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

Percentage Accurate: 99.4% → 99.4%

Time: 31.5s

Alternatives: 11

Speedup: 1.0×

• 22.3% of points produce a very large (infinite) output. You may want to add a precondition.

• could not determine a ground truth

  1. x = 4.4615969743612705e-208
  2. y = 9.639480171657537e+39
  3. z = 1.3895418240950962e-170
  4. t = 5.693610098935886e-286
  5. a = 1.5675405107948216e+153

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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% 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]

Derivation

1. Initial program 99.2%

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

2. Final simplification 99.2%

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

Alternative 2: 88.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+120} \lor \neg \left(t_1 \leq 4 \cdot 10^{+91}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -5e+120) (not (<= t_1 4e+91))) 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 ((t_1 <= -5e+120) || !(t_1 <= 4e+91)) {
		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 ((t_1 <= (-5d+120)) .or. (.not. (t_1 <= 4d+91))) 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 ((t_1 <= -5e+120) || !(t_1 <= 4e+91)) {
		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 (t_1 <= -5e+120) or not (t_1 <= 4e+91):
		tmp = t_1
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -5e+120) || !(t_1 <= 4e+91))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z * Float64(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 ((t_1 <= -5e+120) || ~((t_1 <= 4e+91)))
		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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+120], N[Not[LessEqual[t$95$1, 4e+91]], $MachinePrecision]], t$95$1, N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -5.00000000000000019e120 or 4.00000000000000032e91 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 93.8%

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

   if -5.00000000000000019e120 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.00000000000000032e91

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 85.3%

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

      1. associate-*l/ 85.8%

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

      2. *-commutative 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+120} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 3: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-t\right)\\ t_2 := \frac{y \cdot z}{a}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t))) (t_2 (/ (* y z) a)))
   (if (<= z -3.6e-12)
     t_2
     (if (<= z 6.2e-282)
       t_1
       (if (<= z 1.05e-254) x (if (<= z 6e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -t;
	double t_2 = (y * z) / a;
	double tmp;
	if (z <= -3.6e-12) {
		tmp = t_2;
	} else if (z <= 6.2e-282) {
		tmp = t_1;
	} else if (z <= 1.05e-254) {
		tmp = x;
	} else if (z <= 6e-16) {
		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 / a) * -t
    t_2 = (y * z) / a
    if (z <= (-3.6d-12)) then
        tmp = t_2
    else if (z <= 6.2d-282) then
        tmp = t_1
    else if (z <= 1.05d-254) then
        tmp = x
    else if (z <= 6d-16) 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 / a) * -t;
	double t_2 = (y * z) / a;
	double tmp;
	if (z <= -3.6e-12) {
		tmp = t_2;
	} else if (z <= 6.2e-282) {
		tmp = t_1;
	} else if (z <= 1.05e-254) {
		tmp = x;
	} else if (z <= 6e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -t
	t_2 = (y * z) / a
	tmp = 0
	if z <= -3.6e-12:
		tmp = t_2
	elif z <= 6.2e-282:
		tmp = t_1
	elif z <= 1.05e-254:
		tmp = x
	elif z <= 6e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-t))
	t_2 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (z <= -3.6e-12)
		tmp = t_2;
	elseif (z <= 6.2e-282)
		tmp = t_1;
	elseif (z <= 1.05e-254)
		tmp = x;
	elseif (z <= 6e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -t;
	t_2 = (y * z) / a;
	tmp = 0.0;
	if (z <= -3.6e-12)
		tmp = t_2;
	elseif (z <= 6.2e-282)
		tmp = t_1;
	elseif (z <= 1.05e-254)
		tmp = x;
	elseif (z <= 6e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -3.6e-12], t$95$2, If[LessEqual[z, 6.2e-282], t$95$1, If[LessEqual[z, 1.05e-254], x, If[LessEqual[z, 6e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e-12 or 5.99999999999999987e-16 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 67.1%

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

   3. Taylor expanded in z around inf 63.0%

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

      1. associate-*l/ 71.7%

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

   5. Applied egg-rr 71.7%

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

   if -3.6e-12 < z < 6.20000000000000027e-282 or 1.04999999999999998e-254 < z < 5.99999999999999987e-16

   1. Initial program 98.5%

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

   2. Taylor expanded in y around inf 68.1%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. neg-mul-1 68.1%

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

      2. +-commutative 68.1%

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

      3. sub-neg 68.1%

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

      4. div-sub 68.1%

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

   5. Simplified 68.1%

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

      1. associate-/r/ 71.8%

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

   7. Applied egg-rr 71.8%

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

   8. Taylor expanded in z around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-*l/ 63.9%

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

      3. distribute-rgt-neg-in 63.9%

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

   10. Simplified 63.9%

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

   if 6.20000000000000027e-282 < z < 1.04999999999999998e-254

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 83.4%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-282}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-254}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \]

