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

Percentage Accurate: 93.8% → 97.3%

Time: 10.7s

Alternatives: 12

Speedup: 1.0×

• 25.0% 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: 93.8% 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: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.1%

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

   1. associate-*l/ 97.2%

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

3. Simplified 97.2%

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

   1. *-commutative 97.2%

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

   2. clear-num 97.1%

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

   3. un-div-inv 97.8%

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

5. Applied egg-rr 97.8%

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

6. Final simplification 97.8%

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

Alternative 2: 50.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ t_2 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+86} \lor \neg \left(y \leq 2.7 \cdot 10^{+169}\right) \land y \leq 1.9 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))) (t_2 (* t (/ (- y) a))))
   (if (<= y -1.65e+156)
     t_2
     (if (<= y -5.2e-56)
       t_1
       (if (<= y 2.7e+15)
         x
         (if (or (<= y 1.4e+86) (and (not (<= y 2.7e+169)) (<= y 1.9e+210)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double t_2 = t * (-y / a);
	double tmp;
	if (y <= -1.65e+156) {
		tmp = t_2;
	} else if (y <= -5.2e-56) {
		tmp = t_1;
	} else if (y <= 2.7e+15) {
		tmp = x;
	} else if ((y <= 1.4e+86) || (!(y <= 2.7e+169) && (y <= 1.9e+210))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = y * (z / a)
    t_2 = t * (-y / a)
    if (y <= (-1.65d+156)) then
        tmp = t_2
    else if (y <= (-5.2d-56)) then
        tmp = t_1
    else if (y <= 2.7d+15) then
        tmp = x
    else if ((y <= 1.4d+86) .or. (.not. (y <= 2.7d+169)) .and. (y <= 1.9d+210)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double t_2 = t * (-y / a);
	double tmp;
	if (y <= -1.65e+156) {
		tmp = t_2;
	} else if (y <= -5.2e-56) {
		tmp = t_1;
	} else if (y <= 2.7e+15) {
		tmp = x;
	} else if ((y <= 1.4e+86) || (!(y <= 2.7e+169) && (y <= 1.9e+210))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	t_2 = t * (-y / a)
	tmp = 0
	if y <= -1.65e+156:
		tmp = t_2
	elif y <= -5.2e-56:
		tmp = t_1
	elif y <= 2.7e+15:
		tmp = x
	elif (y <= 1.4e+86) or (not (y <= 2.7e+169) and (y <= 1.9e+210)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	t_2 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (y <= -1.65e+156)
		tmp = t_2;
	elseif (y <= -5.2e-56)
		tmp = t_1;
	elseif (y <= 2.7e+15)
		tmp = x;
	elseif ((y <= 1.4e+86) || (!(y <= 2.7e+169) && (y <= 1.9e+210)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	t_2 = t * (-y / a);
	tmp = 0.0;
	if (y <= -1.65e+156)
		tmp = t_2;
	elseif (y <= -5.2e-56)
		tmp = t_1;
	elseif (y <= 2.7e+15)
		tmp = x;
	elseif ((y <= 1.4e+86) || (~((y <= 2.7e+169)) && (y <= 1.9e+210)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e+156], t$95$2, If[LessEqual[y, -5.2e-56], t$95$1, If[LessEqual[y, 2.7e+15], x, If[Or[LessEqual[y, 1.4e+86], And[N[Not[LessEqual[y, 2.7e+169]], $MachinePrecision], LessEqual[y, 1.9e+210]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e156 or 1.40000000000000002e86 < y < 2.69999999999999991e169 or 1.90000000000000014e210 < y

   1. Initial program 77.4%

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

      1. +-commutative 77.4%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. *-un-lft-identity 68.9%

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

      3. times-frac 87.5%

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

      4. /-rgt-identity 87.5%

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

   8. Applied egg-rr 87.5%

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

   9. Taylor expanded in z around 0 52.8%

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

       1. mul-1-neg 52.8%

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

       2. associate-*l/ 66.7%

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

       3. distribute-rgt-neg-in 66.7%

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

   11. Simplified 66.7%

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

   if -1.6499999999999999e156 < y < -5.19999999999999994e-56 or 2.7e15 < y < 1.40000000000000002e86 or 2.69999999999999991e169 < y < 1.90000000000000014e210

