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

Percentage Accurate: 93.5% → 96.9%

Time: 9.8s

Alternatives: 13

Speedup: 1.0×

• 24.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 93.5% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

   1. *-commutative 96.5%

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

   2. clear-num 96.5%

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

   3. un-div-inv 96.9%

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

5. Applied egg-rr 96.9%

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

6. Final simplification 96.9%

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

Alternative 2: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-72} \lor \neg \left(a \leq 4.3 \cdot 10^{-70} \lor \neg \left(a \leq 4.3 \cdot 10^{+28}\right) \land a \leq 8 \cdot 10^{+81}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.4e-72)
         (not (or (<= a 4.3e-70) (and (not (<= a 4.3e+28)) (<= a 8e+81)))))
   (+ x (* t (/ y a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.4e-72) || !((a <= 4.3e-70) || (!(a <= 4.3e+28) && (a <= 8e+81)))) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - 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 ((a <= (-5.4d-72)) .or. (.not. (a <= 4.3d-70) .or. (.not. (a <= 4.3d+28)) .and. (a <= 8d+81))) then
        tmp = x + (t * (y / a))
    else
        tmp = (y / a) * (t - 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 ((a <= -5.4e-72) || !((a <= 4.3e-70) || (!(a <= 4.3e+28) && (a <= 8e+81)))) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.4e-72) or not ((a <= 4.3e-70) or (not (a <= 4.3e+28) and (a <= 8e+81))):
		tmp = x + (t * (y / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.4e-72) || !((a <= 4.3e-70) || (!(a <= 4.3e+28) && (a <= 8e+81))))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.4e-72) || ~(((a <= 4.3e-70) || (~((a <= 4.3e+28)) && (a <= 8e+81)))))
		tmp = x + (t * (y / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.4e-72], N[Not[Or[LessEqual[a, 4.3e-70], And[N[Not[LessEqual[a, 4.3e+28]], $MachinePrecision], LessEqual[a, 8e+81]]]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.4e-72 or 4.3e-70 < a < 4.29999999999999975e28 or 7.99999999999999937e81 < a

