Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D

Percentage Accurate: 93.3% → 97.8%

Time: 8.1s

Alternatives: 13

Speedup: 1.0×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. *-commutative 94.8%

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

   2. associate-/l* 97.5%

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

4. Applied egg-rr 97.5%

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

Alternative 2: 54.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-y}{t}\\ t_2 := \frac{z}{\frac{t}{y}}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-150}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ (- y) t))) (t_2 (/ z (/ t y))))
   (if (<= t -2.75e+84)
     x
     (if (<= t -4.7e-150)
       t_2
       (if (<= t -3.6e-231)
         t_1
         (if (<= t 4.2e-304)
           t_2
           (if (<= t 1.45e-272) t_1 (if (<= t 1.05e+64) t_2 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (-y / t);
	double t_2 = z / (t / y);
	double tmp;
	if (t <= -2.75e+84) {
		tmp = x;
	} else if (t <= -4.7e-150) {
		tmp = t_2;
	} else if (t <= -3.6e-231) {
		tmp = t_1;
	} else if (t <= 4.2e-304) {
		tmp = t_2;
	} else if (t <= 1.45e-272) {
		tmp = t_1;
	} else if (t <= 1.05e+64) {
		tmp = t_2;
	} else {
		tmp = 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) :: t_2
    real(8) :: tmp
    t_1 = x * (-y / t)
    t_2 = z / (t / y)
    if (t <= (-2.75d+84)) then
        tmp = x
    else if (t <= (-4.7d-150)) then
        tmp = t_2
    else if (t <= (-3.6d-231)) then
        tmp = t_1
    else if (t <= 4.2d-304) then
        tmp = t_2
    else if (t <= 1.45d-272) then
        tmp = t_1
    else if (t <= 1.05d+64) then
        tmp = t_2
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (-y / t);
	double t_2 = z / (t / y);
	double tmp;
	if (t <= -2.75e+84) {
		tmp = x;
	} else if (t <= -4.7e-150) {
		tmp = t_2;
	} else if (t <= -3.6e-231) {
		tmp = t_1;
	} else if (t <= 4.2e-304) {
		tmp = t_2;
	} else if (t <= 1.45e-272) {
		tmp = t_1;
	} else if (t <= 1.05e+64) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (-y / t)
	t_2 = z / (t / y)
	tmp = 0
	if t <= -2.75e+84:
		tmp = x
	elif t <= -4.7e-150:
		tmp = t_2
	elif t <= -3.6e-231:
		tmp = t_1
	elif t <= 4.2e-304:
		tmp = t_2
	elif t <= 1.45e-272:
		tmp = t_1
	elif t <= 1.05e+64:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(Float64(-y) / t))
	t_2 = Float64(z / Float64(t / y))
	tmp = 0.0
	if (t <= -2.75e+84)
		tmp = x;
	elseif (t <= -4.7e-150)
		tmp = t_2;
	elseif (t <= -3.6e-231)
		tmp = t_1;
	elseif (t <= 4.2e-304)
		tmp = t_2;
	elseif (t <= 1.45e-272)
		tmp = t_1;
	elseif (t <= 1.05e+64)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (-y / t);
	t_2 = z / (t / y);
	tmp = 0.0;
	if (t <= -2.75e+84)
		tmp = x;
	elseif (t <= -4.7e-150)
		tmp = t_2;
	elseif (t <= -3.6e-231)
		tmp = t_1;
	elseif (t <= 4.2e-304)
		tmp = t_2;
	elseif (t <= 1.45e-272)
		tmp = t_1;
	elseif (t <= 1.05e+64)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[((-y) / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.75e+84], x, If[LessEqual[t, -4.7e-150], t$95$2, If[LessEqual[t, -3.6e-231], t$95$1, If[LessEqual[t, 4.2e-304], t$95$2, If[LessEqual[t, 1.45e-272], t$95$1, If[LessEqual[t, 1.05e+64], t$95$2, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.7500000000000002e84 or 1.05e64 < t

   1. Initial program 90.7%

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

   3. Taylor expanded in y around 0 66.0%

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

   if -2.7500000000000002e84 < t < -4.6999999999999999e-150 or -3.59999999999999973e-231 < t < 4.20000000000000016e-304 or 1.44999999999999997e-272 < t < 1.05e64