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-*r/ 98.7%

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

      3. fma-def 98.7%

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

   3. Simplified 98.7%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in a around 0 75.2%

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

      1. associate-/l* 77.3%

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

      2. *-un-lft-identity 77.3%

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

      3. div-inv 77.3%

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

      4. frac-times 75.1%

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

      5. associate-*r/ 78.5%

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

      6. div-inv 78.5%

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

      7. remove-double-div 78.5%

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

   8. Applied egg-rr 78.5%

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

   9. Taylor expanded in z around inf 57.4%

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

   if -5.19999999999999994e-56 < y < 2.7e15

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 62.7%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+86} \lor \neg \left(y \leq 2.7 \cdot 10^{+169}\right) \land y \leq 1.9 \cdot 10^{+210}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \end{array} \]

Alternative 3: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ t_2 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))) (t_2 (* t (/ (- y) a))))
   (if (<= y -1.7e+156)
     t_2
     (if (<= y -1.5e-56)
       t_1
       (if (<= y 1.45e+15)
         x
         (if (<= y 1.3e+85)
           t_1
           (if (<= y 2.9e+169)
             t_2
             (if (<= y 2.8e+209) t_1 (* y (/ (- t) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double t_2 = t * (-y / a);
	double tmp;
	if (y <= -1.7e+156) {
		tmp = t_2;
	} else if (y <= -1.5e-56) {
		tmp = t_1;
	} else if (y <= 1.45e+15) {
		tmp = x;
	} else if (y <= 1.3e+85) {
		tmp = t_1;
	} else if (y <= 2.9e+169) {
		tmp = t_2;
	} else if (y <= 2.8e+209) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (z / a)
    t_2 = t * (-y / a)
    if (y <= (-1.7d+156)) then
        tmp = t_2
    else if (y <= (-1.5d-56)) then
        tmp = t_1
    else if (y <= 1.45d+15) then
        tmp = x
    else if (y <= 1.3d+85) then
        tmp = t_1
    else if (y <= 2.9d+169) then
        tmp = t_2
    else if (y <= 2.8d+209) then
        tmp = t_1
    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 t_1 = y * (z / a);
	double t_2 = t * (-y / a);
	double tmp;
	if (y <= -1.7e+156) {
		tmp = t_2;
	} else if (y <= -1.5e-56) {
		tmp = t_1;
	} else if (y <= 1.45e+15) {
		tmp = x;
	} else if (y <= 1.3e+85) {
		tmp = t_1;
	} else if (y <= 2.9e+169) {
		tmp = t_2;
	} else if (y <= 2.8e+209) {
		tmp = t_1;
	} else {
		tmp = y * (-t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	t_2 = t * (-y / a)
	tmp = 0
	if y <= -1.7e+156:
		tmp = t_2
	elif y <= -1.5e-56:
		tmp = t_1
	elif y <= 1.45e+15:
		tmp = x
	elif y <= 1.3e+85:
		tmp = t_1
	elif y <= 2.9e+169:
		tmp = t_2
	elif y <= 2.8e+209:
		tmp = t_1
	else:
		tmp = y * (-t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	t_2 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (y <= -1.7e+156)
		tmp = t_2;
	elseif (y <= -1.5e-56)
		tmp = t_1;
	elseif (y <= 1.45e+15)
		tmp = x;
	elseif (y <= 1.3e+85)
		tmp = t_1;
	elseif (y <= 2.9e+169)
		tmp = t_2;
	elseif (y <= 2.8e+209)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	t_2 = t * (-y / a);
	tmp = 0.0;
	if (y <= -1.7e+156)
		tmp = t_2;
	elseif (y <= -1.5e-56)
		tmp = t_1;
	elseif (y <= 1.45e+15)
		tmp = x;
	elseif (y <= 1.3e+85)
		tmp = t_1;
	elseif (y <= 2.9e+169)
		tmp = t_2;
	elseif (y <= 2.8e+209)
		tmp = t_1;
	else
		tmp = y * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+156], t$95$2, If[LessEqual[y, -1.5e-56], t$95$1, If[LessEqual[y, 1.45e+15], x, If[LessEqual[y, 1.3e+85], t$95$1, If[LessEqual[y, 2.9e+169], t$95$2, If[LessEqual[y, 2.8e+209], t$95$1, N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7e156 or 1.30000000000000005e85 < y < 2.9000000000000001e169

