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

Percentage Accurate: 97.5% → 97.5%

Time: 9.1s

Alternatives: 12

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% 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 97.3%

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

2. Final simplification 97.3%

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

Alternative 2: 65.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ t_2 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+57} \lor \neg \left(\frac{x}{y} \leq 10^{+180}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- t))) (t_2 (/ z (/ y x))))
   (if (<= (/ x y) -2e+191)
     t_2
     (if (<= (/ x y) -4000000.0)
       t_1
       (if (<= (/ x y) 1e-60)
         t
         (if (or (<= (/ x y) 1e+57) (not (<= (/ x y) 1e+180))) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * -t;
	double t_2 = z / (y / x);
	double tmp;
	if ((x / y) <= -2e+191) {
		tmp = t_2;
	} else if ((x / y) <= -4000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-60) {
		tmp = t;
	} else if (((x / y) <= 1e+57) || !((x / y) <= 1e+180)) {
		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) * -t
    t_2 = z / (y / x)
    if ((x / y) <= (-2d+191)) then
        tmp = t_2
    else if ((x / y) <= (-4000000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 1d-60) then
        tmp = t
    else if (((x / y) <= 1d+57) .or. (.not. ((x / y) <= 1d+180))) 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) * -t;
	double t_2 = z / (y / x);
	double tmp;
	if ((x / y) <= -2e+191) {
		tmp = t_2;
	} else if ((x / y) <= -4000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-60) {
		tmp = t;
	} else if (((x / y) <= 1e+57) || !((x / y) <= 1e+180)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * -t
	t_2 = z / (y / x)
	tmp = 0
	if (x / y) <= -2e+191:
		tmp = t_2
	elif (x / y) <= -4000000.0:
		tmp = t_1
	elif (x / y) <= 1e-60:
		tmp = t
	elif ((x / y) <= 1e+57) or not ((x / y) <= 1e+180):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(-t))
	t_2 = Float64(z / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -2e+191)
		tmp = t_2;
	elseif (Float64(x / y) <= -4000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-60)
		tmp = t;
	elseif ((Float64(x / y) <= 1e+57) || !(Float64(x / y) <= 1e+180))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * -t;
	t_2 = z / (y / x);
	tmp = 0.0;
	if ((x / y) <= -2e+191)
		tmp = t_2;
	elseif ((x / y) <= -4000000.0)
		tmp = t_1;
	elseif ((x / y) <= 1e-60)
		tmp = t;
	elseif (((x / y) <= 1e+57) || ~(((x / y) <= 1e+180)))
		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] * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+191], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], -4000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-60], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 1e+57], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+180]], $MachinePrecision]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.00000000000000015e191 or 9.9999999999999997e-61 < (/.f64 x y) < 1.00000000000000005e57 or 1e180 < (/.f64 x y)

   1. Initial program 94.9%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in x around -inf 88.2%

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

   4. Taylor expanded in z around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   if -2.00000000000000015e191 < (/.f64 x y) < -4e6 or 1.00000000000000005e57 < (/.f64 x y) < 1e180

