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

Percentage Accurate: 97.7% → 97.8%

Time: 8.4s

Alternatives: 12

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t + \frac{z - t}{\frac{y}{x}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

2. Taylor expanded in x around 0 94.7%

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

   1. *-commutative 94.7%

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

   2. associate-*r/ 93.9%

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

4. Simplified 93.9%

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

   1. associate-*r/ 94.7%

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

   2. associate-*l/ 97.4%

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

   3. clear-num 97.3%

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

   4. associate-*l/ 97.6%

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

   5. *-un-lft-identity 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

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

Alternative 2: 94.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-9} \lor \neg \left(\frac{x}{y} \leq 10^{-17}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e-9) (not (<= (/ x y) 1e-17)))
   (/ (- z t) (/ y x))
   (+ t (/ (* z x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-9) || !((x / y) <= 1e-17)) {
		tmp = (z - t) / (y / x);
	} else {
		tmp = t + ((z * x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d-9)) .or. (.not. ((x / y) <= 1d-17))) then
        tmp = (z - t) / (y / x)
    else
        tmp = t + ((z * x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e-9) || !((x / y) <= 1e-17)) {
		tmp = (z - t) / (y / x);
	} else {
		tmp = t + ((z * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e-9) or not ((x / y) <= 1e-17):
		tmp = (z - t) / (y / x)
	else:
		tmp = t + ((z * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e-9) || !(Float64(x / y) <= 1e-17))
		tmp = Float64(Float64(z - t) / Float64(y / x));
	else
		tmp = Float64(t + Float64(Float64(z * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e-9) || ~(((x / y) <= 1e-17)))
		tmp = (z - t) / (y / x);
	else
		tmp = t + ((z * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e-9], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e-17]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.00000000000000012e-9 or 1.00000000000000007e-17 < (/.f64 x y)

   1. Initial program 97.0%

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

      1. associate-*l/ 93.2%

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

      2. div-inv 93.1%

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

      3. associate-*r* 92.8%

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

      4. div-inv 92.9%

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

      5. fma-udef 92.9%

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

      6. add-cube-cbrt 92.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)}} \]

      7. pow3 92.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)}\right)}^{3}} \]

      8. fma-udef 92.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot \frac{z - t}{y} + t}}\right)}^{3} \]

      9. associate-*r/ 92.5%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t}\right)}^{3} \]

      10. associate-*l/ 96.4%

          \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{x}{y} \cdot \left(z - t\right)} + t}\right)}^{3} \]

      11. fma-def 96.4%

          \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)}}\right)}^{3} \]

   3. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)}\right)}^{3}} \]

   4. Taylor expanded in x around -inf 91.3%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(z - t\right) \cdot x}{y}}}\right)}^{3} \]
   5. Step-by-step derivation

      1. rem-cube-cbrt 91.9%

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

      2. associate-/l* 96.1%

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

   6. Applied egg-rr 96.1%

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

   if -2.00000000000000012e-9 < (/.f64 x y) < 1.00000000000000007e-17

   1. Initial program 97.8%

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

   2. Taylor expanded in z around inf 97.7%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-9} \lor \neg \left(\frac{x}{y} \leq 10^{-17}\right):\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z \cdot x}{y}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+58}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+61)
   (* t (/ (- x) y))
   (if (<= (/ x y) 5e+58) (+ t (* x (/ z y))) (/ (* t x) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+61) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 5e+58) {
		tmp = t + (x * (z / y));
	} else {
		tmp = (t * x) / -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+61)) then
        tmp = t * (-x / y)
    else if ((x / y) <= 5d+58) then
        tmp = t + (x * (z / y))
    else
        tmp = (t * x) / -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+61) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 5e+58) {
		tmp = t + (x * (z / y));
	} else {
		tmp = (t * x) / -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+61:
		tmp = t * (-x / y)
	elif (x / y) <= 5e+58:
		tmp = t + (x * (z / y))
	else:
		tmp = (t * x) / -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+61)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (Float64(x / y) <= 5e+58)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	else
		tmp = Float64(Float64(t * x) / Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+61)
		tmp = t * (-x / y);
	elseif ((x / y) <= 5e+58)
		tmp = t + (x * (z / y));
	else
		tmp = (t * x) / -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+61], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+58], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.00000000000000018e61