   1. Initial program 74.8%

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

      1. +-commutative 74.8%

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

      2. associate-*r/ 99.8%

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

      3. fma-def 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 67.8%

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

      1. *-commutative 67.8%

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

      2. *-un-lft-identity 67.8%

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

      3. times-frac 89.3%

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

      4. /-rgt-identity 89.3%

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

   8. Applied egg-rr 89.3%

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

   9. Taylor expanded in z around 0 52.2%

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

       1. mul-1-neg 52.2%

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

       2. associate-*l/ 68.6%

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

       3. distribute-rgt-neg-in 68.6%

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

   11. Simplified 68.6%

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

   if -1.7e156 < y < -1.49999999999999995e-56 or 1.45e15 < y < 1.30000000000000005e85 or 2.9000000000000001e169 < y < 2.80000000000000013e209

   1. Initial program 93.5%

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

      1. +-commutative 93.5%

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

      2. associate-*r/ 98.7%

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

      3. fma-def 98.7%

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

   3. Simplified 98.7%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in a around 0 75.2%

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

      1. associate-/l* 77.3%

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

      2. *-un-lft-identity 77.3%

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

      3. div-inv 77.3%

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

      4. frac-times 75.1%

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

      5. associate-*r/ 78.5%

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

      6. div-inv 78.5%

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

      7. remove-double-div 78.5%

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

   8. Applied egg-rr 78.5%

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

   9. Taylor expanded in z around inf 57.4%

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

   if -1.49999999999999995e-56 < y < 1.45e15

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 62.7%

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

   if 2.80000000000000013e209 < y

   1. Initial program 83.7%

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

      1. +-commutative 83.7%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in a around 0 71.4%

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

      1. associate-/l* 82.4%

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

      2. *-un-lft-identity 82.4%

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

      3. div-inv 82.4%

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

      4. frac-times 71.4%

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

      5. associate-*r/ 83.2%

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

      6. div-inv 83.2%

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

      7. remove-double-div 83.2%

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

   8. Applied egg-rr 83.2%

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

   9. Taylor expanded in z around 0 65.9%

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

       1. mul-1-neg 65.9%

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

       2. distribute-neg-frac 65.9%

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

   11. Simplified 65.9%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+169}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \]

Alternative 4: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+124} \lor \neg \left(y \leq -9.3 \cdot 10^{+95}\right) \land \left(y \leq -1.55 \cdot 10^{-73} \lor \neg \left(y \leq 3.4 \cdot 10^{+15}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.8e+124)
         (and (not (<= y -9.3e+95))
              (or (<= y -1.55e-73) (not (<= y 3.4e+15)))))
   (* y (/ (- z t) a))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.8e+124) || (!(y <= -9.3e+95) && ((y <= -1.55e-73) || !(y <= 3.4e+15)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.8d+124)) .or. (.not. (y <= (-9.3d+95))) .and. (y <= (-1.55d-73)) .or. (.not. (y <= 3.4d+15))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.8e+124) || (!(y <= -9.3e+95) && ((y <= -1.55e-73) || !(y <= 3.4e+15)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.8e+124) or (not (y <= -9.3e+95) and ((y <= -1.55e-73) or not (y <= 3.4e+15))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.8e+124) || (!(y <= -9.3e+95) && ((y <= -1.55e-73) || !(y <= 3.4e+15))))
		tmp = Float64(y * Float64(Float64(z - t) / 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 ((y <= -2.8e+124) || (~((y <= -9.3e+95)) && ((y <= -1.55e-73) || ~((y <= 3.4e+15)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.8e+124], And[N[Not[LessEqual[y, -9.3e+95]], $MachinePrecision], Or[LessEqual[y, -1.55e-73], N[Not[LessEqual[y, 3.4e+15]], $MachinePrecision]]]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e124 or -9.29999999999999967e95 < y < -1.54999999999999985e-73 or 3.4e15 < y

   1. Initial program 85.3%

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

      1. +-commutative 85.3%

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

      2. associate-*r/ 99.3%

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

      3. fma-def 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.2%

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

      2. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in a around 0 74.2%

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

      1. *-commutative 74.2%

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

      2. *-un-lft-identity 74.2%

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

      3. times-frac 85.9%

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

      4. /-rgt-identity 85.9%

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

   8. Applied egg-rr 85.9%

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

   if -2.8e124 < y < -9.29999999999999967e95 or -1.54999999999999985e-73 < y < 3.4e15

