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

Percentage Accurate: 97.6% → 97.6%

Time: 10.3s

Alternatives: 15

Speedup: 1.0×

• 25.7% 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: 97.6% 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: 97.6% 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 96.9%

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

   1. *-commutative 96.9%

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

   2. clear-num 96.9%

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

   3. un-div-inv 97.2%

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

4. Applied egg-rr 97.2%

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

5. Final simplification 97.2%

   \[\leadsto t + \frac{z - t}{\frac{y}{x}} \]
6. Add Preprocessing

Alternative 2: 62.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-11}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+97}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -0.05)
     t_1
     (if (<= (/ x y) -4e-78)
       (* z (/ t z))
       (if (<= (/ x y) -1e-100)
         (* x (/ z y))
         (if (<= (/ x y) 5e-76)
           t
           (if (<= (/ x y) 4e-35)
             (/ z (/ y x))
             (if (<= (/ x y) 1e-11)
               t
               (if (<= (/ x y) 1e+97) (* (/ x y) (- t)) t_1)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -0.05) {
		tmp = t_1;
	} else if ((x / y) <= -4e-78) {
		tmp = z * (t / z);
	} else if ((x / y) <= -1e-100) {
		tmp = x * (z / y);
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = z / (y / x);
	} else if ((x / y) <= 1e-11) {
		tmp = t;
	} else if ((x / y) <= 1e+97) {
		tmp = (x / 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 = z * (x / y)
    if ((x / y) <= (-0.05d0)) then
        tmp = t_1
    else if ((x / y) <= (-4d-78)) then
        tmp = z * (t / z)
    else if ((x / y) <= (-1d-100)) then
        tmp = x * (z / y)
    else if ((x / y) <= 5d-76) then
        tmp = t
    else if ((x / y) <= 4d-35) then
        tmp = z / (y / x)
    else if ((x / y) <= 1d-11) then
        tmp = t
    else if ((x / y) <= 1d+97) then
        tmp = (x / 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 = z * (x / y);
	double tmp;
	if ((x / y) <= -0.05) {
		tmp = t_1;
	} else if ((x / y) <= -4e-78) {
		tmp = z * (t / z);
	} else if ((x / y) <= -1e-100) {
		tmp = x * (z / y);
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = z / (y / x);
	} else if ((x / y) <= 1e-11) {
		tmp = t;
	} else if ((x / y) <= 1e+97) {
		tmp = (x / y) * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -0.05:
		tmp = t_1
	elif (x / y) <= -4e-78:
		tmp = z * (t / z)
	elif (x / y) <= -1e-100:
		tmp = x * (z / y)
	elif (x / y) <= 5e-76:
		tmp = t
	elif (x / y) <= 4e-35:
		tmp = z / (y / x)
	elif (x / y) <= 1e-11:
		tmp = t
	elif (x / y) <= 1e+97:
		tmp = (x / y) * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -0.05)
		tmp = t_1;
	elseif (Float64(x / y) <= -4e-78)
		tmp = Float64(z * Float64(t / z));
	elseif (Float64(x / y) <= -1e-100)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= 5e-76)
		tmp = t;
	elseif (Float64(x / y) <= 4e-35)
		tmp = Float64(z / Float64(y / x));
	elseif (Float64(x / y) <= 1e-11)
		tmp = t;
	elseif (Float64(x / y) <= 1e+97)
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -0.05)
		tmp = t_1;
	elseif ((x / y) <= -4e-78)
		tmp = z * (t / z);
	elseif ((x / y) <= -1e-100)
		tmp = x * (z / y);
	elseif ((x / y) <= 5e-76)
		tmp = t;
	elseif ((x / y) <= 4e-35)
		tmp = z / (y / x);
	elseif ((x / y) <= 1e-11)
		tmp = t;
	elseif ((x / y) <= 1e+97)
		tmp = (x / y) * -t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.05], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -4e-78], N[(z * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e-100], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-76], t, If[LessEqual[N[(x / y), $MachinePrecision], 4e-35], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1e-11], t, If[LessEqual[N[(x / y), $MachinePrecision], 1e+97], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (/.f64 x y) < -0.050000000000000003 or 1.0000000000000001e97 < (/.f64 x y)

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf 54.5%

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

      1. associate-/l* 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in z around inf 60.9%

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

      1. +-commutative 60.9%

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

   8. Simplified 60.9%

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

   9. Taylor expanded in x around inf 59.6%

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

   if -0.050000000000000003 < (/.f64 x y) < -4e-78

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 70.3%

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

      1. associate-/l* 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around inf 84.8%

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

      1. +-commutative 84.8%

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

   8. Simplified 84.8%

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

   9. Taylor expanded in x around 0 56.8%

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

   if -4e-78 < (/.f64 x y) < -1e-100

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 52.4%

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

      1. associate-/l* 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in z around inf 27.6%

