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

Percentage Accurate: 92.8% → 95.5%

Time: 9.9s

Alternatives: 13

Speedup: 1.0×

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

Specification

Math

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

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: 92.8% 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: 95.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (* y (- z t)) a) (- INFINITY))
   (* (/ y a) (- t z))
   (+ x (/ (* y (- t z)) a))))

C

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

Java

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

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((y * (z - t)) / a) <= -math.inf:
		tmp = (y / a) * (t - z)
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -inf.0

   1. Initial program 78.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. associate-*r/ 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto y \cdot \color{blue}{\left(0 - \frac{z - t}{a}\right)} \]

      5. div-sub 94.8%

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \]

      6. associate--r- 94.8%

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \]

      7. neg-sub0 94.8%

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

      8. +-commutative 94.8%

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

      9. sub-neg 94.8%

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

      10. distribute-rgt-out-- 92.2%

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

      11. associate-*l/ 80.2%

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

      12. associate-*r/ 92.3%

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

      13. associate-*l/ 82.5%

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

      14. associate-*r/ 87.1%

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

      15. distribute-rgt-out-- 100.0%

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

   9. Simplified 100.0%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 97.7%

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

4. Final simplification 98.0%

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

Alternative 2: 49.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-a}\\ \mathbf{if}\;a \leq -1.62 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-275}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-172}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-126}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a)))))
   (if (<= a -1.62e-87)
     x
     (if (<= a 6e-275)
       (/ t (/ a y))
       (if (<= a 1.85e-172)
         t_1
         (if (<= a 3.6e-126) (* t (/ y a)) (if (<= a 5.0) t_1 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -a);
	double tmp;
	if (a <= -1.62e-87) {
		tmp = x;
	} else if (a <= 6e-275) {
		tmp = t / (a / y);
	} else if (a <= 1.85e-172) {
		tmp = t_1;
	} else if (a <= 3.6e-126) {
		tmp = t * (y / a);
	} else if (a <= 5.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / -a)
    if (a <= (-1.62d-87)) then
        tmp = x
    else if (a <= 6d-275) then
        tmp = t / (a / y)
    else if (a <= 1.85d-172) then
        tmp = t_1
    else if (a <= 3.6d-126) then
        tmp = t * (y / a)
    else if (a <= 5.0d0) then
        tmp = t_1
    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 t_1 = y * (z / -a);
	double tmp;
	if (a <= -1.62e-87) {
		tmp = x;
	} else if (a <= 6e-275) {
		tmp = t / (a / y);
	} else if (a <= 1.85e-172) {
		tmp = t_1;
	} else if (a <= 3.6e-126) {
		tmp = t * (y / a);
	} else if (a <= 5.0) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -a)
	tmp = 0
	if a <= -1.62e-87:
		tmp = x
	elif a <= 6e-275:
		tmp = t / (a / y)
	elif a <= 1.85e-172:
		tmp = t_1
	elif a <= 3.6e-126:
		tmp = t * (y / a)
	elif a <= 5.0:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(-a)))
	tmp = 0.0
	if (a <= -1.62e-87)
		tmp = x;
	elseif (a <= 6e-275)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= 1.85e-172)
		tmp = t_1;
	elseif (a <= 3.6e-126)
		tmp = Float64(t * Float64(y / a));
	elseif (a <= 5.0)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / -a);
	tmp = 0.0;
	if (a <= -1.62e-87)
		tmp = x;
	elseif (a <= 6e-275)
		tmp = t / (a / y);
	elseif (a <= 1.85e-172)
		tmp = t_1;
	elseif (a <= 3.6e-126)
		tmp = t * (y / a);
	elseif (a <= 5.0)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.62e-87], x, If[LessEqual[a, 6e-275], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e-172], t$95$1, If[LessEqual[a, 3.6e-126], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.0], t$95$1, x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.6200000000000001e-87 or 5 < a