   1. Initial program 99.1%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   4. Taylor expanded in z around inf 79.3%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+124} \lor \neg \left(y \leq -9.3 \cdot 10^{+95}\right) \land \left(y \leq -1.55 \cdot 10^{-73} \lor \neg \left(y \leq 3.4 \cdot 10^{+15}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 5: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+162} \lor \neg \left(y \leq -2.1 \cdot 10^{+96}\right) \land \left(y \leq -2.1 \cdot 10^{-74} \lor \neg \left(y \leq 7.5 \cdot 10^{+14}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9e+162)
         (and (not (<= y -2.1e+96)) (or (<= y -2.1e-74) (not (<= y 7.5e+14)))))
   (* y (/ (- z t) a))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9e+162) || (!(y <= -2.1e+96) && ((y <= -2.1e-74) || !(y <= 7.5e+14)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z * (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 ((y <= (-9d+162)) .or. (.not. (y <= (-2.1d+96))) .and. (y <= (-2.1d-74)) .or. (.not. (y <= 7.5d+14))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + (z * (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 ((y <= -9e+162) || (!(y <= -2.1e+96) && ((y <= -2.1e-74) || !(y <= 7.5e+14)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9e+162) or (not (y <= -2.1e+96) and ((y <= -2.1e-74) or not (y <= 7.5e+14))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9e+162) || (!(y <= -2.1e+96) && ((y <= -2.1e-74) || !(y <= 7.5e+14))))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -9e+162) || (~((y <= -2.1e+96)) && ((y <= -2.1e-74) || ~((y <= 7.5e+14)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9e+162], And[N[Not[LessEqual[y, -2.1e+96]], $MachinePrecision], Or[LessEqual[y, -2.1e-74], N[Not[LessEqual[y, 7.5e+14]], $MachinePrecision]]]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999944e162 or -2.1000000000000001e96 < y < -2.1e-74 or 7.5e14 < y

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-*r/ 99.2%

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

      3. fma-def 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in a around 0 73.1%

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

      1. *-commutative 73.1%

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

      2. *-un-lft-identity 73.1%

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

      3. times-frac 85.6%

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

      4. /-rgt-identity 85.6%

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

   8. Applied egg-rr 85.6%

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

   if -8.99999999999999944e162 < y < -2.1000000000000001e96 or -2.1e-74 < y < 7.5e14

   1. Initial program 98.3%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around 0 81.0%

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

      1. associate-*l/ 82.6%

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

      2. *-commutative 82.6%

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

   6. Simplified 82.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+162} \lor \neg \left(y \leq -2.1 \cdot 10^{+96}\right) \land \left(y \leq -2.1 \cdot 10^{-74} \lor \neg \left(y \leq 7.5 \cdot 10^{+14}\right)\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 76.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+162} \lor \neg \left(y \leq -6 \cdot 10^{+98} \lor \neg \left(y \leq -3.2 \cdot 10^{-77}\right) \land y \leq 1.35 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.6e+162)
         (not (or (<= y -6e+98) (and (not (<= y -3.2e-77)) (<= y 1.35e+15)))))
   (* y (/ (- z t) a))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.6e+162) || !((y <= -6e+98) || (!(y <= -3.2e-77) && (y <= 1.35e+15)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z / (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 <= (-6.6d+162)) .or. (.not. (y <= (-6d+98)) .or. (.not. (y <= (-3.2d-77))) .and. (y <= 1.35d+15))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + (z / (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 <= -6.6e+162) || !((y <= -6e+98) || (!(y <= -3.2e-77) && (y <= 1.35e+15)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.6e+162) or not ((y <= -6e+98) or (not (y <= -3.2e-77) and (y <= 1.35e+15))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.6e+162) || !((y <= -6e+98) || (!(y <= -3.2e-77) && (y <= 1.35e+15))))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.6e+162) || ~(((y <= -6e+98) || (~((y <= -3.2e-77)) && (y <= 1.35e+15)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.6e+162], N[Not[Or[LessEqual[y, -6e+98], And[N[Not[LessEqual[y, -3.2e-77]], $MachinePrecision], LessEqual[y, 1.35e+15]]]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.59999999999999975e162 or -6.0000000000000003e98 < y < -3.2e-77 or 1.35e15 < y

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-*r/ 99.2%

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

      3. fma-def 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in a around 0 73.1%