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 94.5%

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

   3. Taylor expanded in x around -inf 93.2%

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

   4. Taylor expanded in z around 0 64.2%

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

      1. associate-*r/ 64.2%

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

      2. mul-1-neg 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

      4. associate-*r/ 65.9%

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

   6. Simplified 65.9%

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

   if -4e6 < (/.f64 x y) < 9.9999999999999997e-61

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 75.3%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+57} \lor \neg \left(\frac{x}{y} \leq 10^{+180}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 3: 65.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;\frac{t}{-\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+57} \lor \neg \left(\frac{x}{y} \leq 10^{+180}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ y x))))
   (if (<= (/ x y) -2e+191)
     t_1
     (if (<= (/ x y) -4000000.0)
       (/ t (- (/ y x)))
       (if (<= (/ x y) 1e-60)
         t
         (if (or (<= (/ x y) 1e+57) (not (<= (/ x y) 1e+180)))
           t_1
           (* (/ x y) (- t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if ((x / y) <= -2e+191) {
		tmp = t_1;
	} else if ((x / y) <= -4000000.0) {
		tmp = t / -(y / x);
	} else if ((x / y) <= 1e-60) {
		tmp = t;
	} else if (((x / y) <= 1e+57) || !((x / y) <= 1e+180)) {
		tmp = t_1;
	} else {
		tmp = (x / y) * -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 = z / (y / x)
    if ((x / y) <= (-2d+191)) then
        tmp = t_1
    else if ((x / y) <= (-4000000.0d0)) then
        tmp = t / -(y / x)
    else if ((x / y) <= 1d-60) then
        tmp = t
    else if (((x / y) <= 1d+57) .or. (.not. ((x / y) <= 1d+180))) then
        tmp = t_1
    else
        tmp = (x / y) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if ((x / y) <= -2e+191) {
		tmp = t_1;
	} else if ((x / y) <= -4000000.0) {
		tmp = t / -(y / x);
	} else if ((x / y) <= 1e-60) {
		tmp = t;
	} else if (((x / y) <= 1e+57) || !((x / y) <= 1e+180)) {
		tmp = t_1;
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (y / x)
	tmp = 0
	if (x / y) <= -2e+191:
		tmp = t_1
	elif (x / y) <= -4000000.0:
		tmp = t / -(y / x)
	elif (x / y) <= 1e-60:
		tmp = t
	elif ((x / y) <= 1e+57) or not ((x / y) <= 1e+180):
		tmp = t_1
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -2e+191)
		tmp = t_1;
	elseif (Float64(x / y) <= -4000000.0)
		tmp = Float64(t / Float64(-Float64(y / x)));
	elseif (Float64(x / y) <= 1e-60)
		tmp = t;
	elseif ((Float64(x / y) <= 1e+57) || !(Float64(x / y) <= 1e+180))
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (y / x);
	tmp = 0.0;
	if ((x / y) <= -2e+191)
		tmp = t_1;
	elseif ((x / y) <= -4000000.0)
		tmp = t / -(y / x);
	elseif ((x / y) <= 1e-60)
		tmp = t;
	elseif (((x / y) <= 1e+57) || ~(((x / y) <= 1e+180)))
		tmp = t_1;
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+191], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -4000000.0], N[(t / (-N[(y / x), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-60], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 1e+57], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+180]], $MachinePrecision]], t$95$1, N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2.00000000000000015e191 or 9.9999999999999997e-61 < (/.f64 x y) < 1.00000000000000005e57 or 1e180 < (/.f64 x y)

   1. Initial program 94.9%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in x around -inf 88.2%

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

   4. Taylor expanded in z around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   if -2.00000000000000015e191 < (/.f64 x y) < -4e6

