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

Percentage Accurate: 98.0% → 98.0%

Time: 5.8s

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: 98.0% 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: 98.0% 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 98.4%

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

2. Final simplification 98.4%

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

Alternative 2: 64.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+230}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+126} \lor \neg \left(\frac{x}{y} \leq 10^{+230}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (* (/ x y) (- t))))
   (if (<= (/ x y) -2e+230)
     (/ (* x (- t)) y)
     (if (<= (/ x y) -6e+88)
       t_1
       (if (<= (/ x y) -2000000000.0)
         t_2
         (if (<= (/ x y) -4e-8)
           t_1
           (if (<= (/ x y) 5e-11)
             t
             (if (or (<= (/ x y) 2e+126) (not (<= (/ x y) 1e+230)))
               t_2
               t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -2e+230) {
		tmp = (x * -t) / y;
	} else if ((x / y) <= -6e+88) {
		tmp = t_1;
	} else if ((x / y) <= -2000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -4e-8) {
		tmp = t_1;
	} else if ((x / y) <= 5e-11) {
		tmp = t;
	} else if (((x / y) <= 2e+126) || !((x / y) <= 1e+230)) {
		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 / y) * z
    t_2 = (x / y) * -t
    if ((x / y) <= (-2d+230)) then
        tmp = (x * -t) / y
    else if ((x / y) <= (-6d+88)) then
        tmp = t_1
    else if ((x / y) <= (-2000000000.0d0)) then
        tmp = t_2
    else if ((x / y) <= (-4d-8)) then
        tmp = t_1
    else if ((x / y) <= 5d-11) then
        tmp = t
    else if (((x / y) <= 2d+126) .or. (.not. ((x / y) <= 1d+230))) 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 / y) * z;
	double t_2 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -2e+230) {
		tmp = (x * -t) / y;
	} else if ((x / y) <= -6e+88) {
		tmp = t_1;
	} else if ((x / y) <= -2000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -4e-8) {
		tmp = t_1;
	} else if ((x / y) <= 5e-11) {
		tmp = t;
	} else if (((x / y) <= 2e+126) || !((x / y) <= 1e+230)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = (x / y) * -t
	tmp = 0
	if (x / y) <= -2e+230:
		tmp = (x * -t) / y
	elif (x / y) <= -6e+88:
		tmp = t_1
	elif (x / y) <= -2000000000.0:
		tmp = t_2
	elif (x / y) <= -4e-8:
		tmp = t_1
	elif (x / y) <= 5e-11:
		tmp = t
	elif ((x / y) <= 2e+126) or not ((x / y) <= 1e+230):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (Float64(x / y) <= -2e+230)
		tmp = Float64(Float64(x * Float64(-t)) / y);
	elseif (Float64(x / y) <= -6e+88)
		tmp = t_1;
	elseif (Float64(x / y) <= -2000000000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= -4e-8)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-11)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+126) || !(Float64(x / y) <= 1e+230))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = (x / y) * -t;
	tmp = 0.0;
	if ((x / y) <= -2e+230)
		tmp = (x * -t) / y;
	elseif ((x / y) <= -6e+88)
		tmp = t_1;
	elseif ((x / y) <= -2000000000.0)
		tmp = t_2;
	elseif ((x / y) <= -4e-8)
		tmp = t_1;
	elseif ((x / y) <= 5e-11)
		tmp = t;
	elseif (((x / y) <= 2e+126) || ~(((x / y) <= 1e+230)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+230], N[(N[(x * (-t)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -6e+88], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2000000000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -4e-8], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-11], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+126], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+230]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2.0000000000000002e230

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in x around -inf 100.0%

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

   4. Taylor expanded in z around 0 74.6%

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

      1. neg-mul-1 74.6%

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

      2. distribute-rgt-neg-in 74.6%

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

   6. Simplified 74.6%

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

   if -2.0000000000000002e230 < (/.f64 x y) < -6.00000000000000011e88 or -2e9 < (/.f64 x y) < -4.0000000000000001e-8 or 1.99999999999999985e126 < (/.f64 x y) < 1.0000000000000001e230