   1. Initial program 88.6%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 77.8%

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

      1. cancel-sign-sub-inv 77.8%

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

      2. metadata-eval 77.8%

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

      3. *-lft-identity 77.8%

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

      4. +-commutative 77.8%

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

      5. associate-*r/ 80.9%

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

   6. Simplified 80.9%

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

   if -5.4e-72 < a < 4.3e-70 or 4.29999999999999975e28 < a < 7.99999999999999937e81

   1. Initial program 99.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

      1. *-commutative 97.1%

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

      2. clear-num 97.1%

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

      3. un-div-inv 98.1%

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

   5. Applied egg-rr 98.1%

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

   6. Taylor expanded in x around 0 90.7%

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

      1. mul-1-neg 90.7%

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

      2. associate-*l/ 88.7%

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

      3. distribute-rgt-out-- 73.2%

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

      4. sub-neg 73.2%

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

      5. +-commutative 73.2%

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

      6. distribute-neg-in 73.2%

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

      7. remove-double-neg 73.2%

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

      8. sub-neg 73.2%

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

      9. distribute-rgt-out-- 88.7%

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

   8. Simplified 88.7%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{-72} \lor \neg \left(a \leq 4.3 \cdot 10^{-70} \lor \neg \left(a \leq 4.3 \cdot 10^{+28}\right) \land a \leq 8 \cdot 10^{+81}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 3: 68.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+131} \lor \neg \left(a \leq -6.4 \cdot 10^{+63}\right) \land a \leq 2.1 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.6e+171)
   x
   (if (or (<= a -9.5e+131) (and (not (<= a -6.4e+63)) (<= a 2.1e+106)))
     (* (/ y a) (- t z))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.6e+171) {
		tmp = x;
	} else if ((a <= -9.5e+131) || (!(a <= -6.4e+63) && (a <= 2.1e+106))) {
		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 (a <= (-3.6d+171)) then
        tmp = x
    else if ((a <= (-9.5d+131)) .or. (.not. (a <= (-6.4d+63))) .and. (a <= 2.1d+106)) 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 (a <= -3.6e+171) {
		tmp = x;
	} else if ((a <= -9.5e+131) || (!(a <= -6.4e+63) && (a <= 2.1e+106))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.6e+171:
		tmp = x
	elif (a <= -9.5e+131) or (not (a <= -6.4e+63) and (a <= 2.1e+106)):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.6e+171)
		tmp = x;
	elseif ((a <= -9.5e+131) || (!(a <= -6.4e+63) && (a <= 2.1e+106)))
		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 (a <= -3.6e+171)
		tmp = x;
	elseif ((a <= -9.5e+131) || (~((a <= -6.4e+63)) && (a <= 2.1e+106)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.6e+171], x, If[Or[LessEqual[a, -9.5e+131], And[N[Not[LessEqual[a, -6.4e+63]], $MachinePrecision], LessEqual[a, 2.1e+106]]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.60000000000000018e171 or -9.50000000000000015e131 < a < -6.40000000000000022e63 or 2.10000000000000005e106 < a

   1. Initial program 87.2%

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

      1. associate-*l/ 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in x around inf 70.0%

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

   if -3.60000000000000018e171 < a < -9.50000000000000015e131 or -6.40000000000000022e63 < a < 2.10000000000000005e106

   1. Initial program 95.6%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

      1. *-commutative 97.1%

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

      2. clear-num 97.1%

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

      3. un-div-inv 97.7%

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

   5. Applied egg-rr 97.7%

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

   6. Taylor expanded in x around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. associate-*l/ 78.1%

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

      3. distribute-rgt-out-- 68.8%

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

      4. sub-neg 68.8%

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

      5. +-commutative 68.8%

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

      6. distribute-neg-in 68.8%

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

      7. remove-double-neg 68.8%

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

      8. sub-neg 68.8%

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

      9. distribute-rgt-out-- 78.1%

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

   8. Simplified 78.1%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+171}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{+131} \lor \neg \left(a \leq -6.4 \cdot 10^{+63}\right) \land a \leq 2.1 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -10500000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+130} \lor \neg \left(z \leq 1.08 \cdot 10^{+176}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a z)))))
   (if (<= z -10500000000000.0)
     t_1
     (if (<= z 1.5e-29)
       (+ x (* t (/ y a)))
       (if (or (<= z 1.65e+130) (not (<= z 1.08e+176)))
         t_1
         (* (/ y a) (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / z));
	double tmp;
	if (z <= -10500000000000.0) {
		tmp = t_1;
	} else if (z <= 1.5e-29) {
		tmp = x + (t * (y / a));
	} else if ((z <= 1.65e+130) || !(z <= 1.08e+176)) {
		tmp = t_1;
	} else {
		tmp = (y / a) * (t - 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (a / z))
    if (z <= (-10500000000000.0d0)) then
        tmp = t_1
    else if (z <= 1.5d-29) then
        tmp = x + (t * (y / a))
    else if ((z <= 1.65d+130) .or. (.not. (z <= 1.08d+176))) then
        tmp = t_1
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / z));
	double tmp;
	if (z <= -10500000000000.0) {
		tmp = t_1;
	} else if (z <= 1.5e-29) {
		tmp = x + (t * (y / a));
	} else if ((z <= 1.65e+130) || !(z <= 1.08e+176)) {
		tmp = t_1;
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / z))
	tmp = 0
	if z <= -10500000000000.0:
		tmp = t_1
	elif z <= 1.5e-29:
		tmp = x + (t * (y / a))
	elif (z <= 1.65e+130) or not (z <= 1.08e+176):
		tmp = t_1
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (z <= -10500000000000.0)
		tmp = t_1;
	elseif (z <= 1.5e-29)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif ((z <= 1.65e+130) || !(z <= 1.08e+176))
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / z));
	tmp = 0.0;
	if (z <= -10500000000000.0)
		tmp = t_1;
	elseif (z <= 1.5e-29)
		tmp = x + (t * (y / a));
	elseif ((z <= 1.65e+130) || ~((z <= 1.08e+176)))
		tmp = t_1;
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -10500000000000.0], t$95$1, If[LessEqual[z, 1.5e-29], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.65e+130], N[Not[LessEqual[z, 1.08e+176]], $MachinePrecision]], t$95$1, N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e13 or 1.5000000000000001e-29 < z < 1.65e130 or 1.08e176 < z