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

      3. *-commutative 60.9%

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

      4. associate-*l/ 66.6%

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

      5. cancel-sign-sub-inv 66.6%

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

      6. *-lft-identity 66.6%

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

      7. mul-1-neg 66.6%

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

      8. distribute-rgt-in 66.6%

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

      9. mul-1-neg 66.6%

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

      10. unsub-neg 66.6%

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

   4. Simplified 66.6%

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

      1. sub-neg 66.6%

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

      2. distribute-lft-in 66.6%

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

      3. *-commutative 66.6%

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

      4. *-un-lft-identity 66.6%

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

      5. distribute-rgt-neg-in 66.6%

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

      6. clear-num 66.5%

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

      7. div-inv 66.7%

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

      8. unsub-neg 66.7%

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

      9. associate-/r/ 52.5%

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

      10. *-commutative 52.5%

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

   6. Applied egg-rr 52.5%

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

   7. Taylor expanded in x around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-*l/ 51.7%

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

      3. *-commutative 51.7%

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

      4. distribute-rgt-neg-out 51.7%

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

      5. distribute-neg-frac 51.7%

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

   9. Simplified 51.7%

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

       1. *-commutative 51.7%

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

       2. div-inv 51.6%

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

       3. associate-*l* 64.5%

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

       4. add-sqr-sqrt 41.5%

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

       5. sqrt-unprod 38.6%

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

       6. sqr-neg 38.6%

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

       7. sqrt-unprod 1.2%

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

       8. add-sqr-sqrt 1.6%

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

       9. associate-/r/ 1.6%

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

       10. div-inv 1.6%

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

       11. frac-2neg 1.6%

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

       12. add-sqr-sqrt 0.4%

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

       13. sqrt-unprod 20.3%

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

       14. sqr-neg 20.3%

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

       15. sqrt-unprod 22.8%

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

       16. add-sqr-sqrt 64.6%

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

       17. distribute-neg-frac 64.6%

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

   11. Applied egg-rr 64.6%

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

   if -4e6 < (/.f64 x y) < 9.9999999999999997e-61

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 75.3%

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

   if 1.00000000000000005e57 < (/.f64 x y) < 1e180

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.6%

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

   3. Taylor expanded in x around -inf 99.6%

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

   4. Taylor expanded in z around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. mul-1-neg 72.3%

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

      3. distribute-rgt-neg-in 72.3%

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

      4. associate-*r/ 67.9%

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

   6. Simplified 67.9%

      \[\leadsto \color{blue}{t \cdot \frac{-x}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;\frac{t}{-\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+57} \lor \neg \left(\frac{x}{y} \leq 10^{+180}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 4: 65.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;\frac{t}{-\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+57} \lor \neg \left(\frac{x}{y} \leq 10^{+180}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ y x))))
   (if (<= (/ x y) -2e+191)
     t_1
     (if (<= (/ x y) -4000000.0)
       (/ t (- (/ y x)))
       (if (<= (/ x y) 1e-60)
         t
         (if (or (<= (/ x y) 1e+57) (not (<= (/ x y) 1e+180)))
           t_1
           (/ (- (* x t)) y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if ((x / y) <= -2e+191) {
		tmp = t_1;
	} else if ((x / y) <= -4000000.0) {
		tmp = t / -(y / x);
	} else if ((x / y) <= 1e-60) {
		tmp = t;
	} else if (((x / y) <= 1e+57) || !((x / y) <= 1e+180)) {
		tmp = t_1;
	} else {
		tmp = -(x * 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 = z / (y / x)
    if ((x / y) <= (-2d+191)) then
        tmp = t_1
    else if ((x / y) <= (-4000000.0d0)) then
        tmp = t / -(y / x)
    else if ((x / y) <= 1d-60) then
        tmp = t
    else if (((x / y) <= 1d+57) .or. (.not. ((x / y) <= 1d+180))) then
        tmp = t_1
    else
        tmp = -(x * t) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if ((x / y) <= -2e+191) {
		tmp = t_1;
	} else if ((x / y) <= -4000000.0) {
		tmp = t / -(y / x);
	} else if ((x / y) <= 1e-60) {
		tmp = t;
	} else if (((x / y) <= 1e+57) || !((x / y) <= 1e+180)) {
		tmp = t_1;
	} else {
		tmp = -(x * t) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (y / x)
	tmp = 0
	if (x / y) <= -2e+191:
		tmp = t_1
	elif (x / y) <= -4000000.0:
		tmp = t / -(y / x)
	elif (x / y) <= 1e-60:
		tmp = t
	elif ((x / y) <= 1e+57) or not ((x / y) <= 1e+180):
		tmp = t_1
	else:
		tmp = -(x * t) / y
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -2e+191)
		tmp = t_1;
	elseif (Float64(x / y) <= -4000000.0)
		tmp = Float64(t / Float64(-Float64(y / x)));
	elseif (Float64(x / y) <= 1e-60)
		tmp = t;
	elseif ((Float64(x / y) <= 1e+57) || !(Float64(x / y) <= 1e+180))
		tmp = t_1;
	else
		tmp = Float64(Float64(-Float64(x * t)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z / (y / x);
	tmp = 0.0;
	if ((x / y) <= -2e+191)
		tmp = t_1;
	elseif ((x / y) <= -4000000.0)
		tmp = t / -(y / x);
	elseif ((x / y) <= 1e-60)
		tmp = t;
	elseif (((x / y) <= 1e+57) || ~(((x / y) <= 1e+180)))
		tmp = t_1;
	else
		tmp = -(x * t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e+191], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -4000000.0], N[(t / (-N[(y / x), $MachinePrecision])), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-60], t, If[Or[LessEqual[N[(x / y), $MachinePrecision], 1e+57], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+180]], $MachinePrecision]], t$95$1, N[((-N[(x * t), $MachinePrecision]) / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2.00000000000000015e191 or 9.9999999999999997e-61 < (/.f64 x y) < 1.00000000000000005e57 or 1e180 < (/.f64 x y)

   1. Initial program 94.9%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in x around -inf 88.2%

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

   4. Taylor expanded in z around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   if -2.00000000000000015e191 < (/.f64 x y) < -4e6

