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

Percentage Accurate: 92.4% → 98.5%

Time: 7.6s

Alternatives: 13

Speedup: 0.6×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+285} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (or (<= t_1 -5e+285) (not (<= t_1 2e+307)))
     (+ x (* y (/ (- z x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -5e+285) || !(t_1 <= 2e+307)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * (z - x)) / t)
    if ((t_1 <= (-5d+285)) .or. (.not. (t_1 <= 2d+307))) then
        tmp = x + (y * ((z - x) / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -5e+285) || !(t_1 <= 2e+307)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if (t_1 <= -5e+285) or not (t_1 <= 2e+307):
		tmp = x + (y * ((z - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if ((t_1 <= -5e+285) || !(t_1 <= 2e+307))
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -5e+285) || ~((t_1 <= 2e+307)))
		tmp = x + (y * ((z - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+285], N[Not[LessEqual[t$95$1, 2e+307]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -5.00000000000000016e285 or 1.99999999999999997e307 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 83.2%

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

      1. +-commutative 83.2%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -5.00000000000000016e285 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 1.99999999999999997e307

   1. Initial program 99.2%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -5 \cdot 10^{+285} \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - x}{t}\\ t_2 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 0.000235:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ (- z x) t))) (t_2 (* x (- 1.0 (/ y t)))))
   (if (<= x -2.6e-52)
     t_2
     (if (<= x -1.6e-199)
       t_1
       (if (<= x 6.5e-198) (/ (* y z) t) (if (<= x 0.000235) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * ((z - x) / t);
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -2.6e-52) {
		tmp = t_2;
	} else if (x <= -1.6e-199) {
		tmp = t_1;
	} else if (x <= 6.5e-198) {
		tmp = (y * z) / t;
	} else if (x <= 0.000235) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - x) / t)
    t_2 = x * (1.0d0 - (y / t))
    if (x <= (-2.6d-52)) then
        tmp = t_2
    else if (x <= (-1.6d-199)) then
        tmp = t_1
    else if (x <= 6.5d-198) then
        tmp = (y * z) / t
    else if (x <= 0.000235d0) 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 t_1 = y * ((z - x) / t);
	double t_2 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -2.6e-52) {
		tmp = t_2;
	} else if (x <= -1.6e-199) {
		tmp = t_1;
	} else if (x <= 6.5e-198) {
		tmp = (y * z) / t;
	} else if (x <= 0.000235) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * ((z - x) / t)
	t_2 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -2.6e-52:
		tmp = t_2
	elif x <= -1.6e-199:
		tmp = t_1
	elif x <= 6.5e-198:
		tmp = (y * z) / t
	elif x <= 0.000235:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(z - x) / t))
	t_2 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -2.6e-52)
		tmp = t_2;
	elseif (x <= -1.6e-199)
		tmp = t_1;
	elseif (x <= 6.5e-198)
		tmp = Float64(Float64(y * z) / t);
	elseif (x <= 0.000235)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * ((z - x) / t);
	t_2 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -2.6e-52)
		tmp = t_2;
	elseif (x <= -1.6e-199)
		tmp = t_1;
	elseif (x <= 6.5e-198)
		tmp = (y * z) / t;
	elseif (x <= 0.000235)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e-52], t$95$2, If[LessEqual[x, -1.6e-199], t$95$1, If[LessEqual[x, 6.5e-198], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[x, 0.000235], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999999e-52 or 2.34999999999999993e-4 < x

   1. Initial program 90.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -2.5999999999999999e-52 < x < -1.6e-199 or 6.5000000000000004e-198 < x < 2.34999999999999993e-4