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 93.3%

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

   3. Taylor expanded in x around -inf 93.3%

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

   4. Taylor expanded in z around inf 70.5%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

   6. Applied egg-rr 74.7%

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

   if -6.00000000000000011e88 < (/.f64 x y) < -2e9 or 5.00000000000000018e-11 < (/.f64 x y) < 1.99999999999999985e126 or 1.0000000000000001e230 < (/.f64 x y)

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 94.6%

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

   3. Taylor expanded in x around -inf 92.5%

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

   4. Taylor expanded in z around 0 59.3%

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

      1. associate-*r/ 59.3%

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

      2. neg-mul-1 59.3%

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

      3. distribute-lft-neg-in 59.3%

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

      4. associate-*r/ 67.4%

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

      5. *-commutative 67.4%

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

   6. Simplified 67.4%

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

   if -4.0000000000000001e-8 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 83.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+230}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+126} \lor \neg \left(\frac{x}{y} \leq 10^{+230}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]

Alternative 3: 65.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+126} \lor \neg \left(\frac{x}{y} \leq 10^{+230}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (* (/ x y) (- t))))
   (if (<= (/ x y) -6e+88)
     t_1
     (if (<= (/ x y) -2000000000.0)
       t_2
       (if (<= (/ x y) -4e-8)
         t_1
         (if (<= (/ x y) 5e-11)
           t
           (if (or (<= (/ x y) 2e+126) (not (<= (/ x y) 1e+230)))
             t_2
             t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -6e+88) {
		tmp = t_1;
	} else if ((x / y) <= -2000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -4e-8) {
		tmp = t_1;
	} else if ((x / y) <= 5e-11) {
		tmp = t;
	} else if (((x / y) <= 2e+126) || !((x / y) <= 1e+230)) {
		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 / y) * z
    t_2 = (x / y) * -t
    if ((x / y) <= (-6d+88)) then
        tmp = t_1
    else if ((x / y) <= (-2000000000.0d0)) then
        tmp = t_2
    else if ((x / y) <= (-4d-8)) then
        tmp = t_1
    else if ((x / y) <= 5d-11) then
        tmp = t
    else if (((x / y) <= 2d+126) .or. (.not. ((x / y) <= 1d+230))) 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 / y) * z;
	double t_2 = (x / y) * -t;
	double tmp;
	if ((x / y) <= -6e+88) {
		tmp = t_1;
	} else if ((x / y) <= -2000000000.0) {
		tmp = t_2;
	} else if ((x / y) <= -4e-8) {
		tmp = t_1;
	} else if ((x / y) <= 5e-11) {
		tmp = t;
	} else if (((x / y) <= 2e+126) || !((x / y) <= 1e+230)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = (x / y) * -t
	tmp = 0
	if (x / y) <= -6e+88:
		tmp = t_1
	elif (x / y) <= -2000000000.0:
		tmp = t_2
	elif (x / y) <= -4e-8:
		tmp = t_1
	elif (x / y) <= 5e-11:
		tmp = t
	elif ((x / y) <= 2e+126) or not ((x / y) <= 1e+230):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(Float64(x / y) * Float64(-t))
	tmp = 0.0
	if (Float64(x / y) <= -6e+88)
		tmp = t_1;
	elseif (Float64(x / y) <= -2000000000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= -4e-8)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-11)
		tmp = t;
	elseif ((Float64(x / y) <= 2e+126) || !(Float64(x / y) <= 1e+230))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = (x / y) * -t;
	tmp = 0.0;
	if ((x / y) <= -6e+88)
		tmp = t_1;
	elseif ((x / y) <= -2000000000.0)
		tmp = t_2;
	elseif ((x / y) <= -4e-8)
		tmp = t_1;
	elseif ((x / y) <= 5e-11)
		tmp = t;
	elseif (((x / y) <= 2e+126) || ~(((x / y) <= 1e+230)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -6e+88], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2000000000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -4e-8], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-11], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 2e+126], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+230]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.00000000000000011e88 or -2e9 < (/.f64 x y) < -4.0000000000000001e-8 or 1.99999999999999985e126 < (/.f64 x y) < 1.0000000000000001e230