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

       1. associate-/l* 75.1%

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

   11. Simplified 75.1%

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

   if -1e-100 < (/.f64 x y) < 4.9999999999999998e-76 or 4.00000000000000003e-35 < (/.f64 x y) < 9.99999999999999939e-12

   1. Initial program 98.2%

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

   3. Taylor expanded in x around 0 83.8%

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

   if 4.9999999999999998e-76 < (/.f64 x y) < 4.00000000000000003e-35

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. associate-/l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 99.6%

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

      1. +-commutative 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in x around inf 85.7%

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

       1. clear-num 86.0%

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

       2. un-div-inv 86.2%

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

   11. Applied egg-rr 86.2%

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

   if 9.99999999999999939e-12 < (/.f64 x y) < 1.0000000000000001e97

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. unsub-neg 55.8%

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

      3. *-rgt-identity 55.8%

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

      4. associate-/l* 59.5%

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

      5. distribute-lft-out-- 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in x around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. distribute-frac-neg2 56.9%

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

   8. Simplified 56.9%

      \[\leadsto t \cdot \color{blue}{\frac{x}{-y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.05:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \frac{t}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-100}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-11}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+97}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ z (/ y x))))
   (if (<= (/ x y) -0.5)
     t_1
     (if (<= (/ x y) 5e-76)
       t
       (if (<= (/ x y) 4e-35) t_1 (if (<= (/ x y) 2e-27) t (* z (/ x y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z / (y / x);
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = t_1;
	} else if ((x / y) <= 2e-27) {
		tmp = t;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = z / (y / x)
    if ((x / y) <= (-0.5d0)) then
        tmp = t_1
    else if ((x / y) <= 5d-76) then
        tmp = t
    else if ((x / y) <= 4d-35) then
        tmp = t_1
    else if ((x / y) <= 2d-27) then
        tmp = t
    else
        tmp = z * (x / 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) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = t_1;
	} else if ((x / y) <= 2e-27) {
		tmp = t;
	} else {
		tmp = z * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z / (y / x)
	tmp = 0
	if (x / y) <= -0.5:
		tmp = t_1
	elif (x / y) <= 5e-76:
		tmp = t
	elif (x / y) <= 4e-35:
		tmp = t_1
	elif (x / y) <= 2e-27:
		tmp = t
	else:
		tmp = z * (x / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z / Float64(y / x))
	tmp = 0.0
	if (Float64(x / y) <= -0.5)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-76)
		tmp = t;
	elseif (Float64(x / y) <= 4e-35)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-27)
		tmp = t;
	else
		tmp = Float64(z * Float64(x / 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) <= -0.5)
		tmp = t_1;
	elseif ((x / y) <= 5e-76)
		tmp = t;
	elseif ((x / y) <= 4e-35)
		tmp = t_1;
	elseif ((x / y) <= 2e-27)
		tmp = t;
	else
		tmp = z * (x / 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], -0.5], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-76], t, If[LessEqual[N[(x / y), $MachinePrecision], 4e-35], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-27], t, N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.5 or 4.9999999999999998e-76 < (/.f64 x y) < 4.00000000000000003e-35

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 57.7%

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

      1. associate-/l* 60.8%

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

   5. Simplified 60.8%

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

   6. Taylor expanded in z around inf 71.3%

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

      1. +-commutative 71.3%

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

   8. Simplified 71.3%

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

   9. Taylor expanded in x around inf 61.3%

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

       1. clear-num 61.3%

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

       2. un-div-inv 61.3%

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

   11. Applied egg-rr 61.3%

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

   if -0.5 < (/.f64 x y) < 4.9999999999999998e-76 or 4.00000000000000003e-35 < (/.f64 x y) < 2.0000000000000001e-27

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 77.7%

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

   if 2.0000000000000001e-27 < (/.f64 x y)

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 51.0%

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

      1. associate-/l* 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in z around inf 49.1%

