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

Percentage Accurate: 97.8% → 98.3%

Time: 5.6s

Alternatives: 8

Speedup: 0.5×

• 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: 97.8% 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: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) (- z t)))))
   (if (<= t_1 5e+299) t_1 (+ t (/ x (/ y (- z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+299) {
		tmp = t_1;
	} else {
		tmp = t + (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) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / y) * (z - t))
    if (t_1 <= 5d+299) then
        tmp = t_1
    else
        tmp = t + (x / (y / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+299) {
		tmp = t_1;
	} else {
		tmp = t + (x / (y / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * (z - t))
	tmp = 0
	if t_1 <= 5e+299:
		tmp = t_1
	else:
		tmp = t + (x / (y / (z - t)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * Float64(z - t)))
	tmp = 0.0
	if (t_1 <= 5e+299)
		tmp = t_1;
	else
		tmp = Float64(t + Float64(x / Float64(y / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * (z - t));
	tmp = 0.0;
	if (t_1 <= 5e+299)
		tmp = t_1;
	else
		tmp = t + (x / (y / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+299], t$95$1, N[(t + N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 5.0000000000000003e299

   1. Initial program 98.4%

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

   if 5.0000000000000003e299 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 85.0%

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

      1. associate-*l/ 97.3%

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

      2. associate-/l* 100.0%

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

   3. Applied egg-rr 100.0%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \]

Alternative 2: 62.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{-t}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -20000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-93}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -3 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+64} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+191}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) z)) (t_2 (/ (- t) (/ y x))))
   (if (<= (/ x y) -2e+151)
     t_1
     (if (<= (/ x y) -2e+124)
       t_2
       (if (<= (/ x y) -1e+51)
         t_1
         (if (<= (/ x y) -1e+26)
           t_2
           (if (<= (/ x y) -20000.0)
             t_1
             (if (<= (/ x y) -1e-93)
               t
               (if (<= (/ x y) -3e-177)
                 t_1
                 (if (<= (/ x y) 5e-84)
                   t
                   (if (or (<= (/ x y) 5e+64) (not (<= (/ x y) 2e+191)))
                     t_1
                     t_2)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = -t / (y / x);
	double tmp;
	if ((x / y) <= -2e+151) {
		tmp = t_1;
	} else if ((x / y) <= -2e+124) {
		tmp = t_2;
	} else if ((x / y) <= -1e+51) {
		tmp = t_1;
	} else if ((x / y) <= -1e+26) {
		tmp = t_2;
	} else if ((x / y) <= -20000.0) {
		tmp = t_1;
	} else if ((x / y) <= -1e-93) {
		tmp = t;
	} else if ((x / y) <= -3e-177) {
		tmp = t_1;
	} else if ((x / y) <= 5e-84) {
		tmp = t;
	} else if (((x / y) <= 5e+64) || !((x / y) <= 2e+191)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / y) * z
    t_2 = -t / (y / x)
    if ((x / y) <= (-2d+151)) then
        tmp = t_1
    else if ((x / y) <= (-2d+124)) then
        tmp = t_2
    else if ((x / y) <= (-1d+51)) then
        tmp = t_1
    else if ((x / y) <= (-1d+26)) then
        tmp = t_2
    else if ((x / y) <= (-20000.0d0)) then
        tmp = t_1
    else if ((x / y) <= (-1d-93)) then
        tmp = t
    else if ((x / y) <= (-3d-177)) then
        tmp = t_1
    else if ((x / y) <= 5d-84) then
        tmp = t
    else if (((x / y) <= 5d+64) .or. (.not. ((x / y) <= 2d+191))) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * z;
	double t_2 = -t / (y / x);
	double tmp;
	if ((x / y) <= -2e+151) {
		tmp = t_1;
	} else if ((x / y) <= -2e+124) {
		tmp = t_2;
	} else if ((x / y) <= -1e+51) {
		tmp = t_1;
	} else if ((x / y) <= -1e+26) {
		tmp = t_2;
	} else if ((x / y) <= -20000.0) {
		tmp = t_1;
	} else if ((x / y) <= -1e-93) {