   1. Initial program 96.9%

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

   2. Taylor expanded in x around 0 95.6%

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

   3. Taylor expanded in x around -inf 95.6%

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

   4. Taylor expanded in z around inf 63.7%

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

      1. associate-*r/ 67.9%

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

      2. *-commutative 67.9%

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

   6. Applied egg-rr 67.9%

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

   if -6.00000000000000011e88 < (/.f64 x y) < -2e9 or 5.00000000000000018e-11 < (/.f64 x y) < 1.99999999999999985e126 or 1.0000000000000001e230 < (/.f64 x y)

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 94.6%

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

   3. Taylor expanded in x around -inf 92.5%

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

   4. Taylor expanded in z around 0 59.3%

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

      1. associate-*r/ 59.3%

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

      2. neg-mul-1 59.3%

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

      3. distribute-lft-neg-in 59.3%

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

      4. associate-*r/ 67.4%

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

      5. *-commutative 67.4%

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

   6. Simplified 67.4%

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

   if -4.0000000000000001e-8 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 83.5%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+126} \lor \neg \left(\frac{x}{y} \leq 10^{+230}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]

Alternative 4: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-8} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e-8) (not (<= (/ x y) 5e-11))) (* (/ x y) (- z t)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e-8) || !((x / y) <= 5e-11)) {
		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) <= (-4d-8)) .or. (.not. ((x / y) <= 5d-11))) 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) <= -4e-8) || !((x / y) <= 5e-11)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e-8) or not ((x / y) <= 5e-11):
		tmp = (x / y) * (z - t)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e-8) || !(Float64(x / y) <= 5e-11))
		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) <= -4e-8) || ~(((x / y) <= 5e-11)))
		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], -4e-8], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.0000000000000001e-8 or 5.00000000000000018e-11 < (/.f64 x y)

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 95.1%

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

   3. Taylor expanded in x around -inf 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 95.7%

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

   5. Applied egg-rr 95.7%

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

   if -4.0000000000000001e-8 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 83.5%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-8} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 96.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5000.0) (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) <= -5000.0) || !((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) <= (-5000.0d0)) .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) <= -5000.0) || !((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) <= -5000.0) 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) <= -5000.0) || !(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) <= -5000.0) || ~(((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], -5000.0], 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) < -5e3 or 5.00000000000000018e-11 < (/.f64 x y)

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 95.0%

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

   3. Taylor expanded in x around -inf 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l/ 95.6%

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

   5. Applied egg-rr 95.6%

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

   if -5e3 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf 96.2%

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

      1. associate-*r/ 98.5%

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

   4. Simplified 98.5%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 6: 95.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2000000000.0)
   (/ (* x (- z t)) y)
   (if (<= (/ x y) 5e-11) (+ t (* (/ x y) z)) (* (/ x y) (- z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2000000000.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 5e-11) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x / y) * (z - 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) <= (-2000000000.0d0)) then
        tmp = (x * (z - t)) / y
    else if ((x / y) <= 5d-11) then
        tmp = t + ((x / y) * z)
    else
        tmp = (x / y) * (z - 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) <= -2000000000.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 5e-11) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = (x / y) * (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2000000000.0:
		tmp = (x * (z - t)) / y
	elif (x / y) <= 5e-11:
		tmp = t + ((x / y) * z)
	else:
		tmp = (x / y) * (z - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2000000000.0)
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	elseif (Float64(x / y) <= 5e-11)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(Float64(x / y) * Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2000000000.0)
		tmp = (x * (z - t)) / y;
	elseif ((x / y) <= 5e-11)
		tmp = t + ((x / y) * z);
	else
		tmp = (x / y) * (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2000000000.0], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-11], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e9

