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

Percentage Accurate: 92.6% → 95.8%

Time: 9.8s

Alternatives: 14

Speedup: 1.0×

• 25.7% 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: 92.6% 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: 95.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- z x) y) t))))
   (if (<= t_1 (- INFINITY)) (+ x (* y (/ (- z x) t))) t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((z - x) * y) / t)
	tmp = 0
	if t_1 <= -math.inf:
		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(Float64(z - x) * y) / t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		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 + (((z - x) * y) / t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		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[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], 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)) < -inf.0

   1. Initial program 84.8%

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

      1. associate-/l* 99.9%

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

      2. *-commutative 99.9%

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

   4. Applied egg-rr 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 97.6%

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

4. Final simplification 98.0%

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

Alternative 2: 52.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{-t}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t)))))
   (if (<= y -1.65e-25)
     t_1
     (if (<= y 8.8e-75) x (if (<= y 7.5e+213) (* y (/ z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / -t);
	double tmp;
	if (y <= -1.65e-25) {
		tmp = t_1;
	} else if (y <= 8.8e-75) {
		tmp = x;
	} else if (y <= 7.5e+213) {
		tmp = y * (z / 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 / -t)
    if (y <= (-1.65d-25)) then
        tmp = t_1
    else if (y <= 8.8d-75) then
        tmp = x
    else if (y <= 7.5d+213) then
        tmp = y * (z / 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 / -t);
	double tmp;
	if (y <= -1.65e-25) {
		tmp = t_1;
	} else if (y <= 8.8e-75) {
		tmp = x;
	} else if (y <= 7.5e+213) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / -t)
	tmp = 0
	if y <= -1.65e-25:
		tmp = t_1
	elif y <= 8.8e-75:
		tmp = x
	elif y <= 7.5e+213:
		tmp = y * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(-t)))
	tmp = 0.0
	if (y <= -1.65e-25)
		tmp = t_1;
	elseif (y <= 8.8e-75)
		tmp = x;
	elseif (y <= 7.5e+213)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / -t);
	tmp = 0.0;
	if (y <= -1.65e-25)
		tmp = t_1;
	elseif (y <= 8.8e-75)
		tmp = x;
	elseif (y <= 7.5e+213)
		tmp = y * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e-25], t$95$1, If[LessEqual[y, 8.8e-75], x, If[LessEqual[y, 7.5e+213], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6499999999999999e-25 or 7.5000000000000003e213 < y

   1. Initial program 90.1%

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

      1. +-commutative 90.1%

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

      2. associate-/l* 96.4%

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

      3. fma-define 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around -inf 79.3%

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

   6. Taylor expanded in z around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-/l* 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

      4. mul-1-neg 54.4%

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

      5. associate-*r/ 54.4%

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

      6. mul-1-neg 54.4%

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

   8. Simplified 54.4%

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

   if -1.6499999999999999e-25 < y < 8.80000000000000022e-75

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-/l* 88.1%

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

      3. fma-define 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around 0 66.7%

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

   if 8.80000000000000022e-75 < y < 7.5000000000000003e213

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      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. Taylor expanded in y around -inf 72.7%

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

   6. Taylor expanded in z around inf 53.3%

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

      1. associate-/l* 59.6%

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

   8. Simplified 59.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-25)
   (/ x (/ t (- y)))
   (if (<= y 1.55e-73)
     x
     (if (<= y 5.6e+213) (* y (/ z t)) (* x (/ y (- t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-25) {
		tmp = x / (t / -y);
	} else if (y <= 1.55e-73) {
		tmp = x;
	} else if (y <= 5.6e+213) {
		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 <= (-1.6d-25)) then
        tmp = x / (t / -y)
    else if (y <= 1.55d-73) then
        tmp = x
    else if (y <= 5.6d+213) 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 <= -1.6e-25) {
		tmp = x / (t / -y);
	} else if (y <= 1.55e-73) {
		tmp = x;
	} else if (y <= 5.6e+213) {
		tmp = y * (z / t);
	} else {
		tmp = x * (y / -t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-25:
		tmp = x / (t / -y)
	elif y <= 1.55e-73:
		tmp = x
	elif y <= 5.6e+213:
		tmp = y * (z / t)
	else:
		tmp = x * (y / -t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-25)
		tmp = Float64(x / Float64(t / Float64(-y)));
	elseif (y <= 1.55e-73)
		tmp = x;
	elseif (y <= 5.6e+213)
		tmp = Float64(y * Float64(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 <= -1.6e-25)
		tmp = x / (t / -y);
	elseif (y <= 1.55e-73)
		tmp = x;
	elseif (y <= 5.6e+213)
		tmp = y * (z / t);
	else
		tmp = x * (y / -t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-25], N[(x / N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-73], x, If[LessEqual[y, 5.6e+213], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e-25

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. associate-/l* 96.8%

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

      3. fma-define 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around -inf 75.8%