Alternative 4: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{a}\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-283}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y z) a)))
   (if (<= z -2.8e-12)
     t_1
     (if (<= z 2.05e-283)
       (* (/ y a) (- t))
       (if (<= z 2.55e-256) x (if (<= z 2.25e-17) (/ (* y t) (- a)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double tmp;
	if (z <= -2.8e-12) {
		tmp = t_1;
	} else if (z <= 2.05e-283) {
		tmp = (y / a) * -t;
	} else if (z <= 2.55e-256) {
		tmp = x;
	} else if (z <= 2.25e-17) {
		tmp = (y * t) / -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * z) / a
    if (z <= (-2.8d-12)) then
        tmp = t_1
    else if (z <= 2.05d-283) then
        tmp = (y / a) * -t
    else if (z <= 2.55d-256) then
        tmp = x
    else if (z <= 2.25d-17) then
        tmp = (y * t) / -a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * z) / a;
	double tmp;
	if (z <= -2.8e-12) {
		tmp = t_1;
	} else if (z <= 2.05e-283) {
		tmp = (y / a) * -t;
	} else if (z <= 2.55e-256) {
		tmp = x;
	} else if (z <= 2.25e-17) {
		tmp = (y * t) / -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * z) / a
	tmp = 0
	if z <= -2.8e-12:
		tmp = t_1
	elif z <= 2.05e-283:
		tmp = (y / a) * -t
	elif z <= 2.55e-256:
		tmp = x
	elif z <= 2.25e-17:
		tmp = (y * t) / -a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (z <= -2.8e-12)
		tmp = t_1;
	elseif (z <= 2.05e-283)
		tmp = Float64(Float64(y / a) * Float64(-t));
	elseif (z <= 2.55e-256)
		tmp = x;
	elseif (z <= 2.25e-17)
		tmp = Float64(Float64(y * t) / Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * z) / a;
	tmp = 0.0;
	if (z <= -2.8e-12)
		tmp = t_1;
	elseif (z <= 2.05e-283)
		tmp = (y / a) * -t;
	elseif (z <= 2.55e-256)
		tmp = x;
	elseif (z <= 2.25e-17)
		tmp = (y * t) / -a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -2.8e-12], t$95$1, If[LessEqual[z, 2.05e-283], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[z, 2.55e-256], x, If[LessEqual[z, 2.25e-17], N[(N[(y * t), $MachinePrecision] / (-a)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8000000000000002e-12 or 2.24999999999999989e-17 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 67.1%

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

   3. Taylor expanded in z around inf 63.0%

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

      1. associate-*l/ 71.7%

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

   5. Applied egg-rr 71.7%

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

   if -2.8000000000000002e-12 < z < 2.04999999999999993e-283

   1. Initial program 98.4%

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

   2. Taylor expanded in y around inf 61.9%

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

   3. Taylor expanded in z around 0 61.9%

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

      1. neg-mul-1 61.9%

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

      2. +-commutative 61.9%

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

      3. sub-neg 61.9%

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

      4. div-sub 61.9%

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

   5. Simplified 61.9%

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

      1. associate-/r/ 66.6%

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

   7. Applied egg-rr 66.6%

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

   8. Taylor expanded in z around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-*l/ 59.1%

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

      3. distribute-rgt-neg-in 59.1%

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

   10. Simplified 59.1%

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

   if 2.04999999999999993e-283 < z < 2.55000000000000005e-256

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 83.4%

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

   if 2.55000000000000005e-256 < z < 2.24999999999999989e-17

   1. Initial program 98.6%

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

   2. Taylor expanded in y around inf 75.1%

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

   3. Taylor expanded in z around 0 65.8%

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

      1. neg-mul-1 65.8%

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

      2. distribute-neg-frac 65.8%

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

   5. Simplified 65.8%

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

      1. frac-2neg 65.8%

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

      2. remove-double-neg 65.8%

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

      3. associate-*l/ 69.7%

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

   7. Applied egg-rr 69.7%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-12}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-283}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-256}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \]

Alternative 5: 73.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-141} \lor \neg \left(y \leq 10^{-118}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.2e-141) (not (<= y 1e-118))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.2e-141) || !(y <= 1e-118)) {
		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 <= (-7.2d-141)) .or. (.not. (y <= 1d-118))) 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 <= -7.2e-141) || !(y <= 1e-118)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.2e-141) or not (y <= 1e-118):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7.2e-141) || !(y <= 1e-118))
		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 <= -7.2e-141) || ~((y <= 1e-118)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7.2e-141], N[Not[LessEqual[y, 1e-118]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.2000000000000003e-141 or 9.99999999999999985e-119 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 86.8%