   1. Initial program 91.3%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 66.6%

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

   if -1.6200000000000001e-87 < a < 6.000000000000001e-275

   1. Initial program 98.0%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

      1. clear-num 77.7%

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

      2. un-div-inv 79.7%

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

   6. Applied egg-rr 79.7%

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

   7. Taylor expanded in t around inf 49.1%

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

      1. associate-*r/ 53.0%

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

   9. Simplified 53.0%

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

   10. Taylor expanded in t around 0 49.1%

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

       1. associate-*l/ 40.3%

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

       2. associate-/r/ 53.0%

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

   12. Simplified 53.0%

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

   if 6.000000000000001e-275 < a < 1.85e-172 or 3.5999999999999999e-126 < a < 5

   1. Initial program 99.9%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 63.0%

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

      1. mul-1-neg 63.0%

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

      2. associate-/l* 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

      4. distribute-frac-neg2 59.5%

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

   7. Simplified 59.5%

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

   if 1.85e-172 < a < 3.5999999999999999e-126

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around inf 76.0%

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

      1. associate-*r/ 87.7%

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

   9. Simplified 87.7%

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

Alternative 3: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-198}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 0.8:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.4e-83)
   x
   (if (<= a -2.7e-198) (/ t (/ a y)) (if (<= a 0.8) (* z (/ (- y) a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.4e-83) {
		tmp = x;
	} else if (a <= -2.7e-198) {
		tmp = t / (a / y);
	} else if (a <= 0.8) {
		tmp = z * (-y / 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 (a <= (-2.4d-83)) then
        tmp = x
    else if (a <= (-2.7d-198)) then
        tmp = t / (a / y)
    else if (a <= 0.8d0) then
        tmp = z * (-y / 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 (a <= -2.4e-83) {
		tmp = x;
	} else if (a <= -2.7e-198) {
		tmp = t / (a / y);
	} else if (a <= 0.8) {
		tmp = z * (-y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.4e-83:
		tmp = x
	elif a <= -2.7e-198:
		tmp = t / (a / y)
	elif a <= 0.8:
		tmp = z * (-y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.4e-83)
		tmp = x;
	elseif (a <= -2.7e-198)
		tmp = Float64(t / Float64(a / y));
	elseif (a <= 0.8)
		tmp = Float64(z * Float64(Float64(-y) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.4e-83)
		tmp = x;
	elseif (a <= -2.7e-198)
		tmp = t / (a / y);
	elseif (a <= 0.8)
		tmp = z * (-y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.4e-83], x, If[LessEqual[a, -2.7e-198], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 0.8], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.4000000000000001e-83 or 0.80000000000000004 < a

   1. Initial program 91.3%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 66.6%

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

   if -2.4000000000000001e-83 < a < -2.7000000000000002e-198

   1. Initial program 99.7%

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

      1. associate-/l* 78.7%

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

   3. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. un-div-inv 78.7%

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

   6. Applied egg-rr 78.7%

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

   7. Taylor expanded in t around inf 57.1%

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

      1. associate-*r/ 61.6%

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

   9. Simplified 61.6%

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

   10. Taylor expanded in t around 0 57.1%

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

       1. associate-*l/ 44.9%

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

       2. associate-/r/ 61.6%

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

   12. Simplified 61.6%

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

   if -2.7000000000000002e-198 < a < 0.80000000000000004

   1. Initial program 98.8%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

      1. clear-num 90.3%

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

      2. un-div-inv 91.5%

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

   6. Applied egg-rr 91.5%

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

   7. Taylor expanded in x around 0 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-*r/ 75.2%

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

      3. distribute-rgt-neg-in 75.2%

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

      4. neg-sub0 75.2%

         \[\leadsto y \cdot \color{blue}{\left(0 - \frac{z - t}{a}\right)} \]

      5. div-sub 70.8%

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \]

      6. associate--r- 70.8%

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \]