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

      1. +-commutative 49.1%

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

   8. Simplified 49.1%

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

   9. Taylor expanded in x around inf 53.2%

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

Alternative 4: 64.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -0.5)
     t_1
     (if (<= (/ x y) 5e-76)
       t
       (if (<= (/ x y) 4e-35) (/ x (/ y z)) (if (<= (/ x y) 2e-27) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = x / (y / z);
	} else if ((x / y) <= 2e-27) {
		tmp = 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 = z * (x / y)
    if ((x / y) <= (-0.5d0)) then
        tmp = t_1
    else if ((x / y) <= 5d-76) then
        tmp = t
    else if ((x / y) <= 4d-35) then
        tmp = x / (y / z)
    else if ((x / y) <= 2d-27) then
        tmp = 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 = z * (x / y);
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = x / (y / z);
	} else if ((x / y) <= 2e-27) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -0.5:
		tmp = t_1
	elif (x / y) <= 5e-76:
		tmp = t
	elif (x / y) <= 4e-35:
		tmp = x / (y / z)
	elif (x / y) <= 2e-27:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -0.5)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-76)
		tmp = t;
	elseif (Float64(x / y) <= 4e-35)
		tmp = Float64(x / Float64(y / z));
	elseif (Float64(x / y) <= 2e-27)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -0.5)
		tmp = t_1;
	elseif ((x / y) <= 5e-76)
		tmp = t;
	elseif ((x / y) <= 4e-35)
		tmp = x / (y / z);
	elseif ((x / y) <= 2e-27)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.5], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-76], t, If[LessEqual[N[(x / y), $MachinePrecision], 4e-35], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-27], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.5 or 2.0000000000000001e-27 < (/.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 53.2%

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

      1. associate-/l* 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

   8. Simplified 57.6%

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

   9. Taylor expanded in x around inf 55.5%

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

   if -0.5 < (/.f64 x y) < 4.9999999999999998e-76 or 4.00000000000000003e-35 < (/.f64 x y) < 2.0000000000000001e-27

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 77.7%

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

   if 4.9999999999999998e-76 < (/.f64 x y) < 4.00000000000000003e-35

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. associate-/l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 99.6%

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

      1. +-commutative 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in z around inf 59.0%

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

       1. associate-/l* 85.7%

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

   11. Simplified 85.7%

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

       1. clear-num 85.5%

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

       2. un-div-inv 86.0%

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

   13. Applied egg-rr 86.0%

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

Alternative 5: 64.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -0.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-76}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-35}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ x y))))
   (if (<= (/ x y) -0.5)
     t_1
     (if (<= (/ x y) 5e-76)
       t
       (if (<= (/ x y) 4e-35) (* x (/ z y)) (if (<= (/ x y) 2e-27) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x / y);
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = x * (z / y);
	} else if ((x / y) <= 2e-27) {
		tmp = 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 = z * (x / y)
    if ((x / y) <= (-0.5d0)) then
        tmp = t_1
    else if ((x / y) <= 5d-76) then
        tmp = t
    else if ((x / y) <= 4d-35) then
        tmp = x * (z / y)
    else if ((x / y) <= 2d-27) then
        tmp = 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 = z * (x / y);
	double tmp;
	if ((x / y) <= -0.5) {
		tmp = t_1;
	} else if ((x / y) <= 5e-76) {
		tmp = t;
	} else if ((x / y) <= 4e-35) {
		tmp = x * (z / y);
	} else if ((x / y) <= 2e-27) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x / y)
	tmp = 0
	if (x / y) <= -0.5:
		tmp = t_1
	elif (x / y) <= 5e-76:
		tmp = t
	elif (x / y) <= 4e-35:
		tmp = x * (z / y)
	elif (x / y) <= 2e-27:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -0.5)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-76)
		tmp = t;
	elseif (Float64(x / y) <= 4e-35)
		tmp = Float64(x * Float64(z / y));
	elseif (Float64(x / y) <= 2e-27)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x / y);
	tmp = 0.0;
	if ((x / y) <= -0.5)
		tmp = t_1;
	elseif ((x / y) <= 5e-76)
		tmp = t;
	elseif ((x / y) <= 4e-35)
		tmp = x * (z / y);
	elseif ((x / y) <= 2e-27)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -0.5], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-76], t, If[LessEqual[N[(x / y), $MachinePrecision], 4e-35], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-27], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -0.5 or 2.0000000000000001e-27 < (/.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 53.2%

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

      1. associate-/l* 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in z around inf 57.6%

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

      1. +-commutative 57.6%

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

   8. Simplified 57.6%

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

   9. Taylor expanded in x around inf 55.5%

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

   if -0.5 < (/.f64 x y) < 4.9999999999999998e-76 or 4.00000000000000003e-35 < (/.f64 x y) < 2.0000000000000001e-27

   1. Initial program 98.5%

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

   3. Taylor expanded in x around 0 77.7%

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

   if 4.9999999999999998e-76 < (/.f64 x y) < 4.00000000000000003e-35

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 72.8%

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

      1. associate-/l* 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around inf 99.6%

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

      1. +-commutative 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in z around inf 59.0%

