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

Percentage Accurate: 92.7% → 97.7%

Time: 8.8s

Alternatives: 8

Speedup: 1.1×

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

Specification

Math

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

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: 92.7% 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: 97.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{t}, z - x, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. associate-/l* N/A

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

   7. *-commutative N/A

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

   8. lower-fma.f64 N/A

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

   9. lower-/.f64 96.9

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

4. Applied rewrites 96.9%

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

Alternative 2: 85.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ t_2 := y \cdot \frac{z - x}{t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;x - \frac{y \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))) (t_2 (* y (/ (- z x) t))))
   (if (<= t_1 -5e+305)
     t_2
     (if (<= t_1 2e+146)
       (+ x (/ (* y z) t))
       (if (<= t_1 2e+306) (- x (/ (* y x) t)) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double t_2 = y * ((z - x) / t);
	double tmp;
	if (t_1 <= -5e+305) {
		tmp = t_2;
	} else if (t_1 <= 2e+146) {
		tmp = x + ((y * z) / t);
	} else if (t_1 <= 2e+306) {
		tmp = x - ((y * x) / t);
	} 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 = x + ((y * (z - x)) / t)
    t_2 = y * ((z - x) / t)
    if (t_1 <= (-5d+305)) then
        tmp = t_2
    else if (t_1 <= 2d+146) then
        tmp = x + ((y * z) / t)
    else if (t_1 <= 2d+306) then
        tmp = x - ((y * x) / t)
    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 = x + ((y * (z - x)) / t);
	double t_2 = y * ((z - x) / t);
	double tmp;
	if (t_1 <= -5e+305) {
		tmp = t_2;
	} else if (t_1 <= 2e+146) {
		tmp = x + ((y * z) / t);
	} else if (t_1 <= 2e+306) {
		tmp = x - ((y * x) / t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	t_2 = y * ((z - x) / t)
	tmp = 0
	if t_1 <= -5e+305:
		tmp = t_2
	elif t_1 <= 2e+146:
		tmp = x + ((y * z) / t)
	elif t_1 <= 2e+306:
		tmp = x - ((y * x) / t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	t_2 = Float64(y * Float64(Float64(z - x) / t))
	tmp = 0.0
	if (t_1 <= -5e+305)
		tmp = t_2;
	elseif (t_1 <= 2e+146)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	elseif (t_1 <= 2e+306)
		tmp = Float64(x - Float64(Float64(y * x) / t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	t_2 = y * ((z - x) / t);
	tmp = 0.0;
	if (t_1 <= -5e+305)
		tmp = t_2;
	elseif (t_1 <= 2e+146)
		tmp = x + ((y * z) / t);
	elseif (t_1 <= 2e+306)
		tmp = x - ((y * x) / t);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+305], t$95$2, If[LessEqual[t$95$1, 2e+146], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+306], N[(x - N[(N[(y * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -5.00000000000000009e305 or 2.00000000000000003e306 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 82.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 93.1

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

   5. Applied rewrites 93.1%

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

   if -5.00000000000000009e305 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 1.99999999999999987e146

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 86.5

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

   5. Applied rewrites 86.5%

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

   if 1.99999999999999987e146 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 2.00000000000000003e306