   1. Initial program 97.1%

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

   3. Taylor expanded in y around -inf 83.9%

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

      1. *-commutative 97.1%

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

      2. associate-/l* 97.0%

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

   5. Applied egg-rr 83.8%

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

   6. Taylor expanded in z around inf 56.8%

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

      1. *-commutative 70.0%

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

      2. associate-*l/ 67.9%

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

      3. associate-/r/ 73.0%

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

   8. Simplified 59.8%

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

   if -4.6999999999999999e-150 < t < -3.59999999999999973e-231 or 4.20000000000000016e-304 < t < 1.44999999999999997e-272

   1. Initial program 97.1%

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

   3. Taylor expanded in y around -inf 85.4%

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

   4. Taylor expanded in z around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. associate-/l* 73.9%

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

      3. distribute-rgt-neg-in 73.9%

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

      4. mul-1-neg 73.9%

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

      5. associate-*r/ 73.9%

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

      6. mul-1-neg 73.9%

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

   6. Simplified 73.9%

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

Alternative 3: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+85} \lor \neg \left(t \leq 3.1 \cdot 10^{-52} \lor \neg \left(t \leq 1.15 \cdot 10^{-28}\right) \land t \leq 1.6 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9e+85)
         (not (or (<= t 3.1e-52) (and (not (<= t 1.15e-28)) (<= t 1.6e+64)))))
   (* x (- 1.0 (/ y t)))
   (* (- z x) (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+85) || !((t <= 3.1e-52) || (!(t <= 1.15e-28) && (t <= 1.6e+64)))) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z - x) * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-9d+85)) .or. (.not. (t <= 3.1d-52) .or. (.not. (t <= 1.15d-28)) .and. (t <= 1.6d+64))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (z - x) * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+85) || !((t <= 3.1e-52) || (!(t <= 1.15e-28) && (t <= 1.6e+64)))) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (z - x) * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9e+85) or not ((t <= 3.1e-52) or (not (t <= 1.15e-28) and (t <= 1.6e+64))):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (z - x) * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9e+85) || !((t <= 3.1e-52) || (!(t <= 1.15e-28) && (t <= 1.6e+64))))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(z - x) * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9e+85) || ~(((t <= 3.1e-52) || (~((t <= 1.15e-28)) && (t <= 1.6e+64)))))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (z - x) * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9e+85], N[Not[Or[LessEqual[t, 3.1e-52], And[N[Not[LessEqual[t, 1.15e-28]], $MachinePrecision], LessEqual[t, 1.6e+64]]]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000013e85 or 3.0999999999999999e-52 < t < 1.14999999999999993e-28 or 1.60000000000000009e64 < t

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   5. Simplified 78.4%

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

   if -9.00000000000000013e85 < t < 3.0999999999999999e-52 or 1.14999999999999993e-28 < t < 1.60000000000000009e64