   1. Initial program 98.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 75.3%

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

      1. associate-/l* 75.5%

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

      2. *-commutative 75.5%

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

   5. Applied egg-rr 75.5%

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

   if -1.6e-199 < x < 6.5000000000000004e-198

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 90.6%

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

   4. Taylor expanded in z around inf 87.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;x \leq 0.000235:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+30} \lor \neg \left(t \leq -125\right) \land t \leq 3.7 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.95e+102)
   x
   (if (or (<= t -6.8e+30) (and (not (<= t -125.0)) (<= t 3.7e+22)))
     (* z (/ y t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e+102) {
		tmp = x;
	} else if ((t <= -6.8e+30) || (!(t <= -125.0) && (t <= 3.7e+22))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.95d+102)) then
        tmp = x
    else if ((t <= (-6.8d+30)) .or. (.not. (t <= (-125.0d0))) .and. (t <= 3.7d+22)) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e+102) {
		tmp = x;
	} else if ((t <= -6.8e+30) || (!(t <= -125.0) && (t <= 3.7e+22))) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.95e+102:
		tmp = x
	elif (t <= -6.8e+30) or (not (t <= -125.0) and (t <= 3.7e+22)):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.95e+102)
		tmp = x;
	elseif ((t <= -6.8e+30) || (!(t <= -125.0) && (t <= 3.7e+22)))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.95e+102)
		tmp = x;
	elseif ((t <= -6.8e+30) || (~((t <= -125.0)) && (t <= 3.7e+22)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.95e+102], x, If[Or[LessEqual[t, -6.8e+30], And[N[Not[LessEqual[t, -125.0]], $MachinePrecision], LessEqual[t, 3.7e+22]]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9499999999999999e102 or -6.8000000000000005e30 < t < -125 or 3.6999999999999998e22 < t

   1. Initial program 86.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 67.0%

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

   if -1.9499999999999999e102 < t < -6.8000000000000005e30 or -125 < t < 3.6999999999999998e22

   1. Initial program 99.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 87.5%

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

   4. Taylor expanded in z around inf 52.4%

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

      1. *-commutative 63.7%

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

      2. associate-*r/ 66.9%

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

   6. Simplified 55.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{+30} \lor \neg \left(t \leq -125\right) \land t \leq 3.7 \cdot 10^{+22}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+29} \lor \neg \left(t \leq -2.25 \cdot 10^{-65}\right) \land t \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.9e+102)
   x
   (if (or (<= t -3.4e+29) (and (not (<= t -2.25e-65)) (<= t 3.5e+17)))
     (* y (/ z t))
     x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.9e+102) {
		tmp = x;
	} else if ((t <= -3.4e+29) || (!(t <= -2.25e-65) && (t <= 3.5e+17))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.9d+102)) then
        tmp = x
    else if ((t <= (-3.4d+29)) .or. (.not. (t <= (-2.25d-65))) .and. (t <= 3.5d+17)) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.9e+102) {
		tmp = x;
	} else if ((t <= -3.4e+29) || (!(t <= -2.25e-65) && (t <= 3.5e+17))) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.9e+102:
		tmp = x
	elif (t <= -3.4e+29) or (not (t <= -2.25e-65) and (t <= 3.5e+17)):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.9e+102)
		tmp = x;
	elseif ((t <= -3.4e+29) || (!(t <= -2.25e-65) && (t <= 3.5e+17)))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.9e+102)
		tmp = x;
	elseif ((t <= -3.4e+29) || (~((t <= -2.25e-65)) && (t <= 3.5e+17)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.9e+102], x, If[Or[LessEqual[t, -3.4e+29], And[N[Not[LessEqual[t, -2.25e-65]], $MachinePrecision], LessEqual[t, 3.5e+17]]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -1.89999999999999989e102 or -3.39999999999999981e29 < t < -2.2499999999999999e-65 or 3.5e17 < t

   1. Initial program 87.9%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 62.6%

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

   if -1.89999999999999989e102 < t < -3.39999999999999981e29 or -2.2499999999999999e-65 < t < 3.5e17