		tmp = t;
	} else if ((x / y) <= -3e-177) {
		tmp = t_1;
	} else if ((x / y) <= 5e-84) {
		tmp = t;
	} else if (((x / y) <= 5e+64) || !((x / y) <= 2e+191)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * z
	t_2 = -t / (y / x)
	tmp = 0
	if (x / y) <= -2e+151:
		tmp = t_1
	elif (x / y) <= -2e+124:
		tmp = t_2
	elif (x / y) <= -1e+51:
		tmp = t_1
	elif (x / y) <= -1e+26:
		tmp = t_2
	elif (x / y) <= -20000.0:
		tmp = t_1
	elif (x / y) <= -1e-93:
		tmp = t
	elif (x / y) <= -3e-177:
		tmp = t_1
	elif (x / y) <= 5e-84:
		tmp = t
	elif ((x / y) <= 5e+64) or not ((x / y) <= 2e+191):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * z)
	t_2 = Float64(Float64(-t) / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -2e+151)
		tmp = t_1;
	elseif (Float64(x / y) <= -2e+124)
		tmp = t_2;
	elseif (Float64(x / y) <= -1e+51)
		tmp = t_1;
	elseif (Float64(x / y) <= -1e+26)
		tmp = t_2;
	elseif (Float64(x / y) <= -20000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= -1e-93)
		tmp = t;
	elseif (Float64(x / y) <= -3e-177)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-84)
		tmp = t;
	elseif ((Float64(x / y) <= 5e+64) || !(Float64(x / y) <= 2e+191))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * z;
	t_2 = -t / (y / x);
	tmp = 0.0;
	if ((x / y) <= -2e+151)
		tmp = t_1;
	elseif ((x / y) <= -2e+124)
		tmp = t_2;
	elseif ((x / y) <= -1e+51)
		tmp = t_1;
	elseif ((x / y) <= -1e+26)
		tmp = t_2;
	elseif ((x / y) <= -20000.0)
		tmp = t_1;
	elseif ((x / y) <= -1e-93)
		tmp = t;
	elseif ((x / y) <= -3e-177)
		tmp = t_1;
	elseif ((x / y) <= 5e-84)
		tmp = t;
	elseif (((x / y) <= 5e+64) || ~(((x / y) <= 2e+191)))
		tmp = t_1;
	else
		tmp = t_2;
	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[((-t) / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+151], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -2e+124], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -1e+51], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1e+26], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -20000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1e-93], t, If[LessEqual[N[(x / y), $MachinePrecision], -3e-177], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-84], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 5e+64], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+191]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.00000000000000003e151 or -1.9999999999999999e124 < (/.f64 x y) < -1e51 or -1.00000000000000005e26 < (/.f64 x y) < -2e4 or -9.999999999999999e-94 < (/.f64 x y) < -3.00000000000000008e-177 or 5.0000000000000002e-84 < (/.f64 x y) < 5e64 or 2.00000000000000015e191 < (/.f64 x y)

   1. Initial program 94.7%

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

   2. Taylor expanded in x around inf 86.0%

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

   3. Taylor expanded in z around inf 62.1%

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

      1. associate-*r/ 71.0%

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

   5. Simplified 71.0%

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

   if -2.00000000000000003e151 < (/.f64 x y) < -1.9999999999999999e124 or -1e51 < (/.f64 x y) < -1.00000000000000005e26 or 5e64 < (/.f64 x y) < 2.00000000000000015e191

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 89.5%

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

   3. Taylor expanded in z around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/l* 74.9%

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

   5. Simplified 74.9%

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

   if -2e4 < (/.f64 x y) < -9.999999999999999e-94 or -3.00000000000000008e-177 < (/.f64 x y) < 5.0000000000000002e-84

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 85.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{+124}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+26}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -20000:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-93}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -3 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+64} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+191}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \end{array} \]

