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

Percentage Accurate: 93.1% → 99.6%

Time: 11.6s

Alternatives: 16

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+243}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+243)))
     (+ x (* y (/ (- z t) a)))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+243)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+243)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+243):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+243))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+243)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+243]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0 or 5.00000000000000037e243 < (*.f64 y (-.f64 z t))

   1. Initial program 67.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 5.00000000000000037e243

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty \lor \neg \left(y \cdot \left(z - t\right) \leq 5 \cdot 10^{+243}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{a}, z - t, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. +-commutative 91.9%

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

   2. associate-*l/ 96.9%

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

   3. fma-def 97.0%

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

3. Simplified 97.0%

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

5. Final simplification 97.0%

   \[\leadsto \mathsf{fma}\left(\frac{y}{a}, z - t, x\right) \]
6. Add Preprocessing

Alternative 3: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-48} \lor \neg \left(y \leq 1.7 \cdot 10^{-261} \lor \neg \left(y \leq 2.9 \cdot 10^{-161}\right) \land \left(y \leq 1.05 \cdot 10^{-152} \lor \neg \left(y \leq 2.1 \cdot 10^{-38}\right) \land y \leq 1.8\right)\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e-48)
         (not
          (or (<= y 1.7e-261)
              (and (not (<= y 2.9e-161))
                   (or (<= y 1.05e-152)
                       (and (not (<= y 2.1e-38)) (<= y 1.8)))))))
   (* (/ y a) (- z t))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-48) || !((y <= 1.7e-261) || (!(y <= 2.9e-161) && ((y <= 1.05e-152) || (!(y <= 2.1e-38) && (y <= 1.8)))))) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.9d-48)) .or. (.not. (y <= 1.7d-261) .or. (.not. (y <= 2.9d-161)) .and. (y <= 1.05d-152) .or. (.not. (y <= 2.1d-38)) .and. (y <= 1.8d0))) then
        tmp = (y / a) * (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 a) {
	double tmp;
	if ((y <= -2.9e-48) || !((y <= 1.7e-261) || (!(y <= 2.9e-161) && ((y <= 1.05e-152) || (!(y <= 2.1e-38) && (y <= 1.8)))))) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e-48) or not ((y <= 1.7e-261) or (not (y <= 2.9e-161) and ((y <= 1.05e-152) or (not (y <= 2.1e-38) and (y <= 1.8))))):
		tmp = (y / a) * (z - t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e-48) || !((y <= 1.7e-261) || (!(y <= 2.9e-161) && ((y <= 1.05e-152) || (!(y <= 2.1e-38) && (y <= 1.8))))))
		tmp = Float64(Float64(y / a) * Float64(z - t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.9e-48) || ~(((y <= 1.7e-261) || (~((y <= 2.9e-161)) && ((y <= 1.05e-152) || (~((y <= 2.1e-38)) && (y <= 1.8)))))))
		tmp = (y / a) * (z - t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e-48], N[Not[Or[LessEqual[y, 1.7e-261], And[N[Not[LessEqual[y, 2.9e-161]], $MachinePrecision], Or[LessEqual[y, 1.05e-152], And[N[Not[LessEqual[y, 2.1e-38]], $MachinePrecision], LessEqual[y, 1.8]]]]]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000003e-48 or 1.7e-261 < y < 2.9e-161 or 1.04999999999999999e-152 < y < 2.10000000000000013e-38 or 1.80000000000000004 < y

   1. Initial program 88.7%

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

      1. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

      1. associate-/l* 88.7%

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

      2. +-commutative 88.7%

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

      3. div-inv 88.6%

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

      4. div-inv 88.7%

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

      5. *-commutative 88.7%

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

      6. associate-*l/ 95.2%

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

      7. fma-def 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in a around 0 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*r/ 73.3%

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

   9. Simplified 73.3%

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

   if -2.9000000000000003e-48 < y < 1.7e-261 or 2.9e-161 < y < 1.04999999999999999e-152 or 2.10000000000000013e-38 < y < 1.80000000000000004