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 89.5%

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

   4. Taylor expanded in z around inf 55.6%

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

      1. associate-/l* 58.8%

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

   6. Simplified 50.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+29} \lor \neg \left(t \leq -2.25 \cdot 10^{-65}\right) \land t \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 54.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+102}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;t \leq -110:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.9e+102)
   x
   (if (<= t -2.6e+30)
     (/ z (/ t y))
     (if (<= t -110.0) x (if (<= t 3.5e+18) (* z (/ y t)) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.9e+102) {
		tmp = x;
	} else if (t <= -2.6e+30) {
		tmp = z / (t / y);
	} else if (t <= -110.0) {
		tmp = x;
	} else if (t <= 3.5e+18) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.9d+102)) then
        tmp = x
    else if (t <= (-2.6d+30)) then
        tmp = z / (t / y)
    else if (t <= (-110.0d0)) then
        tmp = x
    else if (t <= 3.5d+18) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.9e+102) {
		tmp = x;
	} else if (t <= -2.6e+30) {
		tmp = z / (t / y);
	} else if (t <= -110.0) {
		tmp = x;
	} else if (t <= 3.5e+18) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.9e+102:
		tmp = x
	elif t <= -2.6e+30:
		tmp = z / (t / y)
	elif t <= -110.0:
		tmp = x
	elif t <= 3.5e+18:
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.9e+102)
		tmp = x;
	elseif (t <= -2.6e+30)
		tmp = Float64(z / Float64(t / y));
	elseif (t <= -110.0)
		tmp = x;
	elseif (t <= 3.5e+18)
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.9e+102)
		tmp = x;
	elseif (t <= -2.6e+30)
		tmp = z / (t / y);
	elseif (t <= -110.0)
		tmp = x;
	elseif (t <= 3.5e+18)
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.9e+102], x, If[LessEqual[t, -2.6e+30], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -110.0], x, If[LessEqual[t, 3.5e+18], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.89999999999999989e102 or -2.59999999999999988e30 < t < -110 or 3.5e18 < t

   1. Initial program 86.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 67.0%

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

   if -1.89999999999999989e102 < t < -2.59999999999999988e30

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 86.7%

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

   4. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 78.1%

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

      2. associate-*r/ 78.1%

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

   6. Simplified 65.1%

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

      1. clear-num 65.2%

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

      2. un-div-inv 65.2%

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

   8. Applied egg-rr 65.2%

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

   if -110 < t < 3.5e18

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 87.5%

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

   4. Taylor expanded in z around inf 51.0%

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

      1. *-commutative 62.0%

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

      2. associate-*r/ 65.6%

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

   6. Simplified 54.6%

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

Alternative 6: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4700:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4700.0)
   (* z (/ y t))
   (if (<= y 8.2e-122) x (if (<= y 9e+19) (/ (* y z) t) (* x (/ y (- t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4700.0) {
		tmp = z * (y / t);
	} else if (y <= 8.2e-122) {
		tmp = x;
	} else if (y <= 9e+19) {
		tmp = (y * z) / t;
	} else {
		tmp = x * (y / -t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4700.0d0)) then
        tmp = z * (y / t)
    else if (y <= 8.2d-122) then
        tmp = x
    else if (y <= 9d+19) then
        tmp = (y * z) / t
    else
        tmp = x * (y / -t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4700.0) {
		tmp = z * (y / t);
	} else if (y <= 8.2e-122) {
		tmp = x;
	} else if (y <= 9e+19) {
		tmp = (y * z) / t;
	} else {
		tmp = x * (y / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4700.0:
		tmp = z * (y / t)
	elif y <= 8.2e-122:
		tmp = x
	elif y <= 9e+19:
		tmp = (y * z) / t
	else:
		tmp = x * (y / -t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4700.0)
		tmp = Float64(z * Float64(y / t));
	elseif (y <= 8.2e-122)
		tmp = x;
	elseif (y <= 9e+19)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = Float64(x * Float64(y / Float64(-t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4700.0)
		tmp = z * (y / t);
	elseif (y <= 8.2e-122)
		tmp = x;
	elseif (y <= 9e+19)
		tmp = (y * z) / t;
	else
		tmp = x * (y / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4700.0], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-122], x, If[LessEqual[y, 9e+19], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4700