Alternative 3: 81.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := \frac{x}{y} \cdot z\\ t_3 := x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -20000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -3 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 2000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y))))
        (t_2 (* (/ x y) z))
        (t_3 (* x (/ (- z t) y))))
   (if (<= (/ x y) -20000.0)
     t_3
     (if (<= (/ x y) -1e-93)
       t_1
       (if (<= (/ x y) -3e-177)
         t_2
         (if (<= (/ x y) 5e-84)
           t_1
           (if (<= (/ x y) 4e-47) t_2 (if (<= (/ x y) 2000.0) t_1 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = (x / y) * z;
	double t_3 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -20000.0) {
		tmp = t_3;
	} else if ((x / y) <= -1e-93) {
		tmp = t_1;
	} else if ((x / y) <= -3e-177) {
		tmp = t_2;
	} else if ((x / y) <= 5e-84) {
		tmp = t_1;
	} else if ((x / y) <= 4e-47) {
		tmp = t_2;
	} else if ((x / y) <= 2000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    t_2 = (x / y) * z
    t_3 = x * ((z - t) / y)
    if ((x / y) <= (-20000.0d0)) then
        tmp = t_3
    else if ((x / y) <= (-1d-93)) then
        tmp = t_1
    else if ((x / y) <= (-3d-177)) then
        tmp = t_2
    else if ((x / y) <= 5d-84) then
        tmp = t_1
    else if ((x / y) <= 4d-47) then
        tmp = t_2
    else if ((x / y) <= 2000.0d0) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double t_2 = (x / y) * z;
	double t_3 = x * ((z - t) / y);
	double tmp;
	if ((x / y) <= -20000.0) {
		tmp = t_3;
	} else if ((x / y) <= -1e-93) {
		tmp = t_1;
	} else if ((x / y) <= -3e-177) {
		tmp = t_2;
	} else if ((x / y) <= 5e-84) {
		tmp = t_1;
	} else if ((x / y) <= 4e-47) {
		tmp = t_2;
	} else if ((x / y) <= 2000.0) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	t_2 = (x / y) * z
	t_3 = x * ((z - t) / y)
	tmp = 0
	if (x / y) <= -20000.0:
		tmp = t_3
	elif (x / y) <= -1e-93:
		tmp = t_1
	elif (x / y) <= -3e-177:
		tmp = t_2
	elif (x / y) <= 5e-84:
		tmp = t_1
	elif (x / y) <= 4e-47:
		tmp = t_2
	elif (x / y) <= 2000.0:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_2 = Float64(Float64(x / y) * z)
	t_3 = Float64(x * Float64(Float64(z - t) / y))
	tmp = 0.0
	if (Float64(x / y) <= -20000.0)
		tmp = t_3;
	elseif (Float64(x / y) <= -1e-93)
		tmp = t_1;
	elseif (Float64(x / y) <= -3e-177)
		tmp = t_2;
	elseif (Float64(x / y) <= 5e-84)
		tmp = t_1;
	elseif (Float64(x / y) <= 4e-47)
		tmp = t_2;
	elseif (Float64(x / y) <= 2000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	t_2 = (x / y) * z;
	t_3 = x * ((z - t) / y);
	tmp = 0.0;
	if ((x / y) <= -20000.0)
		tmp = t_3;
	elseif ((x / y) <= -1e-93)
		tmp = t_1;
	elseif ((x / y) <= -3e-177)
		tmp = t_2;
	elseif ((x / y) <= 5e-84)
		tmp = t_1;
	elseif ((x / y) <= 4e-47)
		tmp = t_2;
	elseif ((x / y) <= 2000.0)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -20000.0], t$95$3, If[LessEqual[N[(x / y), $MachinePrecision], -1e-93], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -3e-177], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 5e-84], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4e-47], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 2000.0], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e4 or 2e3 < (/.f64 x y)

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 92.2%

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

   3. Taylor expanded in z around 0 92.2%

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

      1. mul-1-neg 92.2%

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

      2. distribute-frac-neg 92.2%

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

      3. +-commutative 92.2%

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

      4. distribute-frac-neg 92.2%

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

      5. sub-neg 92.2%

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

      6. div-sub 95.1%

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

   5. Simplified 95.1%

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

   if -2e4 < (/.f64 x y) < -9.999999999999999e-94 or -3.00000000000000008e-177 < (/.f64 x y) < 5.0000000000000002e-84 or 3.9999999999999999e-47 < (/.f64 x y) < 2e3

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 84.9%

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

      4. associate-/r/ 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in t around 0 84.9%