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 80.5

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

   5. Applied rewrites 80.5%

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

Alternative 3: 48.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot x}{t}\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* t x) t)))
   (if (<= z -7.4e-43)
     (* (/ y t) z)
     (if (<= z -2.8e-277)
       (* y (/ (- x) t))
       (if (<= z -4.8e-304)
         t_1
         (if (<= z 5.1e-264)
           (/ (* x (- y)) t)
           (if (<= z 2.6e-22) t_1 (* y (/ z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * x) / t;
	double tmp;
	if (z <= -7.4e-43) {
		tmp = (y / t) * z;
	} else if (z <= -2.8e-277) {
		tmp = y * (-x / t);
	} else if (z <= -4.8e-304) {
		tmp = t_1;
	} else if (z <= 5.1e-264) {
		tmp = (x * -y) / t;
	} else if (z <= 2.6e-22) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t * x) / t
    if (z <= (-7.4d-43)) then
        tmp = (y / t) * z
    else if (z <= (-2.8d-277)) then
        tmp = y * (-x / t)
    else if (z <= (-4.8d-304)) then
        tmp = t_1
    else if (z <= 5.1d-264) then
        tmp = (x * -y) / t
    else if (z <= 2.6d-22) then
        tmp = t_1
    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 t_1 = (t * x) / t;
	double tmp;
	if (z <= -7.4e-43) {
		tmp = (y / t) * z;
	} else if (z <= -2.8e-277) {
		tmp = y * (-x / t);
	} else if (z <= -4.8e-304) {
		tmp = t_1;
	} else if (z <= 5.1e-264) {
		tmp = (x * -y) / t;
	} else if (z <= 2.6e-22) {
		tmp = t_1;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * x) / t
	tmp = 0
	if z <= -7.4e-43:
		tmp = (y / t) * z
	elif z <= -2.8e-277:
		tmp = y * (-x / t)
	elif z <= -4.8e-304:
		tmp = t_1
	elif z <= 5.1e-264:
		tmp = (x * -y) / t
	elif z <= 2.6e-22:
		tmp = t_1
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * x) / t)
	tmp = 0.0
	if (z <= -7.4e-43)
		tmp = Float64(Float64(y / t) * z);
	elseif (z <= -2.8e-277)
		tmp = Float64(y * Float64(Float64(-x) / t));
	elseif (z <= -4.8e-304)
		tmp = t_1;
	elseif (z <= 5.1e-264)
		tmp = Float64(Float64(x * Float64(-y)) / t);
	elseif (z <= 2.6e-22)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * x) / t;
	tmp = 0.0;
	if (z <= -7.4e-43)
		tmp = (y / t) * z;
	elseif (z <= -2.8e-277)
		tmp = y * (-x / t);
	elseif (z <= -4.8e-304)
		tmp = t_1;
	elseif (z <= 5.1e-264)
		tmp = (x * -y) / t;
	elseif (z <= 2.6e-22)
		tmp = t_1;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * x), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -7.4e-43], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, -2.8e-277], N[(y * N[((-x) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.8e-304], t$95$1, If[LessEqual[z, 5.1e-264], N[(N[(x * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.6e-22], t$95$1, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.4e-43

   1. Initial program 90.3%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 54.5

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

   5. Applied rewrites 54.5%

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

   7. Applied rewrites 59.8%

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

   if -7.4e-43 < z < -2.79999999999999976e-277

   1. Initial program 92.6%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 57.8

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

   5. Applied rewrites 57.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 44.0%

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

   if -2.79999999999999976e-277 < z < -4.8000000000000002e-304 or 5.10000000000000024e-264 < z < 2.6e-22

   1. Initial program 95.5%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 83.5

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

   5. Applied rewrites 83.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.5%

      \[\leadsto \frac{x \cdot t}{t} \]