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

      3. associate-/l* 61.9%

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

      4. associate-/r/ 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in y around 0 61.6%

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

      1. associate-*r/ 61.6%

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

      2. *-commutative 61.6%

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

      3. neg-mul-1 61.6%

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

      4. distribute-rgt-neg-in 61.6%

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

      5. *-commutative 61.6%

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

      6. associate-*r/ 64.9%

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

      7. distribute-lft-neg-out 64.9%

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

      8. distribute-rgt-neg-in 64.9%

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

      9. mul-1-neg 64.9%

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

      10. associate-*r/ 64.9%

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

      11. neg-mul-1 64.9%

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

   7. Simplified 64.9%

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

   if -5.00000000000000018e61 < (/.f64 x y) < 4.99999999999999986e58

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 89.9%

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

      1. div-inv 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*l* 90.4%

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

      4. div-inv 90.4%

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

   4. Applied egg-rr 90.4%

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

   if 4.99999999999999986e58 < (/.f64 x y)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

      3. associate-/l* 72.4%

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

      4. associate-/r/ 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

      3. neg-mul-1 75.7%

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

      4. distribute-rgt-neg-in 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r/ 74.1%

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

      7. distribute-lft-neg-out 74.1%

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

      8. distribute-rgt-neg-in 74.1%

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

      9. mul-1-neg 74.1%

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

      10. associate-*r/ 74.1%

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

      11. neg-mul-1 74.1%

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

   7. Simplified 74.1%

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

      1. frac-2neg 74.1%

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

      2. remove-double-neg 74.1%

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

      3. associate-*r/ 75.7%

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

   9. Applied egg-rr 75.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+58}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \]

Alternative 4: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+58}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+61)
   (* t (/ (- x) y))
   (if (<= (/ x y) 5e+58) (+ t (* z (/ x y))) (/ (* t x) (- y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+61) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 5e+58) {
		tmp = t + (z * (x / y));
	} else {
		tmp = (t * x) / -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d+61)) then
        tmp = t * (-x / y)
    else if ((x / y) <= 5d+58) then
        tmp = t + (z * (x / y))
    else
        tmp = (t * x) / -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+61) {
		tmp = t * (-x / y);
	} else if ((x / y) <= 5e+58) {
		tmp = t + (z * (x / y));
	} else {
		tmp = (t * x) / -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+61:
		tmp = t * (-x / y)
	elif (x / y) <= 5e+58:
		tmp = t + (z * (x / y))
	else:
		tmp = (t * x) / -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+61)
		tmp = Float64(t * Float64(Float64(-x) / y));
	elseif (Float64(x / y) <= 5e+58)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(Float64(t * x) / Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+61)
		tmp = t * (-x / y);
	elseif ((x / y) <= 5e+58)
		tmp = t + (z * (x / y));
	else
		tmp = (t * x) / -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+61], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+58], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.00000000000000018e61

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. unsub-neg 61.7%

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

      3. associate-/l* 61.9%

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

      4. associate-/r/ 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in y around 0 61.6%

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

      1. associate-*r/ 61.6%

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

      2. *-commutative 61.6%

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

      3. neg-mul-1 61.6%

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

      4. distribute-rgt-neg-in 61.6%

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

      5. *-commutative 61.6%

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

      6. associate-*r/ 64.9%

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

      7. distribute-lft-neg-out 64.9%

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

      8. distribute-rgt-neg-in 64.9%

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

      9. mul-1-neg 64.9%

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

      10. associate-*r/ 64.9%

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

      11. neg-mul-1 64.9%

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

   7. Simplified 64.9%

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

   if -5.00000000000000018e61 < (/.f64 x y) < 4.99999999999999986e58

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf 89.9%

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

      1. associate-*r/ 93.2%

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

   4. Simplified 93.2%

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

   if 4.99999999999999986e58 < (/.f64 x y)

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

      3. associate-/l* 72.4%

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

      4. associate-/r/ 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in y around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. *-commutative 75.7%