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

   3. Taylor expanded in z around 0 86.8%

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

      1. neg-mul-1 86.8%

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

      2. +-commutative 86.8%

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

      3. sub-neg 86.8%

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

      4. div-sub 89.1%

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

   5. Simplified 89.1%

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

   if -7.2000000000000003e-141 < y < 9.99999999999999985e-119

   1. Initial program 97.7%

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

   2. Taylor expanded in x around inf 49.0%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-141} \lor \neg \left(y \leq 10^{-118}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 81.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-140} \lor \neg \left(y \leq 7.8 \cdot 10^{-117}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.5e-140) (not (<= y 7.8e-117)))
   (* 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 <= -5.5e-140) || !(y <= 7.8e-117)) {
		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 <= (-5.5d-140)) .or. (.not. (y <= 7.8d-117))) 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 <= -5.5e-140) || !(y <= 7.8e-117)) {
		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 <= -5.5e-140) or not (y <= 7.8e-117):
		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 <= -5.5e-140) || !(y <= 7.8e-117))
		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 <= -5.5e-140) || ~((y <= 7.8e-117)))
		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, -5.5e-140], N[Not[LessEqual[y, 7.8e-117]], $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 < -5.50000000000000026e-140 or 7.79999999999999984e-117 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 86.8%

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

   3. Taylor expanded in z around 0 86.8%

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

      1. neg-mul-1 86.8%

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

      2. +-commutative 86.8%

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

      3. sub-neg 86.8%

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

      4. div-sub 89.1%

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

   5. Simplified 89.1%

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

   if -5.50000000000000026e-140 < y < 7.79999999999999984e-117

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 77.5%

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

      1. associate-*l/ 78.0%

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

      2. *-commutative 78.0%

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

   4. Simplified 78.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-140} \lor \neg \left(y \leq 7.8 \cdot 10^{-117}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-5} \lor \neg \left(t \leq 1.62 \cdot 10^{+74}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.7e-5) (not (<= t 1.62e+74)))
   (- x (* t (/ y a)))
   (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.7e-5) || !(t <= 1.62e+74)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.7d-5)) .or. (.not. (t <= 1.62d+74))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.7e-5) || !(t <= 1.62e+74)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.7e-5) or not (t <= 1.62e+74):
		tmp = x - (t * (y / a))
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.7e-5) || !(t <= 1.62e+74))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.7e-5) || ~((t <= 1.62e+74)))
		tmp = x - (t * (y / a));
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.7e-5], N[Not[LessEqual[t, 1.62e+74]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.69999999999999972e-5 or 1.62e74 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.1%

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

      1. +-commutative 87.1%

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

      2. mul-1-neg 87.1%

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

      3. unsub-neg 87.1%

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

      4. *-commutative 87.1%

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

      5. associate-*r/ 87.2%

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

   4. Simplified 87.2%

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

   if -4.69999999999999972e-5 < t < 1.62e74

   1. Initial program 98.6%

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

   2. Taylor expanded in t around 0 87.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{-5} \lor \neg \left(t \leq 1.62 \cdot 10^{+74}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

Alternative 8: 46.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-134} \lor \neg \left(y \leq 4.5 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.9e-134) (not (<= y 4.5e-47))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.9e-134) || !(y <= 4.5e-47)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.9d-134)) .or. (.not. (y <= 4.5d-47))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.9e-134) || !(y <= 4.5e-47)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.9e-134) or not (y <= 4.5e-47):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.9e-134) || !(y <= 4.5e-47))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.9e-134) || ~((y <= 4.5e-47)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.9e-134], N[Not[LessEqual[y, 4.5e-47]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000001e-134 or 4.5e-47 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 87.2%

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

   3. Taylor expanded in z around inf 52.6%

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

   if -1.90000000000000001e-134 < y < 4.5e-47

   1. Initial program 97.9%

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

   2. Taylor expanded in x around inf 45.5%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-134} \lor \neg \left(y \leq 4.5 \cdot 10^{-47}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-12} \lor \neg \left(z \leq 8.6 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e-12) (not (<= z 8.6e-81))) (/ (* y z) a) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e-12) || !(z <= 8.6e-81)) {
		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 ((z <= (-4.2d-12)) .or. (.not. (z <= 8.6d-81))) 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 ((z <= -4.2e-12) || !(z <= 8.6e-81)) {
		tmp = (y * z) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e-12) or not (z <= 8.6e-81):
		tmp = (y * z) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e-12) || !(z <= 8.6e-81))
		tmp = Float64(Float64(y * z) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e-12) || ~((z <= 8.6e-81)))
		tmp = (y * z) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e-12], N[Not[LessEqual[z, 8.6e-81]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999988e-12 or 8.6000000000000006e-81 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 68.5%

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

   3. Taylor expanded in z around inf 60.9%

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

      1. associate-*l/ 68.9%

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

   5. Applied egg-rr 68.9%

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

   if -4.19999999999999988e-12 < z < 8.6000000000000006e-81

   1. Initial program 98.4%

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

   2. Taylor expanded in x around inf 33.4%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-12} \lor \neg \left(z \leq 8.6 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 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 99.2%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 11: 23.1% 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 99.2%

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

2. Taylor expanded in x around inf 23.4%

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

3. Final simplification 23.4%

   \[\leadsto x \]

Developer target: 99.3% 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 2023278 
(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)))