   1. Initial program 97.0%

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

   3. Taylor expanded in y around -inf 86.1%

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

      1. *-commutative 97.0%

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

      2. associate-/l* 96.9%

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

   5. Applied egg-rr 86.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+85} \lor \neg \left(t \leq 3.1 \cdot 10^{-52} \lor \neg \left(t \leq 1.15 \cdot 10^{-28}\right) \land t \leq 1.6 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-48}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-28} \lor \neg \left(t \leq 7.5 \cdot 10^{+64}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= t -2.9e+83)
     t_1
     (if (<= t 7e-48)
       (* (- z x) (/ y t))
       (if (or (<= t 1.1e-28) (not (<= t 7.5e+64)))
         t_1
         (* y (/ (- z x) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (t <= -2.9e+83) {
		tmp = t_1;
	} else if (t <= 7e-48) {
		tmp = (z - x) * (y / t);
	} else if ((t <= 1.1e-28) || !(t <= 7.5e+64)) {
		tmp = t_1;
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (t <= (-2.9d+83)) then
        tmp = t_1
    else if (t <= 7d-48) then
        tmp = (z - x) * (y / t)
    else if ((t <= 1.1d-28) .or. (.not. (t <= 7.5d+64))) then
        tmp = t_1
    else
        tmp = y * ((z - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (t <= -2.9e+83) {
		tmp = t_1;
	} else if (t <= 7e-48) {
		tmp = (z - x) * (y / t);
	} else if ((t <= 1.1e-28) || !(t <= 7.5e+64)) {
		tmp = t_1;
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if t <= -2.9e+83:
		tmp = t_1
	elif t <= 7e-48:
		tmp = (z - x) * (y / t)
	elif (t <= 1.1e-28) or not (t <= 7.5e+64):
		tmp = t_1
	else:
		tmp = y * ((z - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (t <= -2.9e+83)
		tmp = t_1;
	elseif (t <= 7e-48)
		tmp = Float64(Float64(z - x) * Float64(y / t));
	elseif ((t <= 1.1e-28) || !(t <= 7.5e+64))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(z - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (t <= -2.9e+83)
		tmp = t_1;
	elseif (t <= 7e-48)
		tmp = (z - x) * (y / t);
	elseif ((t <= 1.1e-28) || ~((t <= 7.5e+64)))
		tmp = t_1;
	else
		tmp = y * ((z - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+83], t$95$1, If[LessEqual[t, 7e-48], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.1e-28], N[Not[LessEqual[t, 7.5e+64]], $MachinePrecision]], t$95$1, N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.89999999999999999e83 or 6.99999999999999982e-48 < t < 1.09999999999999998e-28 or 7.5000000000000005e64 < t

   1. Initial program 91.3%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. mul-1-neg 78.4%

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

      2. unsub-neg 78.4%

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

   5. Simplified 78.4%

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

   if -2.89999999999999999e83 < t < 6.99999999999999982e-48

   1. Initial program 96.7%

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

   3. Taylor expanded in y around -inf 85.4%

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

      1. *-commutative 96.7%

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

      2. associate-/l* 96.6%

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

   5. Applied egg-rr 85.3%

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

   if 1.09999999999999998e-28 < t < 7.5000000000000005e64

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 93.5%

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

      1. associate-/l* 93.3%

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

      2. *-commutative 93.3%

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

   5. Applied egg-rr 93.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-48}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-28} \lor \neg \left(t \leq 7.5 \cdot 10^{+64}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{x \cdot y}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.35e+83)
   (+ x (* y (/ z t)))
   (if (<= t 2.3e-48)
     (/ (- z x) (/ t y))
     (if (<= t 1.1e-28)
       (- x (/ (* x y) t))
       (if (<= t 3.5e+50) (/ (* (- z x) y) t) (+ x (/ (* z y) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.35e+83) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.3e-48) {
		tmp = (z - x) / (t / y);
	} else if (t <= 1.1e-28) {
		tmp = x - ((x * y) / t);
	} else if (t <= 3.5e+50) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.35d+83)) then
        tmp = x + (y * (z / t))
    else if (t <= 2.3d-48) then
        tmp = (z - x) / (t / y)
    else if (t <= 1.1d-28) then
        tmp = x - ((x * y) / t)
    else if (t <= 3.5d+50) then
        tmp = ((z - x) * y) / t
    else
        tmp = x + ((z * y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.35e+83) {
		tmp = x + (y * (z / t));
	} else if (t <= 2.3e-48) {
		tmp = (z - x) / (t / y);
	} else if (t <= 1.1e-28) {
		tmp = x - ((x * y) / t);
	} else if (t <= 3.5e+50) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.35e+83:
		tmp = x + (y * (z / t))
	elif t <= 2.3e-48:
		tmp = (z - x) / (t / y)
	elif t <= 1.1e-28:
		tmp = x - ((x * y) / t)
	elif t <= 3.5e+50:
		tmp = ((z - x) * y) / t
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.35e+83)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 2.3e-48)
		tmp = Float64(Float64(z - x) / Float64(t / y));
	elseif (t <= 1.1e-28)
		tmp = Float64(x - Float64(Float64(x * y) / t));
	elseif (t <= 3.5e+50)
		tmp = Float64(Float64(Float64(z - x) * y) / t);
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.35e+83)
		tmp = x + (y * (z / t));
	elseif (t <= 2.3e-48)
		tmp = (z - x) / (t / y);
	elseif (t <= 1.1e-28)
		tmp = x - ((x * y) / t);
	elseif (t <= 3.5e+50)
		tmp = ((z - x) * y) / t;
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.35e+83], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-48], N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-28], N[(x - N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+50], N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.3499999999999999e83