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

      1. *-commutative 73.1%

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

      2. *-un-lft-identity 73.1%

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

      3. times-frac 85.6%

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

      4. /-rgt-identity 85.6%

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

   8. Applied egg-rr 85.6%

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

   if -6.59999999999999975e162 < y < -6.0000000000000003e98 or -3.2e-77 < y < 1.35e15

   1. Initial program 98.3%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around 0 81.0%

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

      1. associate-*l/ 82.6%

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

      2. *-commutative 82.6%

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

   6. Simplified 82.6%

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

      1. clear-num 82.6%

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

      2. un-div-inv 82.6%

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

   8. Applied egg-rr 82.6%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{+162} \lor \neg \left(y \leq -6 \cdot 10^{+98} \lor \neg \left(y \leq -3.2 \cdot 10^{-77}\right) \land y \leq 1.35 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 76.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+92}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-77} \lor \neg \left(y \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) a))))
   (if (<= y -1.7e+163)
     t_1
     (if (<= y -7.6e+92)
       (+ x (/ z (/ a y)))
       (if (or (<= y -2.5e-77) (not (<= y 4.3e+15)))
         t_1
         (+ x (/ (* z y) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double tmp;
	if (y <= -1.7e+163) {
		tmp = t_1;
	} else if (y <= -7.6e+92) {
		tmp = x + (z / (a / y));
	} else if ((y <= -2.5e-77) || !(y <= 4.3e+15)) {
		tmp = t_1;
	} else {
		tmp = x + ((z * 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / a)
    if (y <= (-1.7d+163)) then
        tmp = t_1
    else if (y <= (-7.6d+92)) then
        tmp = x + (z / (a / y))
    else if ((y <= (-2.5d-77)) .or. (.not. (y <= 4.3d+15))) then
        tmp = t_1
    else
        tmp = x + ((z * y) / a)
    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 - t) / a);
	double tmp;
	if (y <= -1.7e+163) {
		tmp = t_1;
	} else if (y <= -7.6e+92) {
		tmp = x + (z / (a / y));
	} else if ((y <= -2.5e-77) || !(y <= 4.3e+15)) {
		tmp = t_1;
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / a)
	tmp = 0
	if y <= -1.7e+163:
		tmp = t_1
	elif y <= -7.6e+92:
		tmp = x + (z / (a / y))
	elif (y <= -2.5e-77) or not (y <= 4.3e+15):
		tmp = t_1
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / a))
	tmp = 0.0
	if (y <= -1.7e+163)
		tmp = t_1;
	elseif (y <= -7.6e+92)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif ((y <= -2.5e-77) || !(y <= 4.3e+15))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / a);
	tmp = 0.0;
	if (y <= -1.7e+163)
		tmp = t_1;
	elseif (y <= -7.6e+92)
		tmp = x + (z / (a / y));
	elseif ((y <= -2.5e-77) || ~((y <= 4.3e+15)))
		tmp = t_1;
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+163], t$95$1, If[LessEqual[y, -7.6e+92], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.5e-77], N[Not[LessEqual[y, 4.3e+15]], $MachinePrecision]], t$95$1, N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7000000000000001e163 or -7.6000000000000001e92 < y < -2.49999999999999982e-77 or 4.3e15 < y

   1. Initial program 85.0%

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

      1. +-commutative 85.0%

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

      2. associate-*r/ 99.2%

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

      3. fma-def 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.1%

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

      2. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in a around 0 73.1%

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

      1. *-commutative 73.1%

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

      2. *-un-lft-identity 73.1%

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

      3. times-frac 85.6%

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

      4. /-rgt-identity 85.6%

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

   8. Applied egg-rr 85.6%

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

   if -1.7000000000000001e163 < y < -7.6000000000000001e92

   1. Initial program 88.0%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 76.6%

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

      1. associate-*l/ 94.1%

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

      2. *-commutative 94.1%

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

   6. Simplified 94.1%

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

      1. clear-num 94.1%

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

      2. un-div-inv 94.3%

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

   8. Applied egg-rr 94.3%

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

   if -2.49999999999999982e-77 < y < 4.3e15

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 81.7%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+163}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+92}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-77} \lor \neg \left(y \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]