   1. Initial program 91.1%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around inf 84.0%

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

   if -1.05e13 < z < 1.5000000000000001e-29

   1. Initial program 95.5%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 90.9%

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

      1. cancel-sign-sub-inv 90.9%

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

      2. metadata-eval 90.9%

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

      3. *-lft-identity 90.9%

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

      4. +-commutative 90.9%

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

      5. associate-*r/ 91.6%

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

   6. Simplified 91.6%

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

   if 1.65e130 < z < 1.08e176

   1. Initial program 90.6%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in x around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. associate-*l/ 90.4%

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

      3. distribute-rgt-out-- 80.4%

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

      4. sub-neg 80.4%

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

      5. +-commutative 80.4%

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

      6. distribute-neg-in 80.4%

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

      7. remove-double-neg 80.4%

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

      8. sub-neg 80.4%

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

      9. distribute-rgt-out-- 90.4%

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

   8. Simplified 90.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10500000000000:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+130} \lor \neg \left(z \leq 1.08 \cdot 10^{+176}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 5: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;z \leq -31000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ y (/ a z)))))
   (if (<= z -31000000000000.0)
     t_1
     (if (<= z 6.5e-31)
       (+ x (* t (/ y a)))
       (if (<= z 7.8e+72)
         (- x (/ (* z y) a))
         (if (<= z 6.8e+91) (* (/ y a) (- t z)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y / (a / z));
	double tmp;
	if (z <= -31000000000000.0) {
		tmp = t_1;
	} else if (z <= 6.5e-31) {
		tmp = x + (t * (y / a));
	} else if (z <= 7.8e+72) {
		tmp = x - ((z * y) / a);
	} else if (z <= 6.8e+91) {
		tmp = (y / a) * (t - 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 = x - (y / (a / z))
    if (z <= (-31000000000000.0d0)) then
        tmp = t_1
    else if (z <= 6.5d-31) then
        tmp = x + (t * (y / a))
    else if (z <= 7.8d+72) then
        tmp = x - ((z * y) / a)
    else if (z <= 6.8d+91) then
        tmp = (y / a) * (t - 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 = x - (y / (a / z));
	double tmp;
	if (z <= -31000000000000.0) {
		tmp = t_1;
	} else if (z <= 6.5e-31) {
		tmp = x + (t * (y / a));
	} else if (z <= 7.8e+72) {
		tmp = x - ((z * y) / a);
	} else if (z <= 6.8e+91) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (y / (a / z))
	tmp = 0
	if z <= -31000000000000.0:
		tmp = t_1
	elif z <= 6.5e-31:
		tmp = x + (t * (y / a))
	elif z <= 7.8e+72:
		tmp = x - ((z * y) / a)
	elif z <= 6.8e+91:
		tmp = (y / a) * (t - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y / Float64(a / z)))
	tmp = 0.0
	if (z <= -31000000000000.0)
		tmp = t_1;
	elseif (z <= 6.5e-31)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (z <= 7.8e+72)
		tmp = Float64(x - Float64(Float64(z * y) / a));
	elseif (z <= 6.8e+91)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (y / (a / z));
	tmp = 0.0;
	if (z <= -31000000000000.0)
		tmp = t_1;
	elseif (z <= 6.5e-31)
		tmp = x + (t * (y / a));
	elseif (z <= 7.8e+72)
		tmp = x - ((z * y) / a);
	elseif (z <= 6.8e+91)
		tmp = (y / a) * (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -31000000000000.0], t$95$1, If[LessEqual[z, 6.5e-31], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+72], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+91], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.1e13 or 6.8000000000000002e91 < z