   1. Initial program 84.6%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   if -2.3499999999999999e83 < t < 2.3000000000000001e-48

   1. Initial program 96.7%

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

   3. Taylor expanded in y around -inf 85.4%

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

      1. *-commutative 96.7%

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

      2. associate-/l* 96.6%

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

   5. Applied egg-rr 85.3%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.9%

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

   7. Applied egg-rr 85.9%

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

   if 2.3000000000000001e-48 < t < 1.09999999999999998e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-lft-neg-out 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if 1.09999999999999998e-28 < t < 3.50000000000000006e50

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 92.5%

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

   if 3.50000000000000006e50 < t

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 89.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-48}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{x \cdot y}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+50}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.2e+83)
   (+ x (* y (/ z t)))
   (if (<= t 3.2e-52)
     (/ (- z x) (/ t y))
     (if (<= t 1.15e-28)
       (* x (- 1.0 (/ y t)))
       (if (<= t 2.6e+47) (/ (* (- z x) y) t) (+ x (/ (* z y) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e+83) {
		tmp = x + (y * (z / t));
	} else if (t <= 3.2e-52) {
		tmp = (z - x) / (t / y);
	} else if (t <= 1.15e-28) {
		tmp = x * (1.0 - (y / t));
	} else if (t <= 2.6e+47) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-5.2d+83)) then
        tmp = x + (y * (z / t))
    else if (t <= 3.2d-52) then
        tmp = (z - x) / (t / y)
    else if (t <= 1.15d-28) then
        tmp = x * (1.0d0 - (y / t))
    else if (t <= 2.6d+47) then
        tmp = ((z - x) * y) / t
    else
        tmp = x + ((z * y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.2e+83) {
		tmp = x + (y * (z / t));
	} else if (t <= 3.2e-52) {
		tmp = (z - x) / (t / y);
	} else if (t <= 1.15e-28) {
		tmp = x * (1.0 - (y / t));
	} else if (t <= 2.6e+47) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5.2e+83:
		tmp = x + (y * (z / t))
	elif t <= 3.2e-52:
		tmp = (z - x) / (t / y)
	elif t <= 1.15e-28:
		tmp = x * (1.0 - (y / t))
	elif t <= 2.6e+47:
		tmp = ((z - x) * y) / t
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.2e+83)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 3.2e-52)
		tmp = Float64(Float64(z - x) / Float64(t / y));
	elseif (t <= 1.15e-28)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (t <= 2.6e+47)
		tmp = Float64(Float64(Float64(z - x) * y) / t);
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -5.2e+83)
		tmp = x + (y * (z / t));
	elseif (t <= 3.2e-52)
		tmp = (z - x) / (t / y);
	elseif (t <= 1.15e-28)
		tmp = x * (1.0 - (y / t));
	elseif (t <= 2.6e+47)
		tmp = ((z - x) * y) / t;
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5.2e+83], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-52], N[(N[(z - x), $MachinePrecision] / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e-28], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+47], N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.2000000000000002e83

   1. Initial program 84.6%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. associate-/l* 87.6%

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

   5. Simplified 87.6%

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

   if -5.2000000000000002e83 < t < 3.2000000000000001e-52

   1. Initial program 96.7%

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

   3. Taylor expanded in y around -inf 85.4%

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

      1. *-commutative 96.7%

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

      2. associate-/l* 96.6%

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

   5. Applied egg-rr 85.3%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.9%

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

   7. Applied egg-rr 85.9%

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

   if 3.2000000000000001e-52 < t < 1.14999999999999993e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   if 1.14999999999999993e-28 < t < 2.60000000000000003e47