Alternative 8: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-152} \lor \neg \left(y \leq 5.5 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.2e-152) (not (<= y 5.5e+14))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.2e-152) || !(y <= 5.5e+14)) {
		tmp = y * ((z - t) / 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 <= (-4.2d-152)) .or. (.not. (y <= 5.5d+14))) then
        tmp = y * ((z - t) / 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 <= -4.2e-152) || !(y <= 5.5e+14)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.2e-152) or not (y <= 5.5e+14):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.2e-152) || !(y <= 5.5e+14))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.2e-152) || ~((y <= 5.5e+14)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.2e-152], N[Not[LessEqual[y, 5.5e+14]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.19999999999999998e-152 or 5.5e14 < y

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. associate-*r/ 98.7%

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

      3. fma-def 98.7%

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

   3. Simplified 98.7%

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

      1. clear-num 98.7%

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

      2. associate-/r/ 98.7%

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

   5. Applied egg-rr 98.7%

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

   6. Taylor expanded in a around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. *-un-lft-identity 70.3%

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

      3. times-frac 80.4%

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

      4. /-rgt-identity 80.4%

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

   8. Applied egg-rr 80.4%

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

   if -4.19999999999999998e-152 < y < 5.5e14

   1. Initial program 99.9%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around inf 66.2%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-152} \lor \neg \left(y \leq 5.5 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 85.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+78} \lor \neg \left(t \leq 3.7 \cdot 10^{-56}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.4e+78) (not (<= t 3.7e-56)))
   (- x (* t (/ y a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.4e+78) || !(t <= 3.7e-56)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (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 ((t <= (-2.4d+78)) .or. (.not. (t <= 3.7d-56))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z / (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 ((t <= -2.4e+78) || !(t <= 3.7e-56)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.4e+78) or not (t <= 3.7e-56):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.4e+78) || !(t <= 3.7e-56))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.4e+78) || ~((t <= 3.7e-56)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.4e+78], N[Not[LessEqual[t, 3.7e-56]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.3999999999999999e78 or 3.7000000000000002e-56 < t

   1. Initial program 88.0%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around 0 81.0%

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

      1. mul-1-neg 81.0%

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

      2. associate-*l/ 88.1%

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

      3. distribute-rgt-neg-out 88.1%

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

      4. +-commutative 88.1%

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

      5. *-commutative 88.1%

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

      6. distribute-lft-neg-out 88.1%

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

      7. unsub-neg 88.1%

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

   6. Simplified 88.1%

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

   if -2.3999999999999999e78 < t < 3.7000000000000002e-56

   1. Initial program 94.1%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in t around 0 82.8%

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

      1. associate-*l/ 87.8%

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

      2. *-commutative 87.8%

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

   6. Simplified 87.8%

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

      1. clear-num 87.8%

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

      2. un-div-inv 88.0%

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

   8. Applied egg-rr 88.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+78} \lor \neg \left(t \leq 3.7 \cdot 10^{-56}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-56} \lor \neg \left(y \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.5e-56) (not (<= y 4.3e+15))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.5e-56) || !(y <= 4.3e+15)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.5d-56)) .or. (.not. (y <= 4.3d+15))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.5e-56) || !(y <= 4.3e+15)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.5e-56) or not (y <= 4.3e+15):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.5e-56) || !(y <= 4.3e+15))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.5e-56) || ~((y <= 4.3e+15)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.5e-56], N[Not[LessEqual[y, 4.3e+15]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999999e-56 or 4.3e15 < y

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. associate-*r/ 99.3%

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

      3. fma-def 99.3%

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

   3. Simplified 99.3%

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

      1. clear-num 99.2%

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

      2. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in a around 0 71.9%

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

      1. associate-/l* 82.5%

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

      2. *-un-lft-identity 82.5%

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

      3. div-inv 82.4%

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

      4. frac-times 71.9%

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

      5. associate-*r/ 83.1%

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

      6. div-inv 83.1%

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

      7. remove-double-div 83.2%

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

   8. Applied egg-rr 83.2%

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

   9. Taylor expanded in z around inf 44.6%

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

   if -5.4999999999999999e-56 < y < 4.3e15

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 62.7%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-56} \lor \neg \left(y \leq 4.3 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.1%

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

   1. associate-*l/ 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 12: 39.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.1%

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

   1. associate-*l/ 97.2%

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

3. Simplified 97.2%

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

4. Taylor expanded in x around inf 36.1%

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

5. Final simplification 36.1%

   \[\leadsto x \]

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 2023185 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

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

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