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 60.9%

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

      1. mul-1-neg 60.9%

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

      2. unsub-neg 60.9%

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

      3. *-commutative 60.9%

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

      4. associate-*l/ 66.6%

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

      5. cancel-sign-sub-inv 66.6%

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

      6. *-lft-identity 66.6%

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

      7. mul-1-neg 66.6%

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

      8. distribute-rgt-in 66.6%

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

      9. mul-1-neg 66.6%

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

      10. unsub-neg 66.6%

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

   4. Simplified 66.6%

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

      1. sub-neg 66.6%

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

      2. distribute-lft-in 66.6%

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

      3. *-commutative 66.6%

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

      4. *-un-lft-identity 66.6%

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

      5. distribute-rgt-neg-in 66.6%

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

      6. clear-num 66.5%

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

      7. div-inv 66.7%

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

      8. unsub-neg 66.7%

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

      9. associate-/r/ 52.5%

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

      10. *-commutative 52.5%

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

   6. Applied egg-rr 52.5%

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

   7. Taylor expanded in x around inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-*l/ 51.7%

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

      3. *-commutative 51.7%

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

      4. distribute-rgt-neg-out 51.7%

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

      5. distribute-neg-frac 51.7%

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

   9. Simplified 51.7%

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

       1. *-commutative 51.7%

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

       2. div-inv 51.6%

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

       3. associate-*l* 64.5%

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

       4. add-sqr-sqrt 41.5%

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

       5. sqrt-unprod 38.6%

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

       6. sqr-neg 38.6%

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

       7. sqrt-unprod 1.2%

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

       8. add-sqr-sqrt 1.6%

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

       9. associate-/r/ 1.6%

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

       10. div-inv 1.6%

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

       11. frac-2neg 1.6%

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

       12. add-sqr-sqrt 0.4%

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

       13. sqrt-unprod 20.3%

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

       14. sqr-neg 20.3%

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

       15. sqrt-unprod 22.8%

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

       16. add-sqr-sqrt 64.6%

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

       17. distribute-neg-frac 64.6%

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

   11. Applied egg-rr 64.6%

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

   if -4e6 < (/.f64 x y) < 9.9999999999999997e-61

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0 75.3%

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

   if 1.00000000000000005e57 < (/.f64 x y) < 1e180

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.6%

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

   3. Taylor expanded in x around -inf 99.6%

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

   4. Taylor expanded in z around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-lft-neg-out 72.3%

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

      3. *-commutative 72.3%

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

   6. Simplified 72.3%

      \[\leadsto \frac{\color{blue}{x \cdot \left(-t\right)}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+191}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -4000000:\\ \;\;\;\;\frac{t}{-\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-60}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+57} \lor \neg \left(\frac{x}{y} \leq 10^{+180}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x \cdot t}{y}\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-64} \lor \neg \left(t \leq 520000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= t -3.3e-95)
     t_1
     (if (<= t 2.9e-139)
       (* (/ x y) z)
       (if (or (<= t 1.05e-64) (not (<= t 520000.0))) t_1 (/ z (/ y x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -3.3e-95) {
		tmp = t_1;
	} else if (t <= 2.9e-139) {
		tmp = (x / y) * z;
	} else if ((t <= 1.05e-64) || !(t <= 520000.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (t <= (-3.3d-95)) then
        tmp = t_1
    else if (t <= 2.9d-139) then
        tmp = (x / y) * z
    else if ((t <= 1.05d-64) .or. (.not. (t <= 520000.0d0))) then
        tmp = t_1
    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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (t <= -3.3e-95) {
		tmp = t_1;
	} else if (t <= 2.9e-139) {
		tmp = (x / y) * z;
	} else if ((t <= 1.05e-64) || !(t <= 520000.0)) {
		tmp = t_1;
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if t <= -3.3e-95:
		tmp = t_1
	elif t <= 2.9e-139:
		tmp = (x / y) * z
	elif (t <= 1.05e-64) or not (t <= 520000.0):
		tmp = t_1
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (t <= -3.3e-95)
		tmp = t_1;
	elseif (t <= 2.9e-139)
		tmp = Float64(Float64(x / y) * z);
	elseif ((t <= 1.05e-64) || !(t <= 520000.0))
		tmp = t_1;
	else
		tmp = Float64(z / Float64(y / x));
	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 <= -3.3e-95)
		tmp = t_1;
	elseif (t <= 2.9e-139)
		tmp = (x / y) * z;
	elseif ((t <= 1.05e-64) || ~((t <= 520000.0)))
		tmp = t_1;
	else
		tmp = z / (y / x);
	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, -3.3e-95], t$95$1, If[LessEqual[t, 2.9e-139], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[Or[LessEqual[t, 1.05e-64], N[Not[LessEqual[t, 520000.0]], $MachinePrecision]], t$95$1, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3e-95 or 2.8999999999999999e-139 < t < 1.05000000000000006e-64 or 5.2e5 < t