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 92.5%

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

   if 2.60000000000000003e47 < t

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 89.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{z - x}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- z x) y) t)))
   (if (<= t -1.9e+82)
     (+ x (* y (/ z t)))
     (if (<= t 5.5e-49)
       t_1
       (if (<= t 1.15e-28)
         (* x (- 1.0 (/ y t)))
         (if (<= t 1.72e+47) t_1 (+ x (/ (* z y) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((z - x) * y) / t;
	double tmp;
	if (t <= -1.9e+82) {
		tmp = x + (y * (z / t));
	} else if (t <= 5.5e-49) {
		tmp = t_1;
	} else if (t <= 1.15e-28) {
		tmp = x * (1.0 - (y / t));
	} else if (t <= 1.72e+47) {
		tmp = t_1;
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z - x) * y) / t
    if (t <= (-1.9d+82)) then
        tmp = x + (y * (z / t))
    else if (t <= 5.5d-49) then
        tmp = t_1
    else if (t <= 1.15d-28) then
        tmp = x * (1.0d0 - (y / t))
    else if (t <= 1.72d+47) then
        tmp = t_1
    else
        tmp = x + ((z * y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((z - x) * y) / t;
	double tmp;
	if (t <= -1.9e+82) {
		tmp = x + (y * (z / t));
	} else if (t <= 5.5e-49) {
		tmp = t_1;
	} else if (t <= 1.15e-28) {
		tmp = x * (1.0 - (y / t));
	} else if (t <= 1.72e+47) {
		tmp = t_1;
	} else {
		tmp = x + ((z * y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((z - x) * y) / t
	tmp = 0
	if t <= -1.9e+82:
		tmp = x + (y * (z / t))
	elif t <= 5.5e-49:
		tmp = t_1
	elif t <= 1.15e-28:
		tmp = x * (1.0 - (y / t))
	elif t <= 1.72e+47:
		tmp = t_1
	else:
		tmp = x + ((z * y) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(z - x) * y) / t)
	tmp = 0.0
	if (t <= -1.9e+82)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (t <= 5.5e-49)
		tmp = t_1;
	elseif (t <= 1.15e-28)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (t <= 1.72e+47)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z * y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((z - x) * y) / t;
	tmp = 0.0;
	if (t <= -1.9e+82)
		tmp = x + (y * (z / t));
	elseif (t <= 5.5e-49)
		tmp = t_1;
	elseif (t <= 1.15e-28)
		tmp = x * (1.0 - (y / t));
	elseif (t <= 1.72e+47)
		tmp = t_1;
	else
		tmp = x + ((z * y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -1.9e+82], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-49], t$95$1, If[LessEqual[t, 1.15e-28], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.72e+47], t$95$1, N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.90000000000000017e82

   1. Initial program 85.3%

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

   3. Taylor expanded in z around inf 77.8%

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

      1. associate-/l* 88.2%

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

   5. Simplified 88.2%

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

   if -1.90000000000000017e82 < t < 5.50000000000000031e-49 or 1.14999999999999993e-28 < t < 1.72000000000000002e47

   1. Initial program 96.9%

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

   3. Taylor expanded in y around -inf 85.8%

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

   if 5.50000000000000031e-49 < t < 1.14999999999999993e-28

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   if 1.72000000000000002e47 < t

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 89.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq 1.72 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-202}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-107}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= x -4.2e-33)
     t_1
     (if (<= x 1.1e-202)
       (+ x (* y (/ z t)))
       (if (<= x 1.7e-107)
         (* (- z x) (/ y t))
         (if (<= x 2.4e-50) (+ x (/ z (/ t y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -4.2e-33) {
		tmp = t_1;
	} else if (x <= 1.1e-202) {
		tmp = x + (y * (z / t));
	} else if (x <= 1.7e-107) {
		tmp = (z - x) * (y / t);
	} else if (x <= 2.4e-50) {
		tmp = x + (z / (t / y));
	} 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 * (1.0d0 - (y / t))
    if (x <= (-4.2d-33)) then
        tmp = t_1
    else if (x <= 1.1d-202) then
        tmp = x + (y * (z / t))
    else if (x <= 1.7d-107) then
        tmp = (z - x) * (y / t)
    else if (x <= 2.4d-50) then
        tmp = x + (z / (t / y))
    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 * (1.0 - (y / t));
	double tmp;
	if (x <= -4.2e-33) {
		tmp = t_1;
	} else if (x <= 1.1e-202) {
		tmp = x + (y * (z / t));
	} else if (x <= 1.7e-107) {
		tmp = (z - x) * (y / t);
	} else if (x <= 2.4e-50) {
		tmp = x + (z / (t / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -4.2e-33:
		tmp = t_1
	elif x <= 1.1e-202:
		tmp = x + (y * (z / t))
	elif x <= 1.7e-107:
		tmp = (z - x) * (y / t)
	elif x <= 2.4e-50:
		tmp = x + (z / (t / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -4.2e-33)
		tmp = t_1;
	elseif (x <= 1.1e-202)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (x <= 1.7e-107)
		tmp = Float64(Float64(z - x) * Float64(y / t));
	elseif (x <= 2.4e-50)
		tmp = Float64(x + Float64(z / Float64(t / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -4.2e-33)
		tmp = t_1;
	elseif (x <= 1.1e-202)
		tmp = x + (y * (z / t));
	elseif (x <= 1.7e-107)
		tmp = (z - x) * (y / t);
	elseif (x <= 2.4e-50)
		tmp = x + (z / (t / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e-33], t$95$1, If[LessEqual[x, 1.1e-202], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e-107], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-50], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e-33 or 2.40000000000000002e-50 < x