   1. Initial program 99.9%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 77.4%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-48} \lor \neg \left(y \leq 1.7 \cdot 10^{-261} \lor \neg \left(y \leq 2.9 \cdot 10^{-161}\right) \land \left(y \leq 1.05 \cdot 10^{-152} \lor \neg \left(y \leq 2.1 \cdot 10^{-38}\right) \land y \leq 1.8\right)\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-249}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- (/ t a)))))
   (if (<= t -6.6e+136)
     t_1
     (if (<= t 1.55e-249)
       x
       (if (<= t 6.5e-172)
         (* y (/ z a))
         (if (<= t 3.1e-125) x (if (<= t 6.8e-13) (* (/ y a) z) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * -(t / a);
	double tmp;
	if (t <= -6.6e+136) {
		tmp = t_1;
	} else if (t <= 1.55e-249) {
		tmp = x;
	} else if (t <= 6.5e-172) {
		tmp = y * (z / a);
	} else if (t <= 3.1e-125) {
		tmp = x;
	} else if (t <= 6.8e-13) {
		tmp = (y / a) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -(t / a)
    if (t <= (-6.6d+136)) then
        tmp = t_1
    else if (t <= 1.55d-249) then
        tmp = x
    else if (t <= 6.5d-172) then
        tmp = y * (z / a)
    else if (t <= 3.1d-125) then
        tmp = x
    else if (t <= 6.8d-13) then
        tmp = (y / a) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * -(t / a);
	double tmp;
	if (t <= -6.6e+136) {
		tmp = t_1;
	} else if (t <= 1.55e-249) {
		tmp = x;
	} else if (t <= 6.5e-172) {
		tmp = y * (z / a);
	} else if (t <= 3.1e-125) {
		tmp = x;
	} else if (t <= 6.8e-13) {
		tmp = (y / a) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * -(t / a)
	tmp = 0
	if t <= -6.6e+136:
		tmp = t_1
	elif t <= 1.55e-249:
		tmp = x
	elif t <= 6.5e-172:
		tmp = y * (z / a)
	elif t <= 3.1e-125:
		tmp = x
	elif t <= 6.8e-13:
		tmp = (y / a) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(-Float64(t / a)))
	tmp = 0.0
	if (t <= -6.6e+136)
		tmp = t_1;
	elseif (t <= 1.55e-249)
		tmp = x;
	elseif (t <= 6.5e-172)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 3.1e-125)
		tmp = x;
	elseif (t <= 6.8e-13)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * -(t / a);
	tmp = 0.0;
	if (t <= -6.6e+136)
		tmp = t_1;
	elseif (t <= 1.55e-249)
		tmp = x;
	elseif (t <= 6.5e-172)
		tmp = y * (z / a);
	elseif (t <= 3.1e-125)
		tmp = x;
	elseif (t <= 6.8e-13)
		tmp = (y / a) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * (-N[(t / a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[t, -6.6e+136], t$95$1, If[LessEqual[t, 1.55e-249], x, If[LessEqual[t, 6.5e-172], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-125], x, If[LessEqual[t, 6.8e-13], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.59999999999999984e136 or 6.80000000000000031e-13 < t

   1. Initial program 86.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

      1. associate-/l* 86.9%

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

      2. +-commutative 86.9%

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

      3. div-inv 86.8%

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

      4. div-inv 86.9%

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

      5. *-commutative 86.9%

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

      6. associate-*l/ 92.9%

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

      7. fma-def 92.9%

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

   6. Applied egg-rr 92.9%

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

   7. Taylor expanded in t around inf 56.9%

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

      1. mul-1-neg 56.9%

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

      2. associate-*l/ 61.8%

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

   9. Simplified 61.8%

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

   if -6.59999999999999984e136 < t < 1.54999999999999993e-249 or 6.50000000000000012e-172 < t < 3.10000000000000013e-125