      7. neg-sub0 70.8%

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

      8. +-commutative 70.8%

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

      9. sub-neg 70.8%

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

      10. distribute-rgt-out-- 69.7%

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

      11. associate-*l/ 71.8%

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

      12. associate-*r/ 69.6%

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

      13. associate-*l/ 74.8%

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

      14. associate-*r/ 74.7%

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

      15. distribute-rgt-out-- 82.4%

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

   9. Simplified 82.4%

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

   10. Taylor expanded in t around 0 54.6%

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

       1. associate-*r/ 54.6%

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

       2. mul-1-neg 54.6%

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

       3. distribute-rgt-neg-out 54.6%

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

       4. associate-/l* 50.4%

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

   12. Simplified 50.4%

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

   13. Taylor expanded in y around 0 54.6%

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

       1. mul-1-neg 54.6%

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

       2. distribute-frac-neg2 54.6%

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

       3. *-commutative 54.6%

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

       4. associate-/l* 60.9%

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

   15. Simplified 60.9%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.4 \cdot 10^{-83}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-198}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq 0.8:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-46} \lor \neg \left(t \leq 6.8 \cdot 10^{+82}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e-46) (not (<= t 6.8e+82)))
   (+ x (* t (/ y a)))
   (- x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e-46) || !(t <= 6.8e+82)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / 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 <= (-2.6d-46)) .or. (.not. (t <= 6.8d+82))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - ((y * z) / 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 <= -2.6e-46) || !(t <= 6.8e+82)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e-46) or not (t <= 6.8e+82):
		tmp = x + (t * (y / a))
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e-46) || !(t <= 6.8e+82))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.6e-46) || ~((t <= 6.8e+82)))
		tmp = x + (t * (y / a));
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e-46], N[Not[LessEqual[t, 6.8e+82]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6000000000000002e-46 or 6.79999999999999989e82 < t

   1. Initial program 92.3%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

      1. clear-num 92.9%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in z around 0 83.3%

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

      1. mul-1-neg 83.3%

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

      2. associate-*r/ 87.8%

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

      3. distribute-lft-neg-out 87.8%

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

      4. cancel-sign-sub 87.8%

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

   9. Simplified 87.8%

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

   if -2.6000000000000002e-46 < t < 6.79999999999999989e82

   1. Initial program 97.0%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around inf 92.1%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-46} \lor \neg \left(t \leq 6.8 \cdot 10^{+82}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-46} \lor \neg \left(t \leq 6.8 \cdot 10^{+82}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e-46) (not (<= t 6.8e+82)))
   (+ x (* t (/ y a)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e-46) || !(t <= 6.8e+82)) {
		tmp = x + (t * (y / 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 <= (-2.1d-46)) .or. (.not. (t <= 6.8d+82))) then
        tmp = x + (t * (y / 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 <= -2.1e-46) || !(t <= 6.8e+82)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e-46) or not (t <= 6.8e+82):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e-46) || !(t <= 6.8e+82))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e-46) || ~((t <= 6.8e+82)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e-46], N[Not[LessEqual[t, 6.8e+82]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.09999999999999987e-46 or 6.79999999999999989e82 < t

   1. Initial program 92.3%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

      1. clear-num 92.9%

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

      2. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in z around 0 83.3%

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

      1. mul-1-neg 83.3%

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

      2. associate-*r/ 87.8%

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

      3. distribute-lft-neg-out 87.8%

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

      4. cancel-sign-sub 87.8%

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

   9. Simplified 87.8%

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

   if -2.09999999999999987e-46 < t < 6.79999999999999989e82

   1. Initial program 97.0%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

      1. clear-num 94.0%

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

      2. un-div-inv 94.0%

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

   6. Applied egg-rr 94.0%

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

   7. Taylor expanded in z around inf 89.8%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-46} \lor \neg \left(t \leq 6.8 \cdot 10^{+82}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+164} \lor \neg \left(z \leq 1.36 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.45e+164) (not (<= z 1.36e+107)))
   (* (/ y a) (- t z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.45e+164) || !(z <= 1.36e+107)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / 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 ((z <= (-1.45d+164)) .or. (.not. (z <= 1.36d+107))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + (t * (y / 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 ((z <= -1.45e+164) || !(z <= 1.36e+107)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.45e+164) or not (z <= 1.36e+107):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.45e+164) || !(z <= 1.36e+107))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.45e+164) || ~((z <= 1.36e+107)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.45e+164], N[Not[LessEqual[z, 1.36e+107]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e164 or 1.35999999999999998e107 < z

   1. Initial program 92.3%

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

      1. associate-/l* 90.3%

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

   3. Simplified 90.3%

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

      1. clear-num 90.3%

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

      2. un-div-inv 90.4%

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

   6. Applied egg-rr 90.4%

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

   7. Taylor expanded in x around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. associate-*r/ 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

      4. neg-sub0 73.0%

         \[\leadsto y \cdot \color{blue}{\left(0 - \frac{z - t}{a}\right)} \]

      5. div-sub 65.0%

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \]

      6. associate--r- 65.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \]