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

   5. Simplified 83.3%

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

   if -4.2e-33 < x < 1.10000000000000004e-202

   1. Initial program 96.2%

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

   3. Taylor expanded in z around inf 89.4%

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

      1. associate-/l* 89.8%

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

   5. Simplified 89.8%

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

   if 1.10000000000000004e-202 < x < 1.69999999999999997e-107

   1. Initial program 90.7%

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

   3. Taylor expanded in y around -inf 79.6%

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

      1. *-commutative 90.7%

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

      2. associate-/l* 99.7%

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

   5. Applied egg-rr 88.6%

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

   if 1.69999999999999997e-107 < x < 2.40000000000000002e-50

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 99.5%

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

      3. associate-/r/ 100.0%

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

   7. Simplified 100.0%

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

Alternative 9: 82.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-98}:\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (* x (- 1.0 (/ y t)))))
   (if (<= x -4.2e-33)
     t_2
     (if (<= x 1.1e-202)
       t_1
       (if (<= x 1.05e-98)
         (* (- z x) (/ y t))
         (if (<= x 2.55e-50) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -4.2e-33) {
		tmp = t_2;
	} else if (x <= 1.1e-202) {
		tmp = t_1;
	} else if (x <= 1.05e-98) {
		tmp = (z - x) * (y / t);
	} else if (x <= 2.55e-50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = x * (1.0d0 - (y / t))
    if (x <= (-4.2d-33)) then
        tmp = t_2
    else if (x <= 1.1d-202) then
        tmp = t_1
    else if (x <= 1.05d-98) then
        tmp = (z - x) * (y / t)
    else if (x <= 2.55d-50) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -4.2e-33) {
		tmp = t_2;
	} else if (x <= 1.1e-202) {
		tmp = t_1;
	} else if (x <= 1.05e-98) {
		tmp = (z - x) * (y / t);
	} else if (x <= 2.55e-50) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	t_2 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -4.2e-33:
		tmp = t_2
	elif x <= 1.1e-202:
		tmp = t_1
	elif x <= 1.05e-98:
		tmp = (z - x) * (y / t)
	elif x <= 2.55e-50:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -4.2e-33)
		tmp = t_2;
	elseif (x <= 1.1e-202)
		tmp = t_1;
	elseif (x <= 1.05e-98)
		tmp = Float64(Float64(z - x) * Float64(y / t));
	elseif (x <= 2.55e-50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	t_2 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -4.2e-33)
		tmp = t_2;
	elseif (x <= 1.1e-202)
		tmp = t_1;
	elseif (x <= 1.05e-98)
		tmp = (z - x) * (y / t);
	elseif (x <= 2.55e-50)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e-33], t$95$2, If[LessEqual[x, 1.1e-202], t$95$1, If[LessEqual[x, 1.05e-98], N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.55e-50], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e-33 or 2.55000000000000023e-50 < x

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

   5. Simplified 83.3%

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

   if -4.2e-33 < x < 1.10000000000000004e-202 or 1.04999999999999996e-98 < x < 2.55000000000000023e-50