   1. Initial program 89.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around inf 82.9%

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

   if -3.1e13 < z < 6.49999999999999967e-31

   1. Initial program 95.5%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 90.9%

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

      1. cancel-sign-sub-inv 90.9%

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

      2. metadata-eval 90.9%

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

      3. *-lft-identity 90.9%

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

      4. +-commutative 90.9%

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

      5. associate-*r/ 91.6%

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

   6. Simplified 91.6%

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

   if 6.49999999999999967e-31 < z < 7.79999999999999984e72

   1. Initial program 99.9%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 89.3%

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

   if 7.79999999999999984e72 < z < 6.8000000000000002e91

   1. Initial program 83.8%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 83.8%

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

      1. mul-1-neg 83.8%

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

      2. associate-*l/ 100.0%

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

      3. distribute-rgt-out-- 83.3%

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

      4. sub-neg 83.3%

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

      5. +-commutative 83.3%

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

      6. distribute-neg-in 83.3%

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

      7. remove-double-neg 83.3%

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

      8. sub-neg 83.3%

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

      9. distribute-rgt-out-- 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31000000000000:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-31}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+91}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{a}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) a))))
   (if (<= y -1.05e+51)
     t_1
     (if (<= y 6.5e-60) x (if (<= y 1.42e+54) t_1 (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (y <= -1.05e+51) {
		tmp = t_1;
	} else if (y <= 6.5e-60) {
		tmp = x;
	} else if (y <= 1.42e+54) {
		tmp = t_1;
	} else {
		tmp = t / (a / y);
	}
	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 = z * (-y / a)
    if (y <= (-1.05d+51)) then
        tmp = t_1
    else if (y <= 6.5d-60) then
        tmp = x
    else if (y <= 1.42d+54) then
        tmp = t_1
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / a);
	double tmp;
	if (y <= -1.05e+51) {
		tmp = t_1;
	} else if (y <= 6.5e-60) {
		tmp = x;
	} else if (y <= 1.42e+54) {
		tmp = t_1;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / a)
	tmp = 0
	if y <= -1.05e+51:
		tmp = t_1
	elif y <= 6.5e-60:
		tmp = x
	elif y <= 1.42e+54:
		tmp = t_1
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / a))
	tmp = 0.0
	if (y <= -1.05e+51)
		tmp = t_1;
	elseif (y <= 6.5e-60)
		tmp = x;
	elseif (y <= 1.42e+54)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / a);
	tmp = 0.0;
	if (y <= -1.05e+51)
		tmp = t_1;
	elseif (y <= 6.5e-60)
		tmp = x;
	elseif (y <= 1.42e+54)
		tmp = t_1;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+51], t$95$1, If[LessEqual[y, 6.5e-60], x, If[LessEqual[y, 1.42e+54], t$95$1, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0500000000000001e51 or 6.49999999999999995e-60 < y < 1.41999999999999995e54