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

      3. neg-mul-1 75.7%

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

      4. distribute-rgt-neg-in 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r/ 74.1%

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

      7. distribute-lft-neg-out 74.1%

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

      8. distribute-rgt-neg-in 74.1%

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

      9. mul-1-neg 74.1%

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

      10. associate-*r/ 74.1%

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

      11. neg-mul-1 74.1%

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

   7. Simplified 74.1%

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

      1. frac-2neg 74.1%

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

      2. remove-double-neg 74.1%

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

      3. associate-*r/ 75.7%

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

   9. Applied egg-rr 75.7%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+58}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{-y}\\ \end{array} \]

Alternative 5: 95.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-17}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2000.0)
   (+ t (* x (/ (- z t) y)))
   (if (<= (/ x y) 1e-17) (+ t (* z (/ x y))) (/ (- z t) (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2000.0) {
		tmp = t + (x * ((z - t) / y));
	} else if ((x / y) <= 1e-17) {
		tmp = t + (z * (x / y));
	} else {
		tmp = (z - t) / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2000.0d0)) then
        tmp = t + (x * ((z - t) / y))
    else if ((x / y) <= 1d-17) then
        tmp = t + (z * (x / y))
    else
        tmp = (z - t) / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2000.0) {
		tmp = t + (x * ((z - t) / y));
	} else if ((x / y) <= 1e-17) {
		tmp = t + (z * (x / y));
	} else {
		tmp = (z - t) / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2000.0:
		tmp = t + (x * ((z - t) / y))
	elif (x / y) <= 1e-17:
		tmp = t + (z * (x / y))
	else:
		tmp = (z - t) / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2000.0)
		tmp = Float64(t + Float64(x * Float64(Float64(z - t) / y)));
	elseif (Float64(x / y) <= 1e-17)
		tmp = Float64(t + Float64(z * Float64(x / y)));
	else
		tmp = Float64(Float64(z - t) / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2000.0)
		tmp = t + (x * ((z - t) / y));
	elseif ((x / y) <= 1e-17)
		tmp = t + (z * (x / y));
	else
		tmp = (z - t) / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2000.0], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-17], N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 94.7%

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

   2. Taylor expanded in x around 0 95.4%

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

      1. *-commutative 95.4%

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

      2. associate-*r/ 98.2%

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

   4. Simplified 98.2%

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

   if -2e3 < (/.f64 x y) < 1.00000000000000007e-17

   1. Initial program 97.9%

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

   2. Taylor expanded in z around inf 96.4%

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

      1. associate-*r/ 96.6%

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

   4. Simplified 96.6%

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

   if 1.00000000000000007e-17 < (/.f64 x y)

   1. Initial program 98.5%

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

      1. associate-*l/ 92.2%

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

      2. div-inv 92.1%

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

      3. associate-*r* 92.1%

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

      4. div-inv 92.2%

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

      5. fma-udef 92.2%

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

      6. add-cube-cbrt 91.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)} \cdot \sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)}} \]

      7. pow3 91.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)}\right)}^{3}} \]

      8. fma-udef 91.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot \frac{z - t}{y} + t}}\right)}^{3} \]

      9. associate-*r/ 91.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t}\right)}^{3} \]

      10. associate-*l/ 97.9%

          \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{x}{y} \cdot \left(z - t\right)} + t}\right)}^{3} \]

      11. fma-def 97.9%

          \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)}}\right)}^{3} \]

   3. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(\frac{x}{y}, z - t, t\right)}\right)}^{3}} \]

   4. Taylor expanded in x around -inf 91.2%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\frac{\left(z - t\right) \cdot x}{y}}}\right)}^{3} \]
   5. Step-by-step derivation

      1. rem-cube-cbrt 91.7%

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

      2. associate-/l* 98.0%

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

   6. Applied egg-rr 98.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-17}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \end{array} \]