   if -4.8000000000000002e-304 < z < 5.10000000000000024e-264

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 77.2

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 85.8%

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

   if 2.6e-22 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.2

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

   5. Applied rewrites 59.2%

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

   7. Applied rewrites 63.8%

      \[\leadsto \frac{z}{t} \cdot \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \frac{-x}{t}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot x}{t}\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* t x) t)))
   (if (<= z -3.05e+38)
     (* (/ y t) z)
     (if (<= z -4.8e-304)
       t_1
       (if (<= z 5.1e-264)
         (/ (* x (- y)) t)
         (if (<= z 2.6e-22) t_1 (* y (/ z t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t * x) / t;
	double tmp;
	if (z <= -3.05e+38) {
		tmp = (y / t) * z;
	} else if (z <= -4.8e-304) {
		tmp = t_1;
	} else if (z <= 5.1e-264) {
		tmp = (x * -y) / t;
	} else if (z <= 2.6e-22) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t * x) / t
    if (z <= (-3.05d+38)) then
        tmp = (y / t) * z
    else if (z <= (-4.8d-304)) then
        tmp = t_1
    else if (z <= 5.1d-264) then
        tmp = (x * -y) / t
    else if (z <= 2.6d-22) then
        tmp = t_1
    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 t_1 = (t * x) / t;
	double tmp;
	if (z <= -3.05e+38) {
		tmp = (y / t) * z;
	} else if (z <= -4.8e-304) {
		tmp = t_1;
	} else if (z <= 5.1e-264) {
		tmp = (x * -y) / t;
	} else if (z <= 2.6e-22) {
		tmp = t_1;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t * x) / t
	tmp = 0
	if z <= -3.05e+38:
		tmp = (y / t) * z
	elif z <= -4.8e-304:
		tmp = t_1
	elif z <= 5.1e-264:
		tmp = (x * -y) / t
	elif z <= 2.6e-22:
		tmp = t_1
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t * x) / t)
	tmp = 0.0
	if (z <= -3.05e+38)
		tmp = Float64(Float64(y / t) * z);
	elseif (z <= -4.8e-304)
		tmp = t_1;
	elseif (z <= 5.1e-264)
		tmp = Float64(Float64(x * Float64(-y)) / t);
	elseif (z <= 2.6e-22)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t * x) / t;
	tmp = 0.0;
	if (z <= -3.05e+38)
		tmp = (y / t) * z;
	elseif (z <= -4.8e-304)
		tmp = t_1;
	elseif (z <= 5.1e-264)
		tmp = (x * -y) / t;
	elseif (z <= 2.6e-22)
		tmp = t_1;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t * x), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -3.05e+38], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, -4.8e-304], t$95$1, If[LessEqual[z, 5.1e-264], N[(N[(x * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.6e-22], t$95$1, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.05e38

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 58.2

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

   5. Applied rewrites 58.2%

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

   7. Applied rewrites 64.4%

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

   if -3.05e38 < z < -4.8000000000000002e-304 or 5.10000000000000024e-264 < z < 2.6e-22

   1. Initial program 94.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 85.2

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

   5. Applied rewrites 85.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.5%

      \[\leadsto \frac{x \cdot t}{t} \]

   if -4.8000000000000002e-304 < z < 5.10000000000000024e-264

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 77.2

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

   5. Applied rewrites 77.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 85.8%

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

   if 2.6e-22 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.2

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

   5. Applied rewrites 59.2%

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

   7. Applied rewrites 63.8%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-304}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-264}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot x}{t}\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ (* y x) t))))
   (if (<= x -3.7e-86) t_1 (if (<= x 4e-24) (* y (/ (- z x) t)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - ((y * x) / t);
	double tmp;
	if (x <= -3.7e-86) {
		tmp = t_1;
	} else if (x <= 4e-24) {
		tmp = 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 * x) / t)
    if (x <= (-3.7d-86)) then
        tmp = t_1
    else if (x <= 4d-24) then
        tmp = 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 * x) / t);
	double tmp;
	if (x <= -3.7e-86) {
		tmp = t_1;
	} else if (x <= 4e-24) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - ((y * x) / t)
	tmp = 0
	if x <= -3.7e-86:
		tmp = t_1
	elif x <= 4e-24:
		tmp = y * ((z - x) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(Float64(y * x) / t))
	tmp = 0.0
	if (x <= -3.7e-86)
		tmp = t_1;
	elseif (x <= 4e-24)
		tmp = 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 * x) / t);
	tmp = 0.0;
	if (x <= -3.7e-86)
		tmp = t_1;
	elseif (x <= 4e-24)
		tmp = 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 * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e-86], t$95$1, If[LessEqual[x, 4e-24], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6999999999999998e-86 or 3.99999999999999969e-24 < x