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

       1. associate-/l* 85.7%

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

   11. Simplified 85.7%

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

Alternative 6: 84.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + z \cdot \frac{x}{y}\\ t_2 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{-40}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-13}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* z (/ x y)))) (t_2 (* t (/ (- y x) y))))
   (if (<= t -4.2e-40)
     t_2
     (if (<= t -2.1e-121)
       t_1
       (if (<= t 1.95e-13)
         (+ t (/ x (/ y z)))
         (if (<= t 2e+61)
           (* t (- 1.0 (/ x y)))
           (if (<= t 1.45e+111) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (z * (x / y));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (t <= -4.2e-40) {
		tmp = t_2;
	} else if (t <= -2.1e-121) {
		tmp = t_1;
	} else if (t <= 1.95e-13) {
		tmp = t + (x / (y / z));
	} else if (t <= 2e+61) {
		tmp = t * (1.0 - (x / y));
	} else if (t <= 1.45e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (z * (x / y))
    t_2 = t * ((y - x) / y)
    if (t <= (-4.2d-40)) then
        tmp = t_2
    else if (t <= (-2.1d-121)) then
        tmp = t_1
    else if (t <= 1.95d-13) then
        tmp = t + (x / (y / z))
    else if (t <= 2d+61) then
        tmp = t * (1.0d0 - (x / y))
    else if (t <= 1.45d+111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + (z * (x / y));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (t <= -4.2e-40) {
		tmp = t_2;
	} else if (t <= -2.1e-121) {
		tmp = t_1;
	} else if (t <= 1.95e-13) {
		tmp = t + (x / (y / z));
	} else if (t <= 2e+61) {
		tmp = t * (1.0 - (x / y));
	} else if (t <= 1.45e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (z * (x / y))
	t_2 = t * ((y - x) / y)
	tmp = 0
	if t <= -4.2e-40:
		tmp = t_2
	elif t <= -2.1e-121:
		tmp = t_1
	elif t <= 1.95e-13:
		tmp = t + (x / (y / z))
	elif t <= 2e+61:
		tmp = t * (1.0 - (x / y))
	elif t <= 1.45e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(z * Float64(x / y)))
	t_2 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (t <= -4.2e-40)
		tmp = t_2;
	elseif (t <= -2.1e-121)
		tmp = t_1;
	elseif (t <= 1.95e-13)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	elseif (t <= 2e+61)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (t <= 1.45e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (z * (x / y));
	t_2 = t * ((y - x) / y);
	tmp = 0.0;
	if (t <= -4.2e-40)
		tmp = t_2;
	elseif (t <= -2.1e-121)
		tmp = t_1;
	elseif (t <= 1.95e-13)
		tmp = t + (x / (y / z));
	elseif (t <= 2e+61)
		tmp = t * (1.0 - (x / y));
	elseif (t <= 1.45e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e-40], t$95$2, If[LessEqual[t, -2.1e-121], t$95$1, If[LessEqual[t, 1.95e-13], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e+61], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+111], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.20000000000000036e-40 or 1.45e111 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

      3. *-rgt-identity 81.2%

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

      4. associate-/l* 90.2%

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

      5. distribute-lft-out-- 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in y around 0 90.2%

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

   if -4.20000000000000036e-40 < t < -2.0999999999999999e-121 or 1.9999999999999999e61 < t < 1.45e111

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.4%

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

      1. associate-/l* 84.5%

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

   5. Simplified 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-/r/ 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. clear-num 90.4%