Alternative 6: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -40.0) (not (<= (/ x y) 5e-5))) (* t (/ (- x) y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -40.0) || !((x / y) <= 5e-5)) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-40.0d0)) .or. (.not. ((x / y) <= 5d-5))) then
        tmp = t * (-x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -40.0) || !((x / y) <= 5e-5)) {
		tmp = t * (-x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -40.0) or not ((x / y) <= 5e-5):
		tmp = t * (-x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -40.0) || !(Float64(x / y) <= 5e-5))
		tmp = Float64(t * Float64(Float64(-x) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -40.0) || ~(((x / y) <= 5e-5)))
		tmp = t * (-x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -40.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-5]], $MachinePrecision]], N[(t * N[((-x) / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -40 or 5.00000000000000024e-5 < (/.f64 x y)

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

      3. associate-/l* 61.3%

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

      4. associate-/r/ 61.0%

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

   4. Simplified 61.0%

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

   5. Taylor expanded in y around 0 60.6%

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

      1. associate-*r/ 60.6%

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

      2. *-commutative 60.6%

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

      3. neg-mul-1 60.6%

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

      4. distribute-rgt-neg-in 60.6%

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

      5. *-commutative 60.6%

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

      6. associate-*r/ 61.9%

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

      7. distribute-lft-neg-out 61.9%

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

      8. distribute-rgt-neg-in 61.9%

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

      9. mul-1-neg 61.9%

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

      10. associate-*r/ 61.9%

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

      11. neg-mul-1 61.9%

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

   7. Simplified 61.9%

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

   if -40 < (/.f64 x y) < 5.00000000000000024e-5

   1. Initial program 97.9%

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

   2. Taylor expanded in x around 0 74.2%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-5}\right):\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+21} \lor \neg \left(t \leq 3.2 \cdot 10^{+107}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.5e+21) (not (<= t 3.2e+107)))
   (- t (* t (/ x y)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.5e+21) || !(t <= 3.2e+107)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.5d+21)) .or. (.not. (t <= 3.2d+107))) then
        tmp = t - (t * (x / y))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.5e+21) || !(t <= 3.2e+107)) {
		tmp = t - (t * (x / y));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.5e+21) or not (t <= 3.2e+107):
		tmp = t - (t * (x / y))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.5e+21) || !(t <= 3.2e+107))
		tmp = Float64(t - Float64(t * Float64(x / y)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.5e+21) || ~((t <= 3.2e+107)))
		tmp = t - (t * (x / y));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.5e+21], N[Not[LessEqual[t, 3.2e+107]], $MachinePrecision]], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e21 or 3.20000000000000029e107 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. unsub-neg 90.3%

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

      3. associate-*r/ 92.1%

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

   4. Simplified 92.1%

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

   if -4.5e21 < t < 3.20000000000000029e107

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 84.9%

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

   4. Simplified 84.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+21} \lor \neg \left(t \leq 3.2 \cdot 10^{+107}\right):\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+21} \lor \neg \left(t \leq 7.2 \cdot 10^{+108}\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.2e+21) (not (<= t 7.2e+108)))
   (- t (/ t (/ y x)))
   (+ t (/ z (/ y x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e+21) || !(t <= 7.2e+108)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-4.2d+21)) .or. (.not. (t <= 7.2d+108))) then
        tmp = t - (t / (y / x))
    else
        tmp = t + (z / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.2e+21) || !(t <= 7.2e+108)) {
		tmp = t - (t / (y / x));
	} else {
		tmp = t + (z / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.2e+21) or not (t <= 7.2e+108):
		tmp = t - (t / (y / x))
	else:
		tmp = t + (z / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.2e+21) || !(t <= 7.2e+108))
		tmp = Float64(t - Float64(t / Float64(y / x)));
	else
		tmp = Float64(t + Float64(z / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.2e+21) || ~((t <= 7.2e+108)))
		tmp = t - (t / (y / x));
	else
		tmp = t + (z / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.2e+21], N[Not[LessEqual[t, 7.2e+108]], $MachinePrecision]], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2e21 or 7.2e108 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. unsub-neg 90.3%