   1. Initial program 97.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.3%

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

   if 1.54999999999999993e-249 < t < 6.50000000000000012e-172

   1. Initial program 85.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/l* 85.4%

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

      2. +-commutative 85.4%

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

      3. div-inv 85.4%

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

      4. div-inv 85.4%

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

      5. *-commutative 85.4%

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

      6. associate-*l/ 99.8%

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

      7. fma-def 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 55.7%

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

      1. associate-*r/ 70.0%

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

   9. Simplified 70.0%

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

   if 3.10000000000000013e-125 < t < 6.80000000000000031e-13

   1. Initial program 89.7%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

      1. associate-/l* 89.7%

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

      2. +-commutative 89.7%

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

      3. div-inv 89.5%

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

      4. div-inv 89.7%

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

      5. *-commutative 89.7%

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

      6. associate-*l/ 88.4%

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

      7. fma-def 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in z around inf 50.5%

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

      1. associate-/l* 53.7%

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

      2. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-249}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-172}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+138}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.16e+138)
   (/ (- y) (/ a t))
   (if (<= t 2.2e-245)
     x
     (if (<= t 1.4e-173)
       (* y (/ z a))
       (if (<= t 1.35e-130)
         x
         (if (<= t 6e-13) (* (/ y a) z) (* y (- (/ t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.16e+138) {
		tmp = -y / (a / t);
	} else if (t <= 2.2e-245) {
		tmp = x;
	} else if (t <= 1.4e-173) {
		tmp = y * (z / a);
	} else if (t <= 1.35e-130) {
		tmp = x;
	} else if (t <= 6e-13) {
		tmp = (y / a) * z;
	} else {
		tmp = y * -(t / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.16d+138)) then
        tmp = -y / (a / t)
    else if (t <= 2.2d-245) then
        tmp = x
    else if (t <= 1.4d-173) then
        tmp = y * (z / a)
    else if (t <= 1.35d-130) then
        tmp = x
    else if (t <= 6d-13) then
        tmp = (y / a) * z
    else
        tmp = y * -(t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.16e+138) {
		tmp = -y / (a / t);
	} else if (t <= 2.2e-245) {
		tmp = x;
	} else if (t <= 1.4e-173) {
		tmp = y * (z / a);
	} else if (t <= 1.35e-130) {
		tmp = x;
	} else if (t <= 6e-13) {
		tmp = (y / a) * z;
	} else {
		tmp = y * -(t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.16e+138:
		tmp = -y / (a / t)
	elif t <= 2.2e-245:
		tmp = x
	elif t <= 1.4e-173:
		tmp = y * (z / a)
	elif t <= 1.35e-130:
		tmp = x
	elif t <= 6e-13:
		tmp = (y / a) * z
	else:
		tmp = y * -(t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.16e+138)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 2.2e-245)
		tmp = x;
	elseif (t <= 1.4e-173)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 1.35e-130)
		tmp = x;
	elseif (t <= 6e-13)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = Float64(y * Float64(-Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.16e+138)
		tmp = -y / (a / t);
	elseif (t <= 2.2e-245)
		tmp = x;
	elseif (t <= 1.4e-173)
		tmp = y * (z / a);
	elseif (t <= 1.35e-130)
		tmp = x;
	elseif (t <= 6e-13)
		tmp = (y / a) * z;
	else
		tmp = y * -(t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.16e+138], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.2e-245], x, If[LessEqual[t, 1.4e-173], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-130], x, If[LessEqual[t, 6e-13], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], N[(y * (-N[(t / a), $MachinePrecision])), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.15999999999999994e138

   1. Initial program 84.3%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

      1. associate-/l* 84.3%

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

      2. +-commutative 84.3%

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

      3. div-inv 84.2%

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

      4. div-inv 84.3%

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

      5. *-commutative 84.3%

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

      6. associate-*l/ 95.6%

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

      7. fma-def 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in t around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-*l/ 74.9%

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

   9. Simplified 74.9%

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

       1. *-commutative 74.9%

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

       2. clear-num 74.8%

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

       3. un-div-inv 74.9%

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

   11. Applied egg-rr 74.9%

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

   if -1.15999999999999994e138 < t < 2.19999999999999993e-245 or 1.39999999999999995e-173 < t < 1.34999999999999996e-130