   1. Initial program 90.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 86.4%

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

   4. Taylor expanded in z around inf 48.9%

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

      1. *-commutative 56.7%

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

      2. associate-*r/ 65.1%

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

   6. Simplified 55.5%

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

   if -4700 < y < 8.2000000000000001e-122

   1. Initial program 99.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 65.8%

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

   if 8.2000000000000001e-122 < y < 9e19

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 71.7%

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

   4. Taylor expanded in z around inf 59.7%

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

   if 9e19 < y

   1. Initial program 85.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 76.7%

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

   4. Taylor expanded in z around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. associate-/l* 66.1%

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

      3. distribute-rgt-neg-in 66.1%

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

      4. distribute-neg-frac2 66.1%

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

   6. Simplified 66.1%

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

Alternative 7: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -105:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -105.0)
   (/ (* y (- z x)) t)
   (if (<= y 4.2e-37) (+ x (/ 1.0 (/ t (* y z)))) (* y (/ (- z x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -105.0) {
		tmp = (y * (z - x)) / t;
	} else if (y <= 4.2e-37) {
		tmp = x + (1.0 / (t / (y * z)));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-105.0d0)) then
        tmp = (y * (z - x)) / t
    else if (y <= 4.2d-37) then
        tmp = x + (1.0d0 / (t / (y * z)))
    else
        tmp = y * ((z - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -105.0) {
		tmp = (y * (z - x)) / t;
	} else if (y <= 4.2e-37) {
		tmp = x + (1.0 / (t / (y * z)));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -105.0:
		tmp = (y * (z - x)) / t
	elif y <= 4.2e-37:
		tmp = x + (1.0 / (t / (y * z)))
	else:
		tmp = y * ((z - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -105.0)
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	elseif (y <= 4.2e-37)
		tmp = Float64(x + Float64(1.0 / Float64(t / Float64(y * z))));
	else
		tmp = Float64(y * Float64(Float64(z - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -105.0)
		tmp = (y * (z - x)) / t;
	elseif (y <= 4.2e-37)
		tmp = x + (1.0 / (t / (y * z)));
	else
		tmp = y * ((z - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -105.0], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 4.2e-37], N[(x + N[(1.0 / N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -105

   1. Initial program 90.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 86.4%

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

   if -105 < y < 4.2000000000000002e-37

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.3%

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

      1. associate-/l* 83.3%

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

   5. Simplified 83.3%

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

      1. associate-*r/ 89.3%

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

      2. clear-num 89.3%

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

   7. Applied egg-rr 89.3%

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

   if 4.2000000000000002e-37 < y

   1. Initial program 86.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 77.6%

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

      1. associate-/l* 86.9%

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

      2. *-commutative 86.9%

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

   5. Applied egg-rr 86.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -105:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+15} \lor \neg \left(y \leq 6.9 \cdot 10^{-37}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.2e+15) (not (<= y 6.9e-37)))
   (* y (/ (- z x) t))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e+15) || !(y <= 6.9e-37)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7.2d+15)) .or. (.not. (y <= 6.9d-37))) then
        tmp = y * ((z - x) / t)
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.2e+15) || !(y <= 6.9e-37)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.2e+15) or not (y <= 6.9e-37):
		tmp = y * ((z - x) / t)
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.2e+15) || !(y <= 6.9e-37))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.2e+15) || ~((y <= 6.9e-37)))
		tmp = y * ((z - x) / t);
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.2e+15], N[Not[LessEqual[y, 6.9e-37]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2e15 or 6.8999999999999999e-37 < y

   1. Initial program 88.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 81.6%

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

      1. associate-/l* 86.0%

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

      2. *-commutative 86.0%

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

   5. Applied egg-rr 86.0%

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

   if -7.2e15 < y < 6.8999999999999999e-37

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-*r/ 88.8%

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

   5. Simplified 88.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+15} \lor \neg \left(y \leq 6.9 \cdot 10^{-37}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.3 \cdot 10^{+18} \lor \neg \left(y \leq 2.7 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.3e+18) (not (<= y 2.7e-40)))
   (* y (/ (- z x) t))
   (+ x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.3e+18) || !(y <= 2.7e-40)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8.3d+18)) .or. (.not. (y <= 2.7d-40))) then
        tmp = y * ((z - x) / t)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.3e+18) || !(y <= 2.7e-40)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.3e+18) or not (y <= 2.7e-40):
		tmp = y * ((z - x) / t)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.3e+18) || !(y <= 2.7e-40))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.3e+18) || ~((y <= 2.7e-40)))
		tmp = y * ((z - x) / t);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.3e+18], N[Not[LessEqual[y, 2.7e-40]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.3e18 or 2.7e-40 < y