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

   if -9.999999999999999e-94 < (/.f64 x y) < -3.00000000000000008e-177 or 5.0000000000000002e-84 < (/.f64 x y) < 3.9999999999999999e-47

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 73.7%

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

   3. Taylor expanded in z around inf 70.8%

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

      1. associate-*r/ 88.4%

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

   5. Simplified 88.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-93}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -3 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 2000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 4: 62.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000 \lor \neg \left(\frac{x}{y} \leq -1 \cdot 10^{-93} \lor \neg \left(\frac{x}{y} \leq -3 \cdot 10^{-177}\right) \land \frac{x}{y} \leq 5 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -20000.0)
         (not
          (or (<= (/ x y) -1e-93)
              (and (not (<= (/ x y) -3e-177)) (<= (/ x y) 5e-84)))))
   (* (/ x y) z)
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000.0) || !(((x / y) <= -1e-93) || (!((x / y) <= -3e-177) && ((x / y) <= 5e-84)))) {
		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) <= (-20000.0d0)) .or. (.not. ((x / y) <= (-1d-93)) .or. (.not. ((x / y) <= (-3d-177))) .and. ((x / y) <= 5d-84))) 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) <= -20000.0) || !(((x / y) <= -1e-93) || (!((x / y) <= -3e-177) && ((x / y) <= 5e-84)))) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -20000.0) or not (((x / y) <= -1e-93) or (not ((x / y) <= -3e-177) and ((x / y) <= 5e-84))):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -20000.0) || !((Float64(x / y) <= -1e-93) || (!(Float64(x / y) <= -3e-177) && (Float64(x / y) <= 5e-84))))
		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) <= -20000.0) || ~((((x / y) <= -1e-93) || (~(((x / y) <= -3e-177)) && ((x / y) <= 5e-84)))))
		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], -20000.0], N[Not[Or[LessEqual[N[(x / y), $MachinePrecision], -1e-93], And[N[Not[LessEqual[N[(x / y), $MachinePrecision], -3e-177]], $MachinePrecision], LessEqual[N[(x / y), $MachinePrecision], 5e-84]]]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e4 or -9.999999999999999e-94 < (/.f64 x y) < -3.00000000000000008e-177 or 5.0000000000000002e-84 < (/.f64 x y)

   1. Initial program 95.8%

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

   2. Taylor expanded in x around inf 86.7%

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

   3. Taylor expanded in z around inf 53.7%

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

      1. associate-*r/ 61.8%

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

   5. Simplified 61.8%

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

   if -2e4 < (/.f64 x y) < -9.999999999999999e-94 or -3.00000000000000008e-177 < (/.f64 x y) < 5.0000000000000002e-84

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 85.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000 \lor \neg \left(\frac{x}{y} \leq -1 \cdot 10^{-93} \lor \neg \left(\frac{x}{y} \leq -3 \cdot 10^{-177}\right) \land \frac{x}{y} \leq 5 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) (- z t)))))
   (if (<= t_1 5e+299) t_1 (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+299) {
		tmp = t_1;
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / y) * (z - t))
    if (t_1 <= 5d+299) then
        tmp = t_1
    else
        tmp = x * ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+299) {
		tmp = t_1;
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + ((x / y) * (z - t))
	tmp = 0
	if t_1 <= 5e+299:
		tmp = t_1
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(Float64(x / y) * Float64(z - t)))
	tmp = 0.0
	if (t_1 <= 5e+299)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + ((x / y) * (z - t));
	tmp = 0.0;
	if (t_1 <= 5e+299)
		tmp = t_1;
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+299], t$95$1, N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 5.0000000000000003e299

   1. Initial program 98.4%

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

   if 5.0000000000000003e299 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 85.0%