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 90.4%

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

   5. Simplified 90.4%

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

   if 1.10000000000000004e-202 < x < 1.04999999999999996e-98

   1. Initial program 91.1%

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

   3. Taylor expanded in y around -inf 80.4%

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

      1. *-commutative 91.1%

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

      2. associate-/l* 99.7%

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

   5. Applied egg-rr 89.0%

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

Alternative 10: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-226} \lor \neg \left(x \leq 2.25 \cdot 10^{-144}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.8e-226) (not (<= x 2.25e-144)))
   (* x (- 1.0 (/ y t)))
   (* y (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.8e-226) || !(x <= 2.25e-144)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.8d-226)) .or. (.not. (x <= 2.25d-144))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.8e-226) || !(x <= 2.25e-144)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.8e-226) or not (x <= 2.25e-144):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.8e-226) || !(x <= 2.25e-144))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.8e-226) || ~((x <= 2.25e-144)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.8e-226], N[Not[LessEqual[x, 2.25e-144]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7999999999999999e-226 or 2.2499999999999999e-144 < x

   1. Initial program 95.9%

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

   3. Taylor expanded in x around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

   if -4.7999999999999999e-226 < x < 2.2499999999999999e-144

   1. Initial program 92.1%

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

   3. Taylor expanded in y around -inf 80.8%

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

   4. Taylor expanded in z around inf 75.7%

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

      1. associate-/l* 89.4%

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

   6. Simplified 78.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{-226} \lor \neg \left(x \leq 2.25 \cdot 10^{-144}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+63}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.5e+84) x (if (<= t 5e+63) (/ z (/ t y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e+84) {
		tmp = x;
	} else if (t <= 5e+63) {
		tmp = z / (t / y);
	} else {
		tmp = 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 <= (-3.5d+84)) then
        tmp = x
    else if (t <= 5d+63) then
        tmp = z / (t / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.5e+84) {
		tmp = x;
	} else if (t <= 5e+63) {
		tmp = z / (t / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.5e+84:
		tmp = x
	elif t <= 5e+63:
		tmp = z / (t / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.5e+84)
		tmp = x;
	elseif (t <= 5e+63)
		tmp = Float64(z / Float64(t / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.5e+84)
		tmp = x;
	elseif (t <= 5e+63)
		tmp = z / (t / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.5e+84], x, If[LessEqual[t, 5e+63], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999999e84 or 5.00000000000000011e63 < t

   1. Initial program 90.7%

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

   3. Taylor expanded in y around 0 66.0%

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

   if -3.4999999999999999e84 < t < 5.00000000000000011e63

   1. Initial program 97.1%

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

   3. Taylor expanded in y around -inf 84.2%

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

      1. *-commutative 97.1%

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

      2. associate-/l* 97.0%

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

   5. Applied egg-rr 84.1%

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

   6. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 63.7%

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

      2. associate-*l/ 61.4%

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

      3. associate-/r/ 65.5%

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

   8. Simplified 53.3%

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

Alternative 12: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+84}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.2e+84) x (if (<= t 4e+61) (* y (/ z t)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e+84) {
		tmp = x;
	} else if (t <= 4e+61) {
		tmp = y * (z / t);
	} else {
		tmp = 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 <= (-9.2d+84)) then
        tmp = x
    else if (t <= 4d+61) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e+84) {
		tmp = x;
	} else if (t <= 4e+61) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.2e+84:
		tmp = x
	elif t <= 4e+61:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.2e+84)
		tmp = x;
	elseif (t <= 4e+61)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.2e+84)
		tmp = x;
	elseif (t <= 4e+61)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.2e+84], x, If[LessEqual[t, 4e+61], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -9.1999999999999996e84 or 3.9999999999999998e61 < t

   1. Initial program 90.7%

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

   3. Taylor expanded in y around 0 66.0%

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

   if -9.1999999999999996e84 < t < 3.9999999999999998e61

   1. Initial program 97.1%

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

   3. Taylor expanded in y around -inf 84.2%

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

   4. Taylor expanded in z around inf 51.4%

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

      1. associate-/l* 61.4%

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

   6. Simplified 49.2%

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

Alternative 13: 38.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

3. Taylor expanded in y around 0 33.2%

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

Developer target: 91.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024091 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

  (+ x (/ (* y (- z x)) t)))