   1. Initial program 93.8%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in z around inf 49.2%

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

      1. mul-1-neg 49.2%

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

      2. associate-*l/ 51.8%

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

      3. *-commutative 51.8%

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

   6. Simplified 51.8%

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

   if -1.0500000000000001e51 < y < 6.49999999999999995e-60

   1. Initial program 98.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 56.5%

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

   if 1.41999999999999995e54 < y

   1. Initial program 80.2%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 55.1%

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

      1. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e+51)
   (* z (/ (- y) a))
   (if (<= y 1.5e-59) x (if (<= y 2.6e+58) (/ (- z) (/ a y)) (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+51) {
		tmp = z * (-y / a);
	} else if (y <= 1.5e-59) {
		tmp = x;
	} else if (y <= 2.6e+58) {
		tmp = -z / (a / y);
	} else {
		tmp = t / (a / y);
	}
	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 <= (-1.05d+51)) then
        tmp = z * (-y / a)
    else if (y <= 1.5d-59) then
        tmp = x
    else if (y <= 2.6d+58) then
        tmp = -z / (a / y)
    else
        tmp = t / (a / y)
    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 <= -1.05e+51) {
		tmp = z * (-y / a);
	} else if (y <= 1.5e-59) {
		tmp = x;
	} else if (y <= 2.6e+58) {
		tmp = -z / (a / y);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+51:
		tmp = z * (-y / a)
	elif y <= 1.5e-59:
		tmp = x
	elif y <= 2.6e+58:
		tmp = -z / (a / y)
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+51)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (y <= 1.5e-59)
		tmp = x;
	elseif (y <= 2.6e+58)
		tmp = Float64(Float64(-z) / Float64(a / y));
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e+51)
		tmp = z * (-y / a);
	elseif (y <= 1.5e-59)
		tmp = x;
	elseif (y <= 2.6e+58)
		tmp = -z / (a / y);
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+51], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-59], x, If[LessEqual[y, 2.6e+58], N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0500000000000001e51

   1. Initial program 91.6%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in z around inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. associate-*l/ 52.1%

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

      3. *-commutative 52.1%

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

   6. Simplified 52.1%

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

   if -1.0500000000000001e51 < y < 1.5e-59

   1. Initial program 98.4%

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

      1. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 56.5%

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

   if 1.5e-59 < y < 2.59999999999999988e58

   1. Initial program 96.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. *-commutative 51.2%

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

      3. associate-/l* 51.4%

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

      4. associate-/r/ 48.4%

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

   6. Simplified 48.4%

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

      1. associate-/r/ 51.4%

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

   8. Applied egg-rr 51.4%

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

   if 2.59999999999999988e58 < y

   1. Initial program 80.2%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 55.1%

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

      1. associate-/l* 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 8: 77.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-77}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.1e-77)
   (+ x (* t (/ y a)))
   (if (<= a 5.8e+52) (/ (* y (- t z)) a) (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.1e-77) {
		tmp = x + (t * (y / a));
	} else if (a <= 5.8e+52) {
		tmp = (y * (t - z)) / 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 (a <= (-5.1d-77)) then
        tmp = x + (t * (y / a))
    else if (a <= 5.8d+52) then
        tmp = (y * (t - z)) / 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 (a <= -5.1e-77) {
		tmp = x + (t * (y / a));
	} else if (a <= 5.8e+52) {
		tmp = (y * (t - z)) / a;
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.1e-77:
		tmp = x + (t * (y / a))
	elif a <= 5.8e+52:
		tmp = (y * (t - z)) / a
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.1e-77)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (a <= 5.8e+52)
		tmp = Float64(Float64(y * Float64(t - z)) / 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 (a <= -5.1e-77)
		tmp = x + (t * (y / a));
	elseif (a <= 5.8e+52)
		tmp = (y * (t - z)) / a;
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.1e-77], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e+52], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.10000000000000032e-77

   1. Initial program 86.9%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 77.0%

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

      1. cancel-sign-sub-inv 77.0%

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

      2. metadata-eval 77.0%

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

      3. *-lft-identity 77.0%

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

      4. +-commutative 77.0%

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

      5. associate-*r/ 84.6%

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

   6. Simplified 84.6%

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

   if -5.10000000000000032e-77 < a < 5.8e52

   1. Initial program 99.2%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. associate-*r/ 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in y around 0 86.5%