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

      2. associate-/r/ 90.4%

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

      3. clear-num 90.5%

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

   9. Applied egg-rr 90.5%

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

   if -2.0999999999999999e-121 < t < 1.95000000000000002e-13

   1. Initial program 93.5%

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

      1. associate-*l/ 91.7%

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

      2. associate-*r/ 96.1%

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

      3. clear-num 96.1%

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

      4. un-div-inv 96.2%

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

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in z around inf 89.6%

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

   if 1.95000000000000002e-13 < t < 1.9999999999999999e61

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 93.3%

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

      1. mul-1-neg 93.3%

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

      2. unsub-neg 93.3%

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

      3. *-rgt-identity 93.3%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-out-- 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-40}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-121}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-13}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+111}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + z \cdot \frac{x}{y}\\ t_2 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 0.00023:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* z (/ x y)))) (t_2 (* t (/ (- y x) y))))
   (if (<= t -1.6e-39)
     t_2
     (if (<= t -2e-121)
       t_1
       (if (<= t 0.00023)
         (+ t (* x (/ z y)))
         (if (<= t 2.45e+67)
           (* t (- 1.0 (/ x y)))
           (if (<= t 1.55e+111) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (z * (x / y));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (t <= -1.6e-39) {
		tmp = t_2;
	} else if (t <= -2e-121) {
		tmp = t_1;
	} else if (t <= 0.00023) {
		tmp = t + (x * (z / y));
	} else if (t <= 2.45e+67) {
		tmp = t * (1.0 - (x / y));
	} else if (t <= 1.55e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t + (z * (x / y))
    t_2 = t * ((y - x) / y)
    if (t <= (-1.6d-39)) then
        tmp = t_2
    else if (t <= (-2d-121)) then
        tmp = t_1
    else if (t <= 0.00023d0) then
        tmp = t + (x * (z / y))
    else if (t <= 2.45d+67) then
        tmp = t * (1.0d0 - (x / y))
    else if (t <= 1.55d+111) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + (z * (x / y));
	double t_2 = t * ((y - x) / y);
	double tmp;
	if (t <= -1.6e-39) {
		tmp = t_2;
	} else if (t <= -2e-121) {
		tmp = t_1;
	} else if (t <= 0.00023) {
		tmp = t + (x * (z / y));
	} else if (t <= 2.45e+67) {
		tmp = t * (1.0 - (x / y));
	} else if (t <= 1.55e+111) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (z * (x / y))
	t_2 = t * ((y - x) / y)
	tmp = 0
	if t <= -1.6e-39:
		tmp = t_2
	elif t <= -2e-121:
		tmp = t_1
	elif t <= 0.00023:
		tmp = t + (x * (z / y))
	elif t <= 2.45e+67:
		tmp = t * (1.0 - (x / y))
	elif t <= 1.55e+111:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(z * Float64(x / y)))
	t_2 = Float64(t * Float64(Float64(y - x) / y))
	tmp = 0.0
	if (t <= -1.6e-39)
		tmp = t_2;
	elseif (t <= -2e-121)
		tmp = t_1;
	elseif (t <= 0.00023)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	elseif (t <= 2.45e+67)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (t <= 1.55e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (z * (x / y));
	t_2 = t * ((y - x) / y);
	tmp = 0.0;
	if (t <= -1.6e-39)
		tmp = t_2;
	elseif (t <= -2e-121)
		tmp = t_1;
	elseif (t <= 0.00023)
		tmp = t + (x * (z / y));
	elseif (t <= 2.45e+67)
		tmp = t * (1.0 - (x / y));
	elseif (t <= 1.55e+111)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e-39], t$95$2, If[LessEqual[t, -2e-121], t$95$1, If[LessEqual[t, 0.00023], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.45e+67], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+111], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5999999999999999e-39 or 1.55e111 < t

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

      3. *-rgt-identity 81.2%

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

      4. associate-/l* 90.2%

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

      5. distribute-lft-out-- 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in y around 0 90.2%

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

   if -1.5999999999999999e-39 < t < -2e-121 or 2.44999999999999995e67 < t < 1.55e111

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.4%

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

      1. associate-/l* 84.5%

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

   5. Simplified 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-/r/ 90.5%

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

   7. Applied egg-rr 90.5%

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

      1. clear-num 90.4%

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

      2. associate-/r/ 90.4%

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

      3. clear-num 90.5%

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

   9. Applied egg-rr 90.5%

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

   if -2e-121 < t < 2.3000000000000001e-4

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 85.2%

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

      1. associate-/l* 89.6%

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

   5. Simplified 89.6%

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

   if 2.3000000000000001e-4 < t < 2.44999999999999995e67

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 93.3%

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

      1. mul-1-neg 93.3%

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

      2. unsub-neg 93.3%

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

      3. *-rgt-identity 93.3%

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

      4. associate-/l* 100.0%

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

      5. distribute-lft-out-- 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-121}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{elif}\;t \leq 0.00023:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{elif}\;t \leq 2.45 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+111}:\\ \;\;\;\;t + z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+196}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.8e+245)
   (* x (/ z y))
   (if (<= z 6.6e+88)
     (* t (/ (- y x) y))
     (if (<= z 6e+137)
       (/ x (/ y z))
       (if (<= z 4.4e+196) (* t (- 1.0 (/ x y))) (/ z (/ y x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+245) {
		tmp = x * (z / y);
	} else if (z <= 6.6e+88) {
		tmp = t * ((y - x) / y);
	} else if (z <= 6e+137) {
		tmp = x / (y / z);
	} else if (z <= 4.4e+196) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.8d+245)) then
        tmp = x * (z / y)
    else if (z <= 6.6d+88) then
        tmp = t * ((y - x) / y)
    else if (z <= 6d+137) then
        tmp = x / (y / z)
    else if (z <= 4.4d+196) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = z / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.8e+245) {
		tmp = x * (z / y);
	} else if (z <= 6.6e+88) {
		tmp = t * ((y - x) / y);
	} else if (z <= 6e+137) {
		tmp = x / (y / z);
	} else if (z <= 4.4e+196) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.8e+245:
		tmp = x * (z / y)
	elif z <= 6.6e+88:
		tmp = t * ((y - x) / y)
	elif z <= 6e+137:
		tmp = x / (y / z)
	elif z <= 4.4e+196:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.8e+245)
		tmp = Float64(x * Float64(z / y));
	elseif (z <= 6.6e+88)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (z <= 6e+137)
		tmp = Float64(x / Float64(y / z));
	elseif (z <= 4.4e+196)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.8e+245)
		tmp = x * (z / y);
	elseif (z <= 6.6e+88)
		tmp = t * ((y - x) / y);
	elseif (z <= 6e+137)
		tmp = x / (y / z);
	elseif (z <= 4.4e+196)
		tmp = t * (1.0 - (x / y));
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.8e+245], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+88], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+137], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+196], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.7999999999999996e245

