
		tmp = z / (y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+223], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e+36], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-62], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-19]], $MachinePrecision]], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -4.99999999999999985e223

   1. Initial program 92.3%

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

      1. associate-*l/ 99.9%

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

      2. div-inv 99.9%

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

      3. fma-def 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 83.5%

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

      1. associate-*r/ 83.5%

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

   6. Simplified 83.5%

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

   if -4.99999999999999985e223 < (/.f64 x y) < -1.00000000000000004e36

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. unsub-neg 67.7%

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

      3. associate-*r/ 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in x around inf 67.6%

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

      1. mul-1-neg 67.6%

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

      2. associate-*r/ 68.6%

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

      3. distribute-rgt-neg-out 68.6%

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

      4. distribute-neg-frac 68.6%

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

   7. Simplified 68.6%

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

   if -1.00000000000000004e36 < (/.f64 x y) < -2.0000000000000001e-62 or 9.9999999999999998e-20 < (/.f64 x y)

   1. Initial program 95.3%

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

      1. associate-*l/ 93.2%

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

      2. div-inv 93.2%

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

      3. fma-def 93.2%

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

   3. Applied egg-rr 93.2%

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

   4. Taylor expanded in z around inf 56.2%

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

      1. associate-*l/ 59.4%

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

   6. Applied egg-rr 59.4%

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

      1. *-commutative 59.4%

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

      2. clear-num 59.4%

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

      3. un-div-inv 59.5%

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

   8. Applied egg-rr 59.5%

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

   if -2.0000000000000001e-62 < (/.f64 x y) < 9.9999999999999998e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 85.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+223}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-62} \lor \neg \left(\frac{x}{y} \leq 10^{-19}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62} \lor \neg \left(\frac{x}{y} \leq 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-62) (not (<= (/ x y) 1e-19))) (* (/ x y) (- z t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-62) || !((x / y) <= 1e-19)) {
		tmp = (x / y) * (z - t);
	} 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) <= (-2d-62)) .or. (.not. ((x / y) <= 1d-19))) then
        tmp = (x / y) * (z - t)
    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) <= -2e-62) || !((x / y) <= 1e-19)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-62) or not ((x / y) <= 1e-19):
		tmp = (x / y) * (z - t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-62) || !(Float64(x / y) <= 1e-19))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-62) || ~(((x / y) <= 1e-19)))
		tmp = (x / y) * (z - t);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-62], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0000000000000001e-62 or 9.9999999999999998e-20 < (/.f64 x y)

   1. Initial program 95.6%

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

      1. associate-*l/ 95.0%

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

      2. div-inv 95.0%

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

      3. fma-def 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in x around inf 86.2%

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

      1. sub-neg 86.2%

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

      2. distribute-rgt-in 77.3%

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

      3. associate-*l/ 79.6%

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

      4. associate-*r/ 77.9%

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

      5. distribute-frac-neg 77.9%

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

      6. associate-*l/ 77.3%

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

      7. associate-*r/ 76.3%

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

      8. distribute-rgt-in 91.9%

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

      9. sub-neg 91.9%

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

      10. *-commutative 91.9%

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

   6. Simplified 91.9%

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

   if -2.0000000000000001e-62 < (/.f64 x y) < 9.9999999999999998e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 85.9%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62} \lor \neg \left(\frac{x}{y} \leq 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 96.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -200000.0) (not (<= (/ x y) 5e-11)))
   (* (/ x y) (- z t))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -200000.0) || !((x / y) <= 5e-11)) {
		tmp = (x / y) * (z - t);
	} 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) <= (-200000.0d0)) .or. (.not. ((x / y) <= 5d-11))) then
        tmp = (x / y) * (z - t)
    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) <= -200000.0) || !((x / y) <= 5e-11)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -200000.0) or not ((x / y) <= 5e-11):
		tmp = (x / y) * (z - t)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -200000.0) || !(Float64(x / y) <= 5e-11))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -200000.0) || ~(((x / y) <= 5e-11)))
		tmp = (x / y) * (z - t);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -200000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e5 or 5.00000000000000018e-11 < (/.f64 x y)

   1. Initial program 95.2%

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

      1. associate-*l/ 96.0%

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

      2. div-inv 96.0%

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

      3. fma-def 96.0%

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

   3. Applied egg-rr 96.0%

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

   4. Taylor expanded in x around inf 90.7%

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

      1. sub-neg 90.7%

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

      2. distribute-rgt-in 81.0%

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

      3. associate-*l/ 82.7%

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

      4. associate-*r/ 79.4%

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

      5. distribute-frac-neg 79.4%

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

      6. associate-*l/ 78.7%

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

      7. associate-*r/ 77.6%

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

      8. distribute-rgt-in 94.8%

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

      9. sub-neg 94.8%

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

      10. *-commutative 94.8%

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

   6. Simplified 94.8%

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

   if -2e5 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 98.2%

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

   2. Taylor expanded in z around inf 96.9%

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

      1. associate-*l/ 98.0%

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

      2. *-commutative 98.0%

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

   4. Simplified 98.0%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 6: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62} \lor \neg \left(\frac{x}{y} \leq 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-62) (not (<= (/ x y) 1e-19))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-62) || !((x / y) <= 1e-19)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d-62)) .or. (.not. ((x / y) <= 1d-19))) then
        tmp = (x / y) * z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-62) || !((x / y) <= 1e-19)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-62) or not ((x / y) <= 1e-19):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-62) || !(Float64(x / y) <= 1e-19))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-62) || ~(((x / y) <= 1e-19)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-62], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0000000000000001e-62 or 9.9999999999999998e-20 < (/.f64 x y)