   1. Initial program 97.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.3%

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

   if 2.19999999999999993e-245 < t < 1.39999999999999995e-173

   1. Initial program 85.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/l* 85.4%

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

      2. +-commutative 85.4%

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

      3. div-inv 85.4%

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

      4. div-inv 85.4%

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

      5. *-commutative 85.4%

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

      6. associate-*l/ 99.8%

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

      7. fma-def 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 55.7%

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

      1. associate-*r/ 70.0%

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

   9. Simplified 70.0%

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

   if 1.34999999999999996e-130 < t < 5.99999999999999968e-13

   1. Initial program 89.7%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

      1. associate-/l* 89.7%

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

      2. +-commutative 89.7%

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

      3. div-inv 89.5%

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

      4. div-inv 89.7%

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

      5. *-commutative 89.7%

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

      6. associate-*l/ 88.4%

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

      7. fma-def 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in z around inf 50.5%

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

      1. associate-/l* 53.7%

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

      2. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

   if 5.99999999999999968e-13 < t

   1. Initial program 87.8%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

      1. associate-/l* 87.8%

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

      2. +-commutative 87.8%

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

      3. div-inv 87.6%

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

      4. div-inv 87.8%

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

      5. *-commutative 87.8%

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

      6. associate-*l/ 92.0%

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

      7. fma-def 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in t around inf 54.8%

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

      1. mul-1-neg 54.8%

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

      2. associate-*l/ 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+138}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-245}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-13}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-\frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -5.5e+136)
   (/ (- y) (/ a t))
   (if (<= t 1.3e-246)
     x
     (if (<= t 2.6e-173)
       (* y (/ z a))
       (if (<= t 6.8e-131)
         x
         (if (<= t 3.9e-12) (* (/ y a) z) (* (/ y a) (- t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+136) {
		tmp = -y / (a / t);
	} else if (t <= 1.3e-246) {
		tmp = x;
	} else if (t <= 2.6e-173) {
		tmp = y * (z / a);
	} else if (t <= 6.8e-131) {
		tmp = x;
	} else if (t <= 3.9e-12) {
		tmp = (y / a) * z;
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-5.5d+136)) then
        tmp = -y / (a / t)
    else if (t <= 1.3d-246) then
        tmp = x
    else if (t <= 2.6d-173) then
        tmp = y * (z / a)
    else if (t <= 6.8d-131) then
        tmp = x
    else if (t <= 3.9d-12) then
        tmp = (y / a) * z
    else
        tmp = (y / a) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.5e+136) {
		tmp = -y / (a / t);
	} else if (t <= 1.3e-246) {
		tmp = x;
	} else if (t <= 2.6e-173) {
		tmp = y * (z / a);
	} else if (t <= 6.8e-131) {
		tmp = x;
	} else if (t <= 3.9e-12) {
		tmp = (y / a) * z;
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -5.5e+136:
		tmp = -y / (a / t)
	elif t <= 1.3e-246:
		tmp = x
	elif t <= 2.6e-173:
		tmp = y * (z / a)
	elif t <= 6.8e-131:
		tmp = x
	elif t <= 3.9e-12:
		tmp = (y / a) * z
	else:
		tmp = (y / a) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.5e+136)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 1.3e-246)
		tmp = x;
	elseif (t <= 2.6e-173)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 6.8e-131)
		tmp = x;
	elseif (t <= 3.9e-12)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = Float64(Float64(y / a) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -5.5e+136)
		tmp = -y / (a / t);
	elseif (t <= 1.3e-246)
		tmp = x;
	elseif (t <= 2.6e-173)
		tmp = y * (z / a);
	elseif (t <= 6.8e-131)
		tmp = x;
	elseif (t <= 3.9e-12)
		tmp = (y / a) * z;
	else
		tmp = (y / a) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.5e+136], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-246], x, If[LessEqual[t, 2.6e-173], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-131], x, If[LessEqual[t, 3.9e-12], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.50000000000000039e136

   1. Initial program 84.3%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

      1. associate-/l* 84.3%

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

      2. +-commutative 84.3%

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

      3. div-inv 84.2%

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

      4. div-inv 84.3%

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

      5. *-commutative 84.3%

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

      6. associate-*l/ 95.6%

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

      7. fma-def 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in t around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-*l/ 74.9%

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

   9. Simplified 74.9%

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

       1. *-commutative 74.9%

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

       2. clear-num 74.8%

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

       3. un-div-inv 74.9%

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

   11. Applied egg-rr 74.9%

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

   if -5.50000000000000039e136 < t < 1.2999999999999999e-246 or 2.60000000000000003e-173 < t < 6.7999999999999999e-131