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 98.1%

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

   3. Taylor expanded in x around -inf 96.4%

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

   if -2e9 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 94.9%

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

      1. associate-*r/ 97.9%

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

   4. Simplified 97.9%

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

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

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 94.8%

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

   3. Taylor expanded in x around -inf 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*l/ 96.8%

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

   5. Applied egg-rr 96.8%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]

Alternative 7: 54.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+111} \lor \neg \left(x \leq -5.6 \cdot 10^{+38} \lor \neg \left(x \leq -49000\right) \land x \leq 2800000000000\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.2e+111)
         (not
          (or (<= x -5.6e+38)
              (and (not (<= x -49000.0)) (<= x 2800000000000.0)))))
   (* x (/ z y))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+111) || !((x <= -5.6e+38) || (!(x <= -49000.0) && (x <= 2800000000000.0)))) {
		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 <= (-4.2d+111)) .or. (.not. (x <= (-5.6d+38)) .or. (.not. (x <= (-49000.0d0))) .and. (x <= 2800000000000.0d0))) 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 <= -4.2e+111) || !((x <= -5.6e+38) || (!(x <= -49000.0) && (x <= 2800000000000.0)))) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.2e+111) or not ((x <= -5.6e+38) or (not (x <= -49000.0) and (x <= 2800000000000.0))):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.2e+111) || !((x <= -5.6e+38) || (!(x <= -49000.0) && (x <= 2800000000000.0))))
		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 <= -4.2e+111) || ~(((x <= -5.6e+38) || (~((x <= -49000.0)) && (x <= 2800000000000.0)))))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.2e+111], N[Not[Or[LessEqual[x, -5.6e+38], And[N[Not[LessEqual[x, -49000.0]], $MachinePrecision], LessEqual[x, 2800000000000.0]]]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999999e111 or -5.6e38 < x < -49000 or 2.8e12 < x

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 89.9%

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

   3. Taylor expanded in x around -inf 84.1%

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

   4. Taylor expanded in z around inf 53.2%

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

      1. *-commutative 53.2%

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

      2. associate-*r/ 54.2%

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

   6. Simplified 54.2%

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

   if -4.1999999999999999e111 < x < -5.6e38 or -49000 < x < 2.8e12

   1. Initial program 98.6%

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

   2. Taylor expanded in x around 0 60.3%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+111} \lor \neg \left(x \leq -5.6 \cdot 10^{+38} \lor \neg \left(x \leq -49000\right) \land x \leq 2800000000000\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 66.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-8} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e-8) (not (<= (/ x y) 5e-11))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e-8) || !((x / y) <= 5e-11)) {
		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) <= (-4d-8)) .or. (.not. ((x / y) <= 5d-11))) 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) <= -4e-8) || !((x / y) <= 5e-11)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e-8) or not ((x / y) <= 5e-11):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e-8) || !(Float64(x / y) <= 5e-11))
		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) <= -4e-8) || ~(((x / y) <= 5e-11)))
		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], -4e-8], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.0000000000000001e-8 or 5.00000000000000018e-11 < (/.f64 x y)

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0 95.1%

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

   3. Taylor expanded in x around -inf 94.0%

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

   4. Taylor expanded in z around inf 53.3%

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

      1. associate-*r/ 54.6%

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

      2. *-commutative 54.6%

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

   6. Applied egg-rr 54.6%

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

   if -4.0000000000000001e-8 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 83.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-8} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e-8) (* (/ x y) z) (if (<= (/ x y) 5e-11) t (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e-8) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 5e-11) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4d-8)) then
        tmp = (x / y) * z
    else if ((x / y) <= 5d-11) then
        tmp = t
    else
        tmp = (x * z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e-8) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 5e-11) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4e-8:
		tmp = (x / y) * z
	elif (x / y) <= 5e-11:
		tmp = t
	else:
		tmp = (x * z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4e-8)
		tmp = Float64(Float64(x / y) * z);
	elseif (Float64(x / y) <= 5e-11)
		tmp = t;
	else
		tmp = Float64(Float64(x * z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4e-8)
		tmp = (x / y) * z;
	elseif ((x / y) <= 5e-11)
		tmp = t;
	else
		tmp = (x * z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4e-8], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-11], t, N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.0000000000000001e-8

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 95.4%

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

   3. Taylor expanded in x around -inf 93.9%

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

   4. Taylor expanded in z around inf 53.2%

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

      1. associate-*r/ 56.1%

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

      2. *-commutative 56.1%

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

   6. Applied egg-rr 56.1%

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

   if -4.0000000000000001e-8 < (/.f64 x y) < 5.00000000000000018e-11

   1. Initial program 99.1%

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

   2. Taylor expanded in x around 0 83.5%

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

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

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 94.8%

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

   3. Taylor expanded in x around -inf 94.0%

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

   4. Taylor expanded in z around inf 53.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]

Alternative 10: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

2. Taylor expanded in x around 0 40.7%

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

3. Final simplification 40.7%

   \[\leadsto t \]

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 2023257 
(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))