      7. neg-sub0 65.0%

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

      8. +-commutative 65.0%

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

      9. sub-neg 65.0%

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

      10. distribute-rgt-out-- 64.9%

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

      11. associate-*l/ 63.0%

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

      12. associate-*r/ 64.9%

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

      13. associate-*l/ 63.0%

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

      14. associate-*r/ 70.5%

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

      15. distribute-rgt-out-- 78.5%

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

   9. Simplified 78.5%

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

   if -1.4499999999999999e164 < z < 1.35999999999999998e107

   1. Initial program 95.3%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.2%

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

      2. un-div-inv 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in z around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. associate-*r/ 84.8%

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

      3. distribute-lft-neg-out 84.8%

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

      4. cancel-sign-sub 84.8%

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

   9. Simplified 84.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+164} \lor \neg \left(z \leq 1.36 \cdot 10^{+107}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3e-46)
   (+ x (/ y (/ a t)))
   (if (<= t 6.8e+82) (- x (/ (* y z) a)) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3e-46) {
		tmp = x + (y / (a / t));
	} else if (t <= 6.8e+82) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (t * (y / 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 <= (-3d-46)) then
        tmp = x + (y / (a / t))
    else if (t <= 6.8d+82) then
        tmp = x - ((y * z) / a)
    else
        tmp = x + (t * (y / 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 <= -3e-46) {
		tmp = x + (y / (a / t));
	} else if (t <= 6.8e+82) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3e-46:
		tmp = x + (y / (a / t))
	elif t <= 6.8e+82:
		tmp = x - ((y * z) / a)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3e-46)
		tmp = Float64(x + Float64(y / Float64(a / t)));
	elseif (t <= 6.8e+82)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3e-46)
		tmp = x + (y / (a / t));
	elseif (t <= 6.8e+82)
		tmp = x - ((y * z) / a);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3e-46], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+82], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.99999999999999987e-46

   1. Initial program 96.0%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

      1. clear-num 93.1%

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

      2. un-div-inv 96.0%

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

   6. Applied egg-rr 96.0%

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

   7. Taylor expanded in z around 0 86.0%

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

      1. associate-*r/ 86.0%

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

      2. mul-1-neg 86.0%

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

   9. Simplified 86.0%

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

   if -2.99999999999999987e-46 < t < 6.79999999999999989e82

   1. Initial program 97.0%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around inf 92.1%

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

   if 6.79999999999999989e82 < t

   1. Initial program 87.2%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.7%

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

      2. un-div-inv 92.8%

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

   6. Applied egg-rr 92.8%

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

   7. Taylor expanded in z around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. associate-*r/ 90.7%

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

      3. distribute-lft-neg-out 90.7%

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

      4. cancel-sign-sub 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+82}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+29}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.2e+29) x (if (<= x 3.1e+66) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.2e+29) {
		tmp = x;
	} else if (x <= 3.1e+66) {
		tmp = (y / a) * (t - 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 (x <= (-1.2d+29)) then
        tmp = x
    else if (x <= 3.1d+66) then
        tmp = (y / a) * (t - 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 (x <= -1.2e+29) {
		tmp = x;
	} else if (x <= 3.1e+66) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.2e+29:
		tmp = x
	elif x <= 3.1e+66:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.2e+29)
		tmp = x;
	elseif (x <= 3.1e+66)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.2e+29)
		tmp = x;
	elseif (x <= 3.1e+66)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.2e+29], x, If[LessEqual[x, 3.1e+66], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e29 or 3.10000000000000019e66 < x

   1. Initial program 96.4%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in x around inf 74.9%

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

   if -1.2e29 < x < 3.10000000000000019e66

   1. Initial program 93.5%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

      1. clear-num 93.3%

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

      2. un-div-inv 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in x around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. associate-*r/ 70.0%

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

      3. distribute-rgt-neg-in 70.0%

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

      4. neg-sub0 70.0%

         \[\leadsto y \cdot \color{blue}{\left(0 - \frac{z - t}{a}\right)} \]

      5. div-sub 68.0%

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \]

      6. associate--r- 68.0%

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \]