   1. Initial program 97.3%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.3%

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

   if 1.2999999999999999e-246 < t < 2.60000000000000003e-173

   1. Initial program 85.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/l* 85.4%

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

      2. +-commutative 85.4%

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

      3. div-inv 85.4%

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

      4. div-inv 85.4%

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

      5. *-commutative 85.4%

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

      6. associate-*l/ 99.8%

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

      7. fma-def 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 55.7%

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

      1. associate-*r/ 70.0%

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

   9. Simplified 70.0%

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

   if 6.7999999999999999e-131 < t < 3.89999999999999994e-12

   1. Initial program 89.7%

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

      1. associate-/l* 88.5%

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

   3. Simplified 88.5%

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

      1. associate-/l* 89.7%

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

      2. +-commutative 89.7%

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

      3. div-inv 89.5%

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

      4. div-inv 89.7%

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

      5. *-commutative 89.7%

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

      6. associate-*l/ 88.4%

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

      7. fma-def 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in z around inf 50.5%

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

      1. associate-/l* 53.7%

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

      2. associate-/r/ 62.0%

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

   9. Applied egg-rr 62.0%

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

   if 3.89999999999999994e-12 < t

   1. Initial program 87.8%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

      1. associate-/l* 87.8%

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

      2. +-commutative 87.8%

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

      3. div-inv 87.6%

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

      4. div-inv 87.8%

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

      5. *-commutative 87.8%

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

      6. associate-*l/ 92.0%

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

      7. fma-def 92.0%

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

   6. Applied egg-rr 92.0%

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

   7. Taylor expanded in t around inf 54.8%

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

      1. associate-*r/ 59.9%

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

      2. neg-mul-1 59.9%

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

      3. distribute-rgt-neg-in 59.9%

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

   9. Simplified 59.9%

      \[\leadsto \color{blue}{t \cdot \left(-\frac{y}{a}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+136}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-246}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-173}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e+112)
   x
   (if (<= a -1.45e+47)
     (* y (/ z a))
     (if (<= a -2.55e-23) x (if (<= a 2.6e-66) (* (/ y a) z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x;
	} else if (a <= -1.45e+47) {
		tmp = y * (z / a);
	} else if (a <= -2.55e-23) {
		tmp = x;
	} else if (a <= 2.6e-66) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d+112)) then
        tmp = x
    else if (a <= (-1.45d+47)) then
        tmp = y * (z / a)
    else if (a <= (-2.55d-23)) then
        tmp = x
    else if (a <= 2.6d-66) then
        tmp = (y / a) * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e+112) {
		tmp = x;
	} else if (a <= -1.45e+47) {
		tmp = y * (z / a);
	} else if (a <= -2.55e-23) {
		tmp = x;
	} else if (a <= 2.6e-66) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e+112:
		tmp = x
	elif a <= -1.45e+47:
		tmp = y * (z / a)
	elif a <= -2.55e-23:
		tmp = x
	elif a <= 2.6e-66:
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e+112)
		tmp = x;
	elseif (a <= -1.45e+47)
		tmp = Float64(y * Float64(z / a));
	elseif (a <= -2.55e-23)
		tmp = x;
	elseif (a <= 2.6e-66)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e+112)
		tmp = x;
	elseif (a <= -1.45e+47)
		tmp = y * (z / a);
	elseif (a <= -2.55e-23)
		tmp = x;
	elseif (a <= 2.6e-66)
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e+112], x, If[LessEqual[a, -1.45e+47], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.55e-23], x, If[LessEqual[a, 2.6e-66], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.5000000000000008e112 or -1.4499999999999999e47 < a < -2.55000000000000005e-23 or 2.5999999999999999e-66 < a