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

   2. Taylor expanded in x around inf 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. div-sub 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq 5 \cdot 10^{+299}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 6: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-82} \lor \neg \left(t \leq 1.18 \cdot 10^{-150}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -3.2e+26)
     t_1
     (if (<= t -2.05e-50)
       (* (/ x y) z)
       (if (or (<= t -3e-82) (not (<= t 1.18e-150))) t_1 (/ x (/ y z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -3.2e+26) {
		tmp = t_1;
	} else if (t <= -2.05e-50) {
		tmp = (x / y) * z;
	} else if ((t <= -3e-82) || !(t <= 1.18e-150)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (t <= (-3.2d+26)) then
        tmp = t_1
    else if (t <= (-2.05d-50)) then
        tmp = (x / y) * z
    else if ((t <= (-3d-82)) .or. (.not. (t <= 1.18d-150))) then
        tmp = t_1
    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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -3.2e+26) {
		tmp = t_1;
	} else if (t <= -2.05e-50) {
		tmp = (x / y) * z;
	} else if ((t <= -3e-82) || !(t <= 1.18e-150)) {
		tmp = t_1;
	} else {
		tmp = x / (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -3.2e+26:
		tmp = t_1
	elif t <= -2.05e-50:
		tmp = (x / y) * z
	elif (t <= -3e-82) or not (t <= 1.18e-150):
		tmp = t_1
	else:
		tmp = x / (y / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -3.2e+26)
		tmp = t_1;
	elseif (t <= -2.05e-50)
		tmp = Float64(Float64(x / y) * z);
	elseif ((t <= -3e-82) || !(t <= 1.18e-150))
		tmp = t_1;
	else
		tmp = Float64(x / Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (t <= -3.2e+26)
		tmp = t_1;
	elseif (t <= -2.05e-50)
		tmp = (x / y) * z;
	elseif ((t <= -3e-82) || ~((t <= 1.18e-150)))
		tmp = t_1;
	else
		tmp = x / (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+26], t$95$1, If[LessEqual[t, -2.05e-50], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[t, -3e-82], N[Not[LessEqual[t, 1.18e-150]], $MachinePrecision]], t$95$1, N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.20000000000000029e26 or -2.04999999999999993e-50 < t < -2.9999999999999999e-82 or 1.18e-150 < t

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

      3. associate-/l* 81.0%

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

      4. associate-/r/ 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in t around 0 81.0%

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

   if -3.20000000000000029e26 < t < -2.04999999999999993e-50

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 78.9%

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

   3. Taylor expanded in z around inf 63.3%

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

      1. associate-*r/ 74.2%

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

   5. Simplified 74.2%

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

   if -2.9999999999999999e-82 < t < 1.18e-150

   1. Initial program 93.1%

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

   2. Taylor expanded in x around inf 78.1%

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

   3. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-/l* 69.8%

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

   5. Simplified 69.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-82} \lor \neg \left(t \leq 1.18 \cdot 10^{-150}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \end{array} \]

Alternative 7: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+26} \lor \neg \left(\frac{x}{y} \leq 5\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+26) (not (<= (/ x y) 5.0)))
   (* x (/ (- z t) y))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+26) || !((x / y) <= 5.0)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+26)) .or. (.not. ((x / y) <= 5.0d0))) then
        tmp = x * ((z - t) / y)
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+26) || !((x / y) <= 5.0)) {
		tmp = x * ((z - t) / y);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+26) or not ((x / y) <= 5.0):
		tmp = x * ((z - t) / y)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+26) || !(Float64(x / y) <= 5.0))
		tmp = Float64(x * Float64(Float64(z - t) / y));
	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) <= -1e+26) || ~(((x / y) <= 5.0)))
		tmp = x * ((z - t) / y);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+26], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5.0]], $MachinePrecision]], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000005e26 or 5 < (/.f64 x y)

   1. Initial program 95.1%

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

   2. Taylor expanded in x around inf 91.8%

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

   3. Taylor expanded in z around 0 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-frac-neg 91.8%

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

      3. +-commutative 91.8%

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

      4. distribute-frac-neg 91.8%

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

      5. sub-neg 91.8%

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

      6. div-sub 94.7%

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

   5. Simplified 94.7%

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

   if -1.00000000000000005e26 < (/.f64 x y) < 5

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 93.6%

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

      1. associate-*r/ 98.1%

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

   4. Simplified 98.1%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+26} \lor \neg \left(\frac{x}{y} \leq 5\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 8: 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 35.5%

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

3. Final simplification 35.5%

   \[\leadsto t \]

Developer target: 97.2% 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 2023238 
(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))