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. unsub-neg 78.6%

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

      3. *-commutative 78.6%

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

      4. associate-*l/ 83.2%

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

      5. cancel-sign-sub-inv 83.2%

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

      6. *-lft-identity 83.2%

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

      7. mul-1-neg 83.2%

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

      8. distribute-rgt-in 83.2%

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

      9. mul-1-neg 83.2%

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

      10. unsub-neg 83.2%

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

   4. Simplified 83.2%

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

   if -3.3e-95 < t < 2.8999999999999999e-139

   1. Initial program 92.6%

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

   2. Taylor expanded in x around 0 95.0%

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

   3. Taylor expanded in x around -inf 78.8%

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

   4. Taylor expanded in z around inf 73.3%

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

      1. associate-/l* 70.8%

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

      2. associate-/r/ 74.5%

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

   6. Applied egg-rr 74.5%

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

   if 1.05000000000000006e-64 < t < 5.2e5

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

   3. Taylor expanded in x around -inf 75.9%

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

   4. Taylor expanded in z around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-/l* 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-139}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-64} \lor \neg \left(t \leq 520000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 6: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000000 \lor \neg \left(\frac{x}{y} \leq 400000\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2000000000000.0) (not (<= (/ x y) 400000.0)))
   (/ (* x (- z t)) y)
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2000000000000.0) || !((x / y) <= 400000.0)) {
		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) <= (-2000000000000.0d0)) .or. (.not. ((x / y) <= 400000.0d0))) 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) <= -2000000000000.0) || !((x / y) <= 400000.0)) {
		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) <= -2000000000000.0) or not ((x / y) <= 400000.0):
		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) <= -2000000000000.0) || !(Float64(x / y) <= 400000.0))
		tmp = Float64(Float64(x * 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) <= -2000000000000.0) || ~(((x / y) <= 400000.0)))
		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], -2000000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 400000.0]], $MachinePrecision]], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e12 or 4e5 < (/.f64 x y)

   1. Initial program 96.2%

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

   2. Taylor expanded in x around 0 96.9%

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

   3. Taylor expanded in x around -inf 96.8%

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

   if -2e12 < (/.f64 x y) < 4e5

   1. Initial program 98.4%

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

   2. Taylor expanded in z around inf 88.8%

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

      1. associate-*l/ 94.6%

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

      2. *-commutative 94.6%

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

   4. Simplified 94.6%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000000000 \lor \neg \left(\frac{x}{y} \leq 400000\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 7: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4000000.0) (not (<= (/ x y) 4e-29)))
   (/ (- z t) (/ y x))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4000000.0) || !((x / y) <= 4e-29)) {
		tmp = (z - t) / (y / x);
	} 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) <= (-4000000.0d0)) .or. (.not. ((x / y) <= 4d-29))) then
        tmp = (z - t) / (y / x)
    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) <= -4000000.0) || !((x / y) <= 4e-29)) {
		tmp = (z - t) / (y / x);
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4000000.0) or not ((x / y) <= 4e-29):
		tmp = (z - t) / (y / x)
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4000000.0) || !(Float64(x / y) <= 4e-29))
		tmp = Float64(Float64(z - t) / Float64(y / x));
	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) <= -4000000.0) || ~(((x / y) <= 4e-29)))
		tmp = (z - t) / (y / x);
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-29]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4e6 or 3.99999999999999977e-29 < (/.f64 x y)

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 93.7%

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

   3. Taylor expanded in x around -inf 92.8%

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

   4. Taylor expanded in z around 0 86.9%

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

      1. mul-1-neg 86.9%

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

      2. associate-*r/ 83.0%

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

      3. distribute-lft-neg-out 83.0%

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

      4. associate-*l/ 84.3%

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

      5. *-commutative 84.3%

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

      6. distribute-rgt-out 94.6%

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

      7. +-commutative 94.6%

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

      8. sub-neg 94.6%

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

      9. *-commutative 94.6%

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

      10. associate-*r/ 92.8%

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

      11. associate-/l* 95.1%

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

   6. Simplified 95.1%

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

   if -4e6 < (/.f64 x y) < 3.99999999999999977e-29

   1. Initial program 98.3%

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

   2. Taylor expanded in z around inf 93.5%

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

      1. associate-*l/ 97.5%

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

      2. *-commutative 97.5%

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

   4. Simplified 97.5%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4000000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 8: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-26} \lor \neg \left(\frac{x}{y} \leq 10^{-60}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-26) (not (<= (/ x y) 1e-60))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-26) || !((x / y) <= 1e-60)) {
		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) <= (-5d-26)) .or. (.not. ((x / y) <= 1d-60))) 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) <= -5e-26) || !((x / y) <= 1e-60)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-26) or not ((x / y) <= 1e-60):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-26) || !(Float64(x / y) <= 1e-60))
		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) <= -5e-26) || ~(((x / y) <= 1e-60)))
		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], -5e-26], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-60]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000019e-26 or 9.9999999999999997e-61 < (/.f64 x y)