   1. Initial program 87.1%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.9%

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

   if -9.5000000000000008e112 < a < -1.4499999999999999e47

   1. Initial program 84.2%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/l* 84.2%

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

      2. +-commutative 84.2%

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

      3. div-inv 84.0%

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

      4. div-inv 84.2%

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

      5. *-commutative 84.2%

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

      6. associate-*l/ 99.9%

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

      7. fma-def 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 43.0%

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

      1. associate-*r/ 50.8%

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

   9. Simplified 50.8%

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

   if -2.55000000000000005e-23 < a < 2.5999999999999999e-66

   1. Initial program 99.3%

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

      1. associate-/l* 84.5%

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

   3. Simplified 84.5%

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

      1. associate-/l* 99.3%

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

      2. +-commutative 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-*l/ 84.4%

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

      7. fma-def 84.4%

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

   6. Applied egg-rr 84.4%

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

   7. Taylor expanded in z around inf 50.4%

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

      1. associate-/l* 43.0%

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

      2. associate-/r/ 52.4%

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

   9. Applied egg-rr 52.4%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{+112}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -2.55 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+118} \lor \neg \left(t \leq 4.1 \cdot 10^{-13}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+118) (not (<= t 4.1e-13)))
   (- x (* y (/ t a)))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+118) || !(t <= 4.1e-13)) {
		tmp = x - (y * (t / a));
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.2d+118)) .or. (.not. (t <= 4.1d-13))) then
        tmp = x - (y * (t / a))
    else
        tmp = x + ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+118) || !(t <= 4.1e-13)) {
		tmp = x - (y * (t / a));
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+118) or not (t <= 4.1e-13):
		tmp = x - (y * (t / a))
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+118) || !(t <= 4.1e-13))
		tmp = Float64(x - Float64(y * Float64(t / a)));
	else
		tmp = Float64(x + Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e+118) || ~((t <= 4.1e-13)))
		tmp = x - (y * (t / a));
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+118], N[Not[LessEqual[t, 4.1e-13]], $MachinePrecision]], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e118 or 4.1000000000000002e-13 < t

   1. Initial program 86.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 81.7%

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

      1. associate-*r/ 89.4%

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

      2. associate-*r* 89.4%

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

      3. neg-mul-1 89.4%

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

      4. cancel-sign-sub-inv 89.4%

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

      5. associate-*r/ 81.7%

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

      6. associate-/l* 88.5%

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

      7. associate-/r/ 87.2%

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

   7. Simplified 87.2%

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

   if -1.2e118 < t < 4.1000000000000002e-13

   1. Initial program 95.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+118} \lor \neg \left(t \leq 4.1 \cdot 10^{-13}\right):\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 4.6 \cdot 10^{-12}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.05e+118) (not (<= t 4.6e-12)))
   (- x (/ y (/ a t)))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 4.6e-12)) {
		tmp = x - (y / (a / t));
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.05d+118)) .or. (.not. (t <= 4.6d-12))) then
        tmp = x - (y / (a / t))
    else
        tmp = x + ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.05e+118) || !(t <= 4.6e-12)) {
		tmp = x - (y / (a / t));
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.05e+118) or not (t <= 4.6e-12):
		tmp = x - (y / (a / t))
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.05e+118) || !(t <= 4.6e-12))
		tmp = Float64(x - Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.05e+118) || ~((t <= 4.6e-12)))
		tmp = x - (y / (a / t));
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.05e+118], N[Not[LessEqual[t, 4.6e-12]], $MachinePrecision]], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e118 or 4.59999999999999979e-12 < t