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

   if 5.8e52 < a

   1. Initial program 89.2%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 83.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-77}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 77.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.6e-70)
   (- x (/ y (/ (- a) t)))
   (if (<= a 7.5e+54) (/ (* y (- t z)) a) (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.6e-70) {
		tmp = x - (y / (-a / t));
	} else if (a <= 7.5e+54) {
		tmp = (y * (t - z)) / 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 (a <= (-6.6d-70)) then
        tmp = x - (y / (-a / t))
    else if (a <= 7.5d+54) then
        tmp = (y * (t - z)) / 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 (a <= -6.6e-70) {
		tmp = x - (y / (-a / t));
	} else if (a <= 7.5e+54) {
		tmp = (y * (t - z)) / a;
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.6e-70:
		tmp = x - (y / (-a / t))
	elif a <= 7.5e+54:
		tmp = (y * (t - z)) / a
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.6e-70)
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	elseif (a <= 7.5e+54)
		tmp = Float64(Float64(y * Float64(t - z)) / 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 (a <= -6.6e-70)
		tmp = x - (y / (-a / t));
	elseif (a <= 7.5e+54)
		tmp = (y * (t - z)) / a;
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.6e-70], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+54], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.60000000000000033e-70

   1. Initial program 86.9%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 85.7%

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

      1. associate-*r/ 85.7%

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

      2. neg-mul-1 85.7%

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

   6. Simplified 85.7%

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

   if -6.60000000000000033e-70 < a < 7.50000000000000042e54

   1. Initial program 99.2%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. associate-*r/ 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in y around 0 86.5%

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

   if 7.50000000000000042e54 < a

   1. Initial program 89.2%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 83.5%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+54}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+52} \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.12e+52) (not (<= y 1.15))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.12e+52) || !(y <= 1.15)) {
		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 ((y <= (-1.12d+52)) .or. (.not. (y <= 1.15d0))) 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 ((y <= -1.12e+52) || !(y <= 1.15)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.12e+52) or not (y <= 1.15):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.12e+52) || !(y <= 1.15))
		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 ((y <= -1.12e+52) || ~((y <= 1.15)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.12e+52], N[Not[LessEqual[y, 1.15]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.12000000000000002e52 or 1.1499999999999999 < y

   1. Initial program 86.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in t around inf 47.7%

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

      1. associate-*r/ 52.2%

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

   6. Simplified 52.2%

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

   if -1.12000000000000002e52 < y < 1.1499999999999999

   1. Initial program 98.5%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 54.6%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+52} \lor \neg \left(y \leq 1.15\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.5e+51) (* t (/ y a)) (if (<= y 14000.0) x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.5e+51) {
		tmp = t * (y / a);
	} else if (y <= 14000.0) {
		tmp = x;
	} 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 (y <= (-7.5d+51)) then
        tmp = t * (y / a)
    else if (y <= 14000.0d0) then
        tmp = x
    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 (y <= -7.5e+51) {
		tmp = t * (y / a);
	} else if (y <= 14000.0) {
		tmp = x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.5e+51:
		tmp = t * (y / a)
	elif y <= 14000.0:
		tmp = x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.5e+51)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= 14000.0)
		tmp = x;
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.5e+51)
		tmp = t * (y / a);
	elseif (y <= 14000.0)
		tmp = x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.5e+51], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 14000.0], x, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999999e51

   1. Initial program 91.5%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in t around inf 45.9%

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

      1. associate-*r/ 48.0%

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

   6. Simplified 48.0%

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

   if -7.4999999999999999e51 < y < 14000

   1. Initial program 98.5%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 54.6%

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

   if 14000 < y

   1. Initial program 84.2%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 48.7%

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

      1. associate-/l* 54.7%

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

      2. associate-/r/ 55.0%

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

   6. Applied egg-rr 55.0%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

Alternative 12: 96.9% accurate, 1.0× speedup

Math

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

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(Float64(y / 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[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 13: 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 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Taylor expanded in x around inf 36.4%

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

5. Final simplification 36.4%

   \[\leadsto x \]

Developer target: 99.2% 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 2023297 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))