      7. neg-sub0 68.0%

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

      8. +-commutative 68.0%

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

      9. sub-neg 68.0%

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

      10. distribute-rgt-out-- 66.6%

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

      11. associate-*l/ 66.0%

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

      12. associate-*r/ 69.3%

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

      13. associate-*l/ 69.3%

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

      14. associate-*r/ 71.1%

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

      15. distribute-rgt-out-- 75.8%

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

   9. Simplified 75.8%

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

Alternative 9: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.8e+24) x (if (<= x 2.8e+65) (* y (/ (- t z) a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.8e+24) {
		tmp = x;
	} else if (x <= 2.8e+65) {
		tmp = y * ((t - 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 (x <= (-4.8d+24)) then
        tmp = x
    else if (x <= 2.8d+65) then
        tmp = y * ((t - 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 (x <= -4.8e+24) {
		tmp = x;
	} else if (x <= 2.8e+65) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.8e+24:
		tmp = x
	elif x <= 2.8e+65:
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.8e+24)
		tmp = x;
	elseif (x <= 2.8e+65)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.8e+24)
		tmp = x;
	elseif (x <= 2.8e+65)
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.8e+24], x, If[LessEqual[x, 2.8e+65], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000001e24 or 2.7999999999999999e65 < x

   1. Initial program 96.4%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 74.5%

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

   if -4.8000000000000001e24 < x < 2.7999999999999999e65

   1. Initial program 93.4%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

      1. clear-num 93.9%

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

      2. un-div-inv 94.0%

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

   6. Applied egg-rr 94.0%

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

   7. Taylor expanded in x around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r/ 70.9%

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

      3. distribute-rgt-neg-in 70.9%

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

      4. neg-sub0 70.9%

         \[\leadsto y \cdot \color{blue}{\left(0 - \frac{z - t}{a}\right)} \]

      5. div-sub 68.9%

         \[\leadsto y \cdot \left(0 - \color{blue}{\left(\frac{z}{a} - \frac{t}{a}\right)}\right) \]

      6. associate--r- 68.9%

         \[\leadsto y \cdot \color{blue}{\left(\left(0 - \frac{z}{a}\right) + \frac{t}{a}\right)} \]

      7. neg-sub0 68.9%

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

      8. +-commutative 68.9%

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

      9. sub-neg 68.9%

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

      10. distribute-rgt-out-- 67.5%

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

      11. associate-*l/ 66.2%

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

      12. associate-*r/ 69.5%

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

      13. associate-*l/ 69.5%

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

      14. associate-*r/ 71.4%

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

      15. distribute-rgt-out-- 76.1%

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

   9. Simplified 76.1%

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

   10. Taylor expanded in y around 0 70.3%

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

       1. associate-/l* 70.9%

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

   12. Simplified 70.9%

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

Alternative 10: 48.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.6e-22) x (if (<= x 1.7e+63) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.6e-22) {
		tmp = x;
	} else if (x <= 1.7e+63) {
		tmp = t * (y / 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 (x <= (-6.6d-22)) then
        tmp = x
    else if (x <= 1.7d+63) then
        tmp = t * (y / 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 (x <= -6.6e-22) {
		tmp = x;
	} else if (x <= 1.7e+63) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.6e-22:
		tmp = x
	elif x <= 1.7e+63:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.6e-22)
		tmp = x;
	elseif (x <= 1.7e+63)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.6e-22)
		tmp = x;
	elseif (x <= 1.7e+63)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.6e-22], x, If[LessEqual[x, 1.7e+63], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6000000000000002e-22 or 1.6999999999999999e63 < x

   1. Initial program 96.7%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in x around inf 71.7%

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

   if -6.6000000000000002e-22 < x < 1.6999999999999999e63

   1. Initial program 92.9%

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

      1. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

      1. clear-num 93.4%

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

      2. un-div-inv 93.6%

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

   6. Applied egg-rr 93.6%

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

   7. Taylor expanded in t around inf 42.9%

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

      1. associate-*r/ 46.4%

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

   9. Simplified 46.4%

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

Alternative 11: 93.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (a / (t - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

   1. associate-/l* 93.5%

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

3. Simplified 93.5%

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

   1. clear-num 93.5%

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

   2. un-div-inv 94.3%

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

6. Applied egg-rr 94.3%

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

7. Final simplification 94.3%

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

Alternative 12: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

   1. associate-/l* 93.5%

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

3. Simplified 93.5%

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

5. Final simplification 93.5%

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

Alternative 13: 39.3% 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 94.7%

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

   1. associate-/l* 93.5%

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

3. Simplified 93.5%

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

5. Taylor expanded in x around inf 46.3%

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

Developer target: 99.1% accurate, 0.5× 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 2024084 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (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)))