   1. Initial program 86.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 81.7%

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

      1. associate-*r/ 89.4%

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

      2. associate-*r* 89.4%

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

      3. neg-mul-1 89.4%

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

      4. cancel-sign-sub-inv 89.4%

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

      5. associate-*r/ 81.7%

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

      6. associate-/l* 88.5%

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

      7. associate-/r/ 87.2%

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

   7. Simplified 87.2%

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

      1. *-commutative 60.8%

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

      2. clear-num 60.7%

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

      3. un-div-inv 60.8%

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

   9. Applied egg-rr 87.3%

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

   if -1.05e118 < t < 4.59999999999999979e-12

   1. Initial program 95.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+118} \lor \neg \left(t \leq 4.6 \cdot 10^{-12}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{-12}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.1e+118) (not (<= t 2.35e-12)))
   (- x (* (/ y a) t))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 2.35e-12)) {
		tmp = x - ((y / a) * t);
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.1d+118)) .or. (.not. (t <= 2.35d-12))) then
        tmp = x - ((y / a) * t)
    else
        tmp = x + ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.1e+118) || !(t <= 2.35e-12)) {
		tmp = x - ((y / a) * t);
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.1e+118) or not (t <= 2.35e-12):
		tmp = x - ((y / a) * t)
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.1e+118) || !(t <= 2.35e-12))
		tmp = Float64(x - Float64(Float64(y / a) * t));
	else
		tmp = Float64(x + Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.1e+118) || ~((t <= 2.35e-12)))
		tmp = x - ((y / a) * t);
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.1e+118], N[Not[LessEqual[t, 2.35e-12]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.09999999999999993e118 or 2.34999999999999988e-12 < t

   1. Initial program 86.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 81.7%

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

      1. associate-*r/ 89.4%

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

      2. neg-mul-1 89.4%

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

      3. distribute-rgt-neg-in 89.4%

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

      4. distribute-neg-frac 89.4%

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

   7. Simplified 89.4%

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

   if -1.09999999999999993e118 < t < 2.34999999999999988e-12

   1. Initial program 95.3%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*l/ 89.7%

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

      3. *-commutative 89.7%

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

   7. Simplified 89.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{+118} \lor \neg \left(t \leq 2.35 \cdot 10^{-12}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.7e+151)
   (/ (- y) (/ a t))
   (if (<= t 3.45e-102) (+ x (/ (* y z) a)) (* (/ y a) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e+151) {
		tmp = -y / (a / t);
	} else if (t <= 3.45e-102) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = (y / a) * (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.7d+151)) then
        tmp = -y / (a / t)
    else if (t <= 3.45d-102) then
        tmp = x + ((y * z) / a)
    else
        tmp = (y / a) * (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7e+151) {
		tmp = -y / (a / t);
	} else if (t <= 3.45e-102) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = (y / a) * (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.7e+151:
		tmp = -y / (a / t)
	elif t <= 3.45e-102:
		tmp = x + ((y * z) / a)
	else:
		tmp = (y / a) * (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.7e+151)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 3.45e-102)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(Float64(y / a) * Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.7e+151)
		tmp = -y / (a / t);
	elseif (t <= 3.45e-102)
		tmp = x + ((y * z) / a);
	else
		tmp = (y / a) * (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.7e+151], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.45e-102], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.69999999999999989e151

   1. Initial program 83.6%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. associate-/l* 83.6%

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

      2. +-commutative 83.6%

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

      3. div-inv 83.6%

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

      4. div-inv 83.6%

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

      5. *-commutative 83.6%

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

      6. associate-*l/ 95.4%

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

      7. fma-def 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in t around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. associate-*l/ 73.8%