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

      3. associate-/l* 92.1%

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

      4. associate-/r/ 86.6%

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

   4. Simplified 86.6%

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

      1. associate-*l/ 90.3%

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

      2. associate-/l* 92.1%

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

   6. Applied egg-rr 92.1%

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

   if -4.2e21 < t < 7.2e108

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 84.9%

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

   4. Simplified 84.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+21} \lor \neg \left(t \leq 7.2 \cdot 10^{+108}\right):\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+22}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+104}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.42e+22)
   (- t (/ (* t x) y))
   (if (<= t 2.4e+104) (+ t (/ z (/ y x))) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.42e+22) {
		tmp = t - ((t * x) / y);
	} else if (t <= 2.4e+104) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.42d+22)) then
        tmp = t - ((t * x) / y)
    else if (t <= 2.4d+104) then
        tmp = t + (z / (y / x))
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.42e+22) {
		tmp = t - ((t * x) / y);
	} else if (t <= 2.4e+104) {
		tmp = t + (z / (y / x));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.42e+22:
		tmp = t - ((t * x) / y)
	elif t <= 2.4e+104:
		tmp = t + (z / (y / x))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.42e+22)
		tmp = Float64(t - Float64(Float64(t * x) / y));
	elseif (t <= 2.4e+104)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.42e+22)
		tmp = t - ((t * x) / y);
	elseif (t <= 2.4e+104)
		tmp = t + (z / (y / x));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.42e+22], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+104], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.42e22

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. unsub-neg 88.3%

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

      3. associate-/l* 86.8%

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

      4. associate-/r/ 85.2%

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

   4. Simplified 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-*r/ 88.3%

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

   6. Applied egg-rr 88.3%

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

   if -1.42e22 < t < 2.4e104

   1. Initial program 95.7%

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

   2. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 84.9%

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

   4. Simplified 84.9%

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

   if 2.4e104 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 93.2%

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

      1. mul-1-neg 93.2%

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

      2. unsub-neg 93.2%

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

      3. associate-/l* 99.9%

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

      4. associate-/r/ 88.6%

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

   4. Simplified 88.6%

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

      1. associate-*l/ 93.2%

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

      2. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+22}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+104}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 10: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

2. Final simplification 97.4%

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

Alternative 11: 39.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+185}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -2.45e+185) (* t (/ x y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.45e+185) {
		tmp = t * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.45d+185)) then
        tmp = t * (x / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.45e+185) {
		tmp = t * (x / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.45e+185:
		tmp = t * (x / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.45e+185)
		tmp = Float64(t * Float64(x / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.45e+185)
		tmp = t * (x / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.45e+185], N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -2.44999999999999992e185

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 41.8%

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

      1. mul-1-neg 41.8%

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

      2. unsub-neg 41.8%

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

      3. associate-/l* 34.9%

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

      4. associate-/r/ 38.4%

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

   4. Simplified 38.4%

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

   5. Taylor expanded in y around 0 41.8%

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

      1. associate-*r/ 41.8%

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

      2. *-commutative 41.8%

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

      3. neg-mul-1 41.8%

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

      4. distribute-rgt-neg-in 41.8%

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

      5. *-commutative 41.8%

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

      6. associate-*r/ 42.0%

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

      7. distribute-lft-neg-out 42.0%

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

      8. distribute-rgt-neg-in 42.0%

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

      9. mul-1-neg 42.0%

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

      10. associate-*r/ 42.0%

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

      11. neg-mul-1 42.0%

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

   7. Simplified 42.0%

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

      1. distribute-frac-neg 42.0%

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

      2. distribute-rgt-neg-in 42.0%

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

      3. clear-num 42.0%

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

      4. div-inv 34.9%

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

      5. distribute-neg-frac 34.9%

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

   9. Applied egg-rr 34.9%

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

       1. div-inv 42.0%

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

       2. clear-num 42.0%

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

       3. *-commutative 42.0%

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

       4. add-sqr-sqrt 30.4%

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

       5. sqrt-unprod 30.5%

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

       6. sqr-neg 30.5%

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

       7. sqrt-unprod 15.3%

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

       8. add-sqr-sqrt 20.2%

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

   11. Applied egg-rr 20.2%

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

   if -2.44999999999999992e185 < x

   1. Initial program 97.5%

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

   2. Taylor expanded in x around 0 42.2%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{+185}:\\ \;\;\;\;t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.4%

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

2. Taylor expanded in x around 0 38.0%

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

3. Final simplification 38.0%

   \[\leadsto t \]

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 2023224 
(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))