   1. Initial program 88.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 81.7%

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

      1. associate-/l* 86.1%

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

      2. *-commutative 86.1%

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

   5. Applied egg-rr 86.1%

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

   if -8.3e18 < y < 2.7e-40

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.2%

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

      1. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.3 \cdot 10^{+18} \lor \neg \left(y \leq 2.7 \cdot 10^{-40}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-146} \lor \neg \left(x \leq 1.4 \cdot 10^{-71}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.55e-146) (not (<= x 1.4e-71)))
   (* x (- 1.0 (/ y t)))
   (/ (* y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.55e-146) || !(x <= 1.4e-71)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.55d-146)) .or. (.not. (x <= 1.4d-71))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.55e-146) || !(x <= 1.4e-71)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.55e-146) or not (x <= 1.4e-71):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.55e-146) || !(x <= 1.4e-71))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y * z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.55e-146) || ~((x <= 1.4e-71)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y * z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.55e-146], N[Not[LessEqual[x, 1.4e-71]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5499999999999999e-146 or 1.4e-71 < x

   1. Initial program 91.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 85.5%

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

      1. mul-1-neg 85.5%

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

      2. unsub-neg 85.5%

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

   5. Simplified 85.5%

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

   if -1.5499999999999999e-146 < x < 1.4e-71

   1. Initial program 98.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 81.9%

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

   4. Taylor expanded in z around inf 72.6%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-146} \lor \neg \left(x \leq 1.4 \cdot 10^{-71}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -180000:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-37}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -180000.0)
   (/ (* y (- z x)) t)
   (if (<= y 6.9e-37) (+ x (* z (/ y t))) (* y (/ (- z x) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -180000.0) {
		tmp = (y * (z - x)) / t;
	} else if (y <= 6.9e-37) {
		tmp = x + (z * (y / t));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-180000.0d0)) then
        tmp = (y * (z - x)) / t
    else if (y <= 6.9d-37) then
        tmp = x + (z * (y / t))
    else
        tmp = y * ((z - x) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -180000.0) {
		tmp = (y * (z - x)) / t;
	} else if (y <= 6.9e-37) {
		tmp = x + (z * (y / t));
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -180000.0:
		tmp = (y * (z - x)) / t
	elif y <= 6.9e-37:
		tmp = x + (z * (y / t))
	else:
		tmp = y * ((z - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -180000.0)
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	elseif (y <= 6.9e-37)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(y * Float64(Float64(z - x) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -180000.0)
		tmp = (y * (z - x)) / t;
	elseif (y <= 6.9e-37)
		tmp = x + (z * (y / t));
	else
		tmp = y * ((z - x) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -180000.0], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 6.9e-37], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e5

   1. Initial program 90.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 86.4%

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

   if -1.8e5 < y < 6.8999999999999999e-37

   1. Initial program 99.1%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.3%

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

      1. *-commutative 89.3%

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

      2. associate-*r/ 88.8%

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

   5. Simplified 88.8%

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

   if 6.8999999999999999e-37 < y

   1. Initial program 86.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 77.6%

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

      1. associate-/l* 86.9%

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

      2. *-commutative 86.9%

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

   5. Applied egg-rr 86.9%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -180000:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{-37}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 93.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+151}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4e+151) (* x (- 1.0 (/ y t))) (+ x (/ (* y (- z x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e+151) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y * (z - x)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4d+151)) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + ((y * (z - x)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4e+151) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + ((y * (z - x)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4e+151:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + ((y * (z - x)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4e+151)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - x)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4e+151)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + ((y * (z - x)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4e+151], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000007e151

   1. Initial program 79.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

   5. Simplified 97.1%

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

   if -4.00000000000000007e151 < x

   1. Initial program 96.0%

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

Alternative 13: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \frac{y \cdot \left(z - x\right)}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 36.8%

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

Developer target: 90.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024086 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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