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

   9. Simplified 73.8%

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

       1. *-commutative 73.8%

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

       2. clear-num 73.7%

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

       3. un-div-inv 73.8%

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

   11. Applied egg-rr 73.8%

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

   if -4.69999999999999989e151 < t < 3.45e-102

   1. Initial program 96.4%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 89.1%

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

   if 3.45e-102 < t

   1. Initial program 87.0%

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

      1. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

      1. associate-/l* 87.0%

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

      2. +-commutative 87.0%

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

      3. div-inv 86.9%

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

      4. div-inv 87.0%

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

      5. *-commutative 87.0%

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

      6. associate-*l/ 91.8%

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

      7. fma-def 91.8%

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

   6. Applied egg-rr 91.8%

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

   7. Taylor expanded in a around 0 62.3%

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

      1. *-commutative 62.3%

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

      2. associate-*r/ 70.1%

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

   9. Simplified 70.1%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 3.45 \cdot 10^{-102}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+151}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.55e+151)
   (/ (- y) (/ a t))
   (if (<= t 2.1e-16) (+ x (* (/ y a) z)) (* (/ y a) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+151) {
		tmp = -y / (a / t);
	} else if (t <= 2.1e-16) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = (y / a) * (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.55d+151)) then
        tmp = -y / (a / t)
    else if (t <= 2.1d-16) then
        tmp = x + ((y / a) * z)
    else
        tmp = (y / a) * (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.55e+151) {
		tmp = -y / (a / t);
	} else if (t <= 2.1e-16) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = (y / a) * (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.55e+151:
		tmp = -y / (a / t)
	elif t <= 2.1e-16:
		tmp = x + ((y / a) * z)
	else:
		tmp = (y / a) * (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.55e+151)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 2.1e-16)
		tmp = Float64(x + Float64(Float64(y / a) * z));
	else
		tmp = Float64(Float64(y / a) * Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.55e+151)
		tmp = -y / (a / t);
	elseif (t <= 2.1e-16)
		tmp = x + ((y / a) * z);
	else
		tmp = (y / a) * (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.55e+151], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-16], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.54999999999999998e151

   1. Initial program 83.6%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

      1. associate-/l* 83.6%

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

      2. +-commutative 83.6%

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

      3. div-inv 83.6%

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

      4. div-inv 83.6%

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

      5. *-commutative 83.6%

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

      6. associate-*l/ 95.4%

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

      7. fma-def 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in t around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. associate-*l/ 73.8%

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

   9. Simplified 73.8%

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

       1. *-commutative 73.8%

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

       2. clear-num 73.7%

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

       3. un-div-inv 73.8%

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

   11. Applied egg-rr 73.8%

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

   if -2.54999999999999998e151 < t < 2.1000000000000001e-16

   1. Initial program 94.7%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 85.7%

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

      1. +-commutative 85.7%

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

      2. associate-*l/ 88.7%

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

      3. *-commutative 88.7%

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

   7. Simplified 88.7%

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

   if 2.1000000000000001e-16 < t

   1. Initial program 88.3%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

      1. associate-/l* 88.3%

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

      2. +-commutative 88.3%

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

      3. div-inv 88.1%

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

      4. div-inv 88.3%

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

      5. *-commutative 88.3%

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

      6. associate-*l/ 92.3%

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

      7. fma-def 92.3%

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

   6. Applied egg-rr 92.3%

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

   7. Taylor expanded in a around 0 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*r/ 68.8%

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

   9. Simplified 68.8%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+151}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+70} \lor \neg \left(y \leq 10^{+96}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.36e+70) (not (<= y 1e+96))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.36e+70) || !(y <= 1e+96)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.36d+70)) .or. (.not. (y <= 1d+96))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.36e+70) || !(y <= 1e+96)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.36e+70) or not (y <= 1e+96):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.36e+70) || !(y <= 1e+96))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.36e+70) || ~((y <= 1e+96)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.36e+70], N[Not[LessEqual[y, 1e+96]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.35999999999999995e70 or 1.00000000000000005e96 < y

   1. Initial program 82.4%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

      1. associate-/l* 82.4%

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

      2. +-commutative 82.4%

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

      3. div-inv 82.3%

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

      4. div-inv 82.4%

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

      5. *-commutative 82.4%

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

      6. associate-*l/ 98.8%

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

      7. fma-def 98.8%

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

   6. Applied egg-rr 98.8%

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

   7. Taylor expanded in z around inf 44.7%

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

      1. associate-*r/ 49.5%

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

   9. Simplified 49.5%

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

   if -1.35999999999999995e70 < y < 1.00000000000000005e96

   1. Initial program 97.8%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 53.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+70} \lor \neg \left(y \leq 10^{+96}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. associate-/l* 92.9%

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

3. Simplified 92.9%

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

   1. clear-num 92.9%

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

   2. associate-/r/ 92.9%

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

   3. clear-num 93.2%

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

6. Applied egg-rr 93.2%

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

7. Final simplification 93.2%

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

Alternative 15: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. *-commutative 91.9%

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

   2. associate-/l* 96.6%

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

3. Simplified 96.6%

   \[\leadsto \color{blue}{x + \frac{z - t}{\frac{a}{y}}} \]
4. Add Preprocessing

5. Final simplification 96.6%

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

Alternative 16: 39.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.9%

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

   1. associate-/l* 92.9%

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

3. Simplified 92.9%

   \[\leadsto \color{blue}{x + \frac{y}{\frac{a}{z - t}}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 38.5%

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

6. Final simplification 38.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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