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in x around -inf 87.5%

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

   4. Taylor expanded in z around inf 53.4%

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

      1. associate-/l* 51.6%

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

      2. associate-/r/ 58.3%

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

   6. Applied egg-rr 58.3%

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

   if -5.00000000000000019e-26 < (/.f64 x y) < 9.9999999999999997e-61

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 77.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-26} \lor \neg \left(\frac{x}{y} \leq 10^{-60}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-26} \lor \neg \left(\frac{x}{y} \leq 10^{-60}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-26) (not (<= (/ x y) 1e-60))) (/ z (/ y x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-26) || !((x / y) <= 1e-60)) {
		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-26)) .or. (.not. ((x / y) <= 1d-60))) 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-26) || !((x / y) <= 1e-60)) {
		tmp = z / (y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-26) or not ((x / y) <= 1e-60):
		tmp = z / (y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-26) || !(Float64(x / y) <= 1e-60))
		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-26) || ~(((x / y) <= 1e-60)))
		tmp = z / (y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-26], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-60]], $MachinePrecision]], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000019e-26 or 9.9999999999999997e-61 < (/.f64 x y)

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 91.9%

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

   3. Taylor expanded in x around -inf 87.5%

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

   4. Taylor expanded in z around inf 53.4%

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

      1. *-commutative 53.4%

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

      2. associate-/l* 58.7%

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

   6. Simplified 58.7%

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

   if -5.00000000000000019e-26 < (/.f64 x y) < 9.9999999999999997e-61

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0 77.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-26} \lor \neg \left(\frac{x}{y} \leq 10^{-60}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -118000000000 \lor \neg \left(t \leq 2.1 \cdot 10^{+159}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -118000000000.0) (not (<= t 2.1e+159)))
   (* t (- 1.0 (/ x y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -118000000000.0) || !(t <= 2.1e+159)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-118000000000.0d0)) .or. (.not. (t <= 2.1d+159))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -118000000000.0) || !(t <= 2.1e+159)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -118000000000.0) or not (t <= 2.1e+159):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -118000000000.0) || !(t <= 2.1e+159))
		tmp = Float64(t * Float64(1.0 - Float64(x / 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 ((t <= -118000000000.0) || ~((t <= 2.1e+159)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -118000000000.0], N[Not[LessEqual[t, 2.1e+159]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.18e11 or 2.09999999999999989e159 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

      3. *-commutative 86.1%

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

      4. associate-*l/ 93.2%

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

      5. cancel-sign-sub-inv 93.2%

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

      6. *-lft-identity 93.2%

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

      7. mul-1-neg 93.2%

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

      8. distribute-rgt-in 93.2%

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

      9. mul-1-neg 93.2%

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

      10. unsub-neg 93.2%

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

   4. Simplified 93.2%

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

   if -1.18e11 < t < 2.09999999999999989e159

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf 83.1%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

   4. Simplified 87.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -118000000000 \lor \neg \left(t \leq 2.1 \cdot 10^{+159}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 11: 55.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0041 \lor \neg \left(x \leq 126\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -0.0041) (not (<= x 126.0))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -0.0041) || !(x <= 126.0)) {
		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 <= (-0.0041d0)) .or. (.not. (x <= 126.0d0))) 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 <= -0.0041) || !(x <= 126.0)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -0.0041) or not (x <= 126.0):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -0.0041) || !(x <= 126.0))
		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 <= -0.0041) || ~((x <= 126.0)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -0.0041], N[Not[LessEqual[x, 126.0]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -0.00410000000000000035 or 126 < x

   1. Initial program 96.4%

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

   2. Taylor expanded in x around 0 85.9%

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

   3. Taylor expanded in x around -inf 78.0%

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

   4. Taylor expanded in z around inf 51.0%

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

      1. associate-*r/ 56.7%

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

   6. Simplified 56.7%

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

   if -0.00410000000000000035 < x < 126

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 59.7%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0041 \lor \neg \left(x \leq 126\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 39.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in x around 0 35.3%

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

3. Final simplification 35.3%

   \[\leadsto t \]

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 2023308 
(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))