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 91.0%

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

      1. associate-/l* 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in z around inf 86.2%

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

      1. +-commutative 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in z around inf 64.7%

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

       1. associate-/l* 69.0%

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

   11. Simplified 69.0%

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

   if -4.7999999999999996e245 < z < 6.6000000000000006e88

   1. Initial program 96.9%

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

   3. Taylor expanded in z around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. unsub-neg 71.4%

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

      3. *-rgt-identity 71.4%

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

      4. associate-/l* 76.3%

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

      5. distribute-lft-out-- 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in y around 0 76.3%

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

   if 6.6000000000000006e88 < z < 6.0000000000000002e137

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 63.3%

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

      1. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around inf 87.1%

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

      1. +-commutative 87.1%

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

   8. Simplified 87.1%

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

   9. Taylor expanded in z around inf 63.3%

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

       1. associate-/l* 75.9%

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

   11. Simplified 75.9%

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

       1. clear-num 75.7%

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

       2. un-div-inv 76.1%

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

   13. Applied egg-rr 76.1%

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

   if 6.0000000000000002e137 < z < 4.39999999999999995e196

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. unsub-neg 63.8%

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

      3. *-rgt-identity 63.8%

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

      4. associate-/l* 69.6%

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

      5. distribute-lft-out-- 69.6%

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

   5. Simplified 69.6%

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

   if 4.39999999999999995e196 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x around inf 75.2%

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

       1. clear-num 75.2%

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

       2. un-div-inv 75.2%

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

   11. Applied egg-rr 75.2%

       \[\leadsto \color{blue}{\frac{z}{\frac{y}{x}}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 71.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= z -9e+244)
     (* x (/ z y))
     (if (<= z 2.5e+89)
       t_1
       (if (<= z 4.8e+137)
         (/ x (/ y z))
         (if (<= z 4.8e+197) 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 (z <= -9e+244) {
		tmp = x * (z / y);
	} else if (z <= 2.5e+89) {
		tmp = t_1;
	} else if (z <= 4.8e+137) {
		tmp = x / (y / z);
	} else if (z <= 4.8e+197) {
		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 (z <= (-9d+244)) then
        tmp = x * (z / y)
    else if (z <= 2.5d+89) then
        tmp = t_1
    else if (z <= 4.8d+137) then
        tmp = x / (y / z)
    else if (z <= 4.8d+197) 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 (z <= -9e+244) {
		tmp = x * (z / y);
	} else if (z <= 2.5e+89) {
		tmp = t_1;
	} else if (z <= 4.8e+137) {
		tmp = x / (y / z);
	} else if (z <= 4.8e+197) {
		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 z <= -9e+244:
		tmp = x * (z / y)
	elif z <= 2.5e+89:
		tmp = t_1
	elif z <= 4.8e+137:
		tmp = x / (y / z)
	elif z <= 4.8e+197:
		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 (z <= -9e+244)
		tmp = Float64(x * Float64(z / y));
	elseif (z <= 2.5e+89)
		tmp = t_1;
	elseif (z <= 4.8e+137)
		tmp = Float64(x / Float64(y / z));
	elseif (z <= 4.8e+197)
		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 (z <= -9e+244)
		tmp = x * (z / y);
	elseif (z <= 2.5e+89)
		tmp = t_1;
	elseif (z <= 4.8e+137)
		tmp = x / (y / z);
	elseif (z <= 4.8e+197)
		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[z, -9e+244], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+89], t$95$1, If[LessEqual[z, 4.8e+137], N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+197], t$95$1, N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.0000000000000005e244

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 91.0%

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

      1. associate-/l* 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in z around inf 86.2%

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

      1. +-commutative 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in z around inf 64.7%

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

       1. associate-/l* 69.0%

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

   11. Simplified 69.0%

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

   if -9.0000000000000005e244 < z < 2.49999999999999992e89 or 4.79999999999999966e137 < z < 4.7999999999999998e197

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. unsub-neg 70.8%

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

      3. *-rgt-identity 70.8%

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

      4. associate-/l* 75.8%

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

      5. distribute-lft-out-- 75.8%

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

   5. Simplified 75.8%

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

   if 2.49999999999999992e89 < z < 4.79999999999999966e137

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 63.3%

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

      1. associate-/l* 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around inf 87.1%