   1. Initial program 95.3%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. distribute-lft-out-- N/A

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

      4. *-rgt-identity N/A

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

      5. associate-/l* N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 85.6

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

   5. Applied rewrites 85.6%

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

   if -3.6999999999999998e-86 < x < 3.99999999999999969e-24

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 77.2

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

   5. Applied rewrites 77.2%

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

Alternative 6: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - x}{t}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ (- z x) t))))
   (if (<= y -5e-111) t_1 (if (<= y 3.5e-90) (/ (* t x) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * ((z - x) / t);
	double tmp;
	if (y <= -5e-111) {
		tmp = t_1;
	} else if (y <= 3.5e-90) {
		tmp = (t * 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 = y * ((z - x) / t)
    if (y <= (-5d-111)) then
        tmp = t_1
    else if (y <= 3.5d-90) then
        tmp = (t * 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 = y * ((z - x) / t);
	double tmp;
	if (y <= -5e-111) {
		tmp = t_1;
	} else if (y <= 3.5e-90) {
		tmp = (t * x) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * ((z - x) / t)
	tmp = 0
	if y <= -5e-111:
		tmp = t_1
	elif y <= 3.5e-90:
		tmp = (t * x) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(Float64(z - x) / t))
	tmp = 0.0
	if (y <= -5e-111)
		tmp = t_1;
	elseif (y <= 3.5e-90)
		tmp = Float64(Float64(t * x) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * ((z - x) / t);
	tmp = 0.0;
	if (y <= -5e-111)
		tmp = t_1;
	elseif (y <= 3.5e-90)
		tmp = (t * x) / t;
	else
		tmp = t_1;
	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]}, If[LessEqual[y, -5e-111], t$95$1, If[LessEqual[y, 3.5e-90], N[(N[(t * x), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000003e-111 or 3.4999999999999999e-90 < y

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf

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

      1. div-sub N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -5.0000000000000003e-111 < y < 3.4999999999999999e-90

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 86.0

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

   5. Applied rewrites 86.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.6%

      \[\leadsto \frac{x \cdot t}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-111}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-90}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.05e+38)
   (* (/ y t) z)
   (if (<= z 2.6e-22) (/ (* t x) t) (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.05e+38) {
		tmp = (y / t) * z;
	} else if (z <= 2.6e-22) {
		tmp = (t * x) / 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 (z <= (-3.05d+38)) then
        tmp = (y / t) * z
    else if (z <= 2.6d-22) then
        tmp = (t * x) / 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 (z <= -3.05e+38) {
		tmp = (y / t) * z;
	} else if (z <= 2.6e-22) {
		tmp = (t * x) / t;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.05e+38:
		tmp = (y / t) * z
	elif z <= 2.6e-22:
		tmp = (t * x) / t
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.05e+38)
		tmp = Float64(Float64(y / t) * z);
	elseif (z <= 2.6e-22)
		tmp = Float64(Float64(t * x) / t);
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.05e+38)
		tmp = (y / t) * z;
	elseif (z <= 2.6e-22)
		tmp = (t * x) / t;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.05e+38], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 2.6e-22], N[(N[(t * x), $MachinePrecision] / t), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.05e38

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 58.2

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

   5. Applied rewrites 58.2%

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

   7. Applied rewrites 64.4%

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

   if -3.05e38 < z < 2.6e-22

   1. Initial program 95.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 84.9

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

   5. Applied rewrites 84.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot x}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.2%

      \[\leadsto \frac{x \cdot t}{t} \]

   if 2.6e-22 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.2

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

   5. Applied rewrites 59.2%

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

   7. Applied rewrites 63.8%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-22}:\\ \;\;\;\;\frac{t \cdot x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{y}{t} \cdot z \end{array} \]

FPCore

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

C

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

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 = (y / t) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

3. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 35.9

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

5. Applied rewrites 35.9%

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

7. Applied rewrites 38.4%

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

8. Final simplification 38.4%

   \[\leadsto \frac{y}{t} \cdot z \]
9. Add Preprocessing

Developer Target 1: 91.4% 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 2024233 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (+ (* x (/ y t)) (* (- z) (/ y t)))))

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