   1. Initial program 95.6%

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

      1. associate-*l/ 95.0%

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

      2. div-inv 95.0%

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

      3. fma-def 95.0%

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

   3. Applied egg-rr 95.0%

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

   4. Taylor expanded in z around inf 56.9%

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

      1. associate-*l/ 58.3%

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

      2. *-commutative 58.3%

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

   6. Simplified 58.3%

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

   if -2.0000000000000001e-62 < (/.f64 x y) < 9.9999999999999998e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 85.9%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62} \lor \neg \left(\frac{x}{y} \leq 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e-62)
   (/ x (/ y z))
   (if (<= (/ x y) 1e-19) t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-62) {
		tmp = x / (y / z);
	} else if ((x / y) <= 1e-19) {
		tmp = t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2d-62)) then
        tmp = x / (y / z)
    else if ((x / y) <= 1d-19) then
        tmp = t
    else
        tmp = (x / y) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-62) {
		tmp = x / (y / z);
	} else if ((x / y) <= 1e-19) {
		tmp = t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e-62:
		tmp = x / (y / z)
	elif (x / y) <= 1e-19:
		tmp = t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e-62)
		tmp = Float64(x / Float64(y / z));
	elseif (Float64(x / y) <= 1e-19)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e-62)
		tmp = x / (y / z);
	elseif ((x / y) <= 1e-19)
		tmp = t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e-62], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-19], t, N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.0000000000000001e-62

   1. Initial program 97.1%

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

      1. associate-*l/ 95.7%

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

      2. div-inv 95.5%

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

      3. fma-def 95.5%

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

   3. Applied egg-rr 95.5%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. associate-*l/ 59.1%

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

   6. Applied egg-rr 59.1%

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

      1. associate-*l/ 57.7%

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

      2. associate-/l* 59.8%

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

   8. Applied egg-rr 59.8%

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

   if -2.0000000000000001e-62 < (/.f64 x y) < 9.9999999999999998e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 85.9%

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

   if 9.9999999999999998e-20 < (/.f64 x y)

   1. Initial program 94.3%

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

      1. associate-*l/ 94.4%

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

      2. div-inv 94.4%

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

      3. fma-def 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in z around inf 56.2%

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

      1. associate-*l/ 57.5%

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

      2. *-commutative 57.5%

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

   6. Simplified 57.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]

Alternative 8: 63.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e-62)
   (/ x (/ y z))
   (if (<= (/ x y) 1e-19) t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-62) {
		tmp = x / (y / z);
	} else if ((x / y) <= 1e-19) {
		tmp = t;
	} else {
		tmp = 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) <= (-2d-62)) then
        tmp = x / (y / z)
    else if ((x / y) <= 1d-19) then
        tmp = t
    else
        tmp = 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) <= -2e-62) {
		tmp = x / (y / z);
	} else if ((x / y) <= 1e-19) {
		tmp = t;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e-62:
		tmp = x / (y / z)
	elif (x / y) <= 1e-19:
		tmp = t
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e-62)
		tmp = Float64(x / Float64(y / z));
	elseif (Float64(x / y) <= 1e-19)
		tmp = t;
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e-62)
		tmp = x / (y / z);
	elseif ((x / y) <= 1e-19)
		tmp = t;
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e-62], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-19], t, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.0000000000000001e-62

   1. Initial program 97.1%

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

      1. associate-*l/ 95.7%

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

      2. div-inv 95.5%

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

      3. fma-def 95.5%

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

   3. Applied egg-rr 95.5%

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

   4. Taylor expanded in z around inf 57.7%

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

      1. associate-*l/ 59.1%

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

   6. Applied egg-rr 59.1%

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

      1. associate-*l/ 57.7%

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

      2. associate-/l* 59.8%

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

   8. Applied egg-rr 59.8%

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

   if -2.0000000000000001e-62 < (/.f64 x y) < 9.9999999999999998e-20

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 85.9%

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

   if 9.9999999999999998e-20 < (/.f64 x y)

   1. Initial program 94.3%

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

      1. associate-*l/ 94.4%

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

      2. div-inv 94.4%

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

      3. fma-def 94.4%

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

   3. Applied egg-rr 94.4%

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

   4. Taylor expanded in z around inf 56.2%

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

      1. associate-*l/ 57.5%

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

   6. Applied egg-rr 57.5%

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

      1. *-commutative 57.5%

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

      2. clear-num 57.5%

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

      3. un-div-inv 57.6%

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

   8. Applied egg-rr 57.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 54.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-7} \lor \neg \left(x \leq 1.6 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4e-7) (not (<= x 1.6e-85))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4e-7) || !(x <= 1.6e-85)) {
		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 <= (-4d-7)) .or. (.not. (x <= 1.6d-85))) 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 <= -4e-7) || !(x <= 1.6e-85)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4e-7) or not (x <= 1.6e-85):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4e-7) || !(x <= 1.6e-85))
		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 <= -4e-7) || ~((x <= 1.6e-85)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4e-7], N[Not[LessEqual[x, 1.6e-85]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999998e-7 or 1.60000000000000014e-85 < x

   1. Initial program 95.9%

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

      1. associate-*l/ 93.9%

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

      2. div-inv 93.9%

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

      3. fma-def 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in z around inf 50.7%

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

      1. associate-*r/ 50.6%

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

   6. Simplified 50.6%

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

   if -3.9999999999999998e-7 < x < 1.60000000000000014e-85

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0 73.6%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-7} \lor \neg \left(x \leq 1.6 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

2. Taylor expanded in x around 0 43.1%

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

3. Final simplification 43.1%

   \[\leadsto t \]

Developer target: 97.7% accurate, 0.7× 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 2023271 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (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))