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

      1. +-commutative 87.1%

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

   8. Simplified 87.1%

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

   9. Taylor expanded in z around inf 63.3%

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

       1. associate-/l* 75.9%

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

   11. Simplified 75.9%

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

       1. clear-num 75.7%

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

       2. un-div-inv 76.1%

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

   13. Applied egg-rr 76.1%

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

   if 4.7999999999999998e197 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 82.9%

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

      1. associate-/l* 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in z around inf 99.9%

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

      1. +-commutative 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in x around inf 75.2%

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

       1. clear-num 75.2%

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

       2. un-div-inv 75.2%

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

   11. Applied egg-rr 75.2%

       \[\leadsto \color{blue}{\frac{z}{\frac{y}{x}}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+64} \lor \neg \left(y \leq 1.05 \cdot 10^{+98}\right) \land y \leq 1.75 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+115)
   t
   (if (or (<= y 7.5e+64) (and (not (<= y 1.05e+98)) (<= y 1.75e+101)))
     (* x (/ z y))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+115) {
		tmp = t;
	} else if ((y <= 7.5e+64) || (!(y <= 1.05e+98) && (y <= 1.75e+101))) {
		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 (y <= (-6.5d+115)) then
        tmp = t
    else if ((y <= 7.5d+64) .or. (.not. (y <= 1.05d+98)) .and. (y <= 1.75d+101)) 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 (y <= -6.5e+115) {
		tmp = t;
	} else if ((y <= 7.5e+64) || (!(y <= 1.05e+98) && (y <= 1.75e+101))) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e+115:
		tmp = t
	elif (y <= 7.5e+64) or (not (y <= 1.05e+98) and (y <= 1.75e+101)):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+115)
		tmp = t;
	elseif ((y <= 7.5e+64) || (!(y <= 1.05e+98) && (y <= 1.75e+101)))
		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 (y <= -6.5e+115)
		tmp = t;
	elseif ((y <= 7.5e+64) || (~((y <= 1.05e+98)) && (y <= 1.75e+101)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+115], t, If[Or[LessEqual[y, 7.5e+64], And[N[Not[LessEqual[y, 1.05e+98]], $MachinePrecision], LessEqual[y, 1.75e+101]]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999966e115 or 7.5000000000000005e64 < y < 1.05000000000000002e98 or 1.75000000000000012e101 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 69.8%

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

   if -6.49999999999999966e115 < y < 7.5000000000000005e64 or 1.05000000000000002e98 < y < 1.75000000000000012e101

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 67.9%

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

      1. associate-/l* 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in z around inf 69.3%

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

      1. +-commutative 69.3%

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

   8. Simplified 69.3%

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

   9. Taylor expanded in z around inf 47.6%

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

       1. associate-/l* 49.3%

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

   11. Simplified 49.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+115}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+64} \lor \neg \left(y \leq 1.05 \cdot 10^{+98}\right) \land y \leq 1.75 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.4e-41)
   (/ t (/ y (- y x)))
   (if (<= t 6.4e-40) (+ t (/ x (/ y z))) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-41) {
		tmp = t / (y / (y - x));
	} else if (t <= 6.4e-40) {
		tmp = t + (x / (y / z));
	} 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 <= (-1.4d-41)) then
        tmp = t / (y / (y - x))
    else if (t <= 6.4d-40) then
        tmp = t + (x / (y / z))
    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 <= -1.4e-41) {
		tmp = t / (y / (y - x));
	} else if (t <= 6.4e-40) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.4e-41:
		tmp = t / (y / (y - x))
	elif t <= 6.4e-40:
		tmp = t + (x / (y / z))
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.4e-41)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	elseif (t <= 6.4e-40)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	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 <= -1.4e-41)
		tmp = t / (y / (y - x));
	elseif (t <= 6.4e-40)
		tmp = t + (x / (y / z));
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.4e-41], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-40], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.4000000000000001e-41

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

      3. *-rgt-identity 79.2%

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

      4. associate-/l* 86.3%

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

      5. distribute-lft-out-- 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 86.3%

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

      1. clear-num 86.3%

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

      2. un-div-inv 86.7%

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

   8. Applied egg-rr 86.7%

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

   if -1.4000000000000001e-41 < t < 6.40000000000000004e-40

   1. Initial program 94.3%

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

      1. associate-*l/ 91.9%

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

      2. associate-*r/ 96.5%

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

      3. clear-num 96.5%

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

      4. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around inf 90.1%

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

   if 6.40000000000000004e-40 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. *-commutative 80.3%

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

      3. associate-/l* 82.1%

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

      4. distribute-rgt-neg-in 82.1%

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

      5. distribute-neg-frac2 82.1%

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

   5. Simplified 82.1%

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

      1. *-commutative 82.1%

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

      2. add-sqr-sqrt 44.0%

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

      3. sqrt-unprod 57.3%

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

      4. sqr-neg 57.3%

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

      5. sqrt-unprod 20.8%

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

      6. add-sqr-sqrt 52.0%

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

      7. associate-/r/ 55.3%

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

      8. frac-2neg 55.3%

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

      9. distribute-neg-frac 55.3%

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

      10. add-sqr-sqrt 31.2%

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

      11. sqrt-unprod 70.3%

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

      12. sqr-neg 70.3%

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

      13. sqrt-unprod 43.4%

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

      14. add-sqr-sqrt 88.6%

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

   7. Applied egg-rr 88.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e-39)
   (/ t (/ y (- y x)))
   (if (<= t 8.5e-40) (+ t (/ x (/ y z))) (* t (/ (- y x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-39) {
		tmp = t / (y / (y - x));
	} else if (t <= 8.5e-40) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t * ((y - 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 (t <= (-1.6d-39)) then
        tmp = t / (y / (y - x))
    else if (t <= 8.5d-40) then
        tmp = t + (x / (y / z))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-39) {
		tmp = t / (y / (y - x));
	} else if (t <= 8.5e-40) {
		tmp = t + (x / (y / z));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e-39:
		tmp = t / (y / (y - x))
	elif t <= 8.5e-40:
		tmp = t + (x / (y / z))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e-39)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	elseif (t <= 8.5e-40)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e-39)
		tmp = t / (y / (y - x));
	elseif (t <= 8.5e-40)
		tmp = t + (x / (y / z));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e-39], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-40], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5999999999999999e-39

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

      3. *-rgt-identity 79.2%

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

      4. associate-/l* 86.3%

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

      5. distribute-lft-out-- 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 86.3%

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

      1. clear-num 86.3%

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

      2. un-div-inv 86.7%

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

   8. Applied egg-rr 86.7%

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

   if -1.5999999999999999e-39 < t < 8.4999999999999998e-40

   1. Initial program 94.3%

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

      1. associate-*l/ 91.9%

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

      2. associate-*r/ 96.5%

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

      3. clear-num 96.5%

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

      4. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around inf 90.1%

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

   if 8.4999999999999998e-40 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. *-rgt-identity 80.3%

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

      4. associate-/l* 88.6%

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

      5. distribute-lft-out-- 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in y around 0 88.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-40}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-41}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.6e+71)
   (* t (- 1.0 (/ x y)))
   (if (<= t 3.6e-41) (+ t (* x (/ z y))) (* t (/ (- y x) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.6e+71) {
		tmp = t * (1.0 - (x / y));
	} else if (t <= 3.6e-41) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * ((y - 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 (t <= (-7.6d+71)) then
        tmp = t * (1.0d0 - (x / y))
    else if (t <= 3.6d-41) then
        tmp = t + (x * (z / y))
    else
        tmp = t * ((y - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.6e+71) {
		tmp = t * (1.0 - (x / y));
	} else if (t <= 3.6e-41) {
		tmp = t + (x * (z / y));
	} else {
		tmp = t * ((y - x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.6e+71:
		tmp = t * (1.0 - (x / y))
	elif t <= 3.6e-41:
		tmp = t + (x * (z / y))
	else:
		tmp = t * ((y - x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.6e+71)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (t <= 3.6e-41)
		tmp = Float64(t + Float64(x * Float64(z / y)));
	else
		tmp = Float64(t * Float64(Float64(y - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7.6e+71)
		tmp = t * (1.0 - (x / y));
	elseif (t <= 3.6e-41)
		tmp = t + (x * (z / y));
	else
		tmp = t * ((y - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.6e+71], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-41], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.6000000000000001e71

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. unsub-neg 79.2%

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

      3. *-rgt-identity 79.2%

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

      4. associate-/l* 91.2%

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

      5. distribute-lft-out-- 91.2%

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

   5. Simplified 91.2%

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

   if -7.6000000000000001e71 < t < 3.6e-41

   1. Initial program 94.4%

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

   3. Taylor expanded in z around inf 82.5%

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

      1. associate-/l* 87.2%

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

   5. Simplified 87.2%

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

   if 3.6e-41 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. unsub-neg 80.3%

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

      3. *-rgt-identity 80.3%

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

      4. associate-/l* 88.6%

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

      5. distribute-lft-out-- 88.5%

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

   5. Simplified 88.5%

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

   6. Taylor expanded in y around 0 88.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-41}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.6% 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 96.9%

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

3. Final simplification 96.9%

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

Alternative 15: 38.1% 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 96.9%

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

3. Taylor expanded in x around 0 41.2%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Developer target: 97.2% accurate, 0.5× 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 2024107 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (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))