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

   6. Taylor expanded in z around 0 45.6%

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

      1. mul-1-neg 45.6%

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

      2. associate-/l* 50.4%

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

      3. distribute-rgt-neg-in 50.4%

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

      4. mul-1-neg 50.4%

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

      5. associate-*r/ 50.4%

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

      6. mul-1-neg 50.4%

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

   8. Simplified 50.4%

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

      1. add-sqr-sqrt 50.4%

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

      2. sqrt-unprod 48.7%

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

      3. sqr-neg 48.7%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 5.1%

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

      6. clear-num 5.1%

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

      7. div-inv 5.1%

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

      8. frac-2neg 5.1%

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

      9. distribute-frac-neg2 5.1%

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

      10. add-sqr-sqrt 5.1%

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

      11. sqrt-unprod 6.4%

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

      12. sqr-neg 6.4%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 50.5%

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

   10. Applied egg-rr 50.5%

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

   if -1.6000000000000001e-25 < y < 1.54999999999999985e-73

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-/l* 88.1%

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

      3. fma-define 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around 0 66.7%

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

   if 1.54999999999999985e-73 < y < 5.59999999999999979e213

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      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. Taylor expanded in y around -inf 72.7%

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

   6. Taylor expanded in z around inf 53.3%

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

      1. associate-/l* 59.6%

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

   8. Simplified 59.6%

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

   if 5.59999999999999979e213 < y

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 94.9%

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

      3. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around -inf 90.0%

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

   6. Taylor expanded in z around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. associate-/l* 66.6%

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

      3. distribute-rgt-neg-in 66.6%

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

      4. mul-1-neg 66.6%

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

      5. associate-*r/ 66.6%

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

      6. mul-1-neg 66.6%

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

   8. Simplified 66.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+213}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e-25)
   (/ x (/ t (- y)))
   (if (<= y 4.3e-75)
     x
     (if (<= y 1.35e+214) (* y (/ z t)) (/ (* x y) (- t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-25) {
		tmp = x / (t / -y);
	} else if (y <= 4.3e-75) {
		tmp = x;
	} else if (y <= 1.35e+214) {
		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 <= (-1.65d-25)) then
        tmp = x / (t / -y)
    else if (y <= 4.3d-75) then
        tmp = x
    else if (y <= 1.35d+214) 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 <= -1.65e-25) {
		tmp = x / (t / -y);
	} else if (y <= 4.3e-75) {
		tmp = x;
	} else if (y <= 1.35e+214) {
		tmp = y * (z / t);
	} else {
		tmp = (x * y) / -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e-25:
		tmp = x / (t / -y)
	elif y <= 4.3e-75:
		tmp = x
	elif y <= 1.35e+214:
		tmp = y * (z / t)
	else:
		tmp = (x * y) / -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e-25)
		tmp = Float64(x / Float64(t / Float64(-y)));
	elseif (y <= 4.3e-75)
		tmp = x;
	elseif (y <= 1.35e+214)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(Float64(x * y) / Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e-25)
		tmp = x / (t / -y);
	elseif (y <= 4.3e-75)
		tmp = x;
	elseif (y <= 1.35e+214)
		tmp = y * (z / t);
	else
		tmp = (x * y) / -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e-25], N[(x / N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e-75], x, If[LessEqual[y, 1.35e+214], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / (-t)), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6499999999999999e-25

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. associate-/l* 96.8%

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

      3. fma-define 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in y around -inf 75.8%

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

   6. Taylor expanded in z around 0 45.6%

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

      1. mul-1-neg 45.6%

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

      2. associate-/l* 50.4%

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

      3. distribute-rgt-neg-in 50.4%

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

      4. mul-1-neg 50.4%

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

      5. associate-*r/ 50.4%

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

      6. mul-1-neg 50.4%

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

   8. Simplified 50.4%

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

      1. add-sqr-sqrt 50.4%

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

      2. sqrt-unprod 48.7%

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

      3. sqr-neg 48.7%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 5.1%

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

      6. clear-num 5.1%

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

      7. div-inv 5.1%

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

      8. frac-2neg 5.1%

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

      9. distribute-frac-neg2 5.1%

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

      10. add-sqr-sqrt 5.1%

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

      11. sqrt-unprod 6.4%

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

      12. sqr-neg 6.4%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 50.5%

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

   10. Applied egg-rr 50.5%

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

   if -1.6499999999999999e-25 < y < 4.2999999999999999e-75

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-/l* 88.1%

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

      3. fma-define 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around 0 66.7%

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

   if 4.2999999999999999e-75 < y < 1.35000000000000005e214

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      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. Taylor expanded in y around -inf 72.7%

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

   6. Taylor expanded in z around inf 53.3%

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

      1. associate-/l* 59.6%

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

   8. Simplified 59.6%

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

   if 1.35000000000000005e214 < y

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-/l* 94.9%

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

      3. fma-define 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in y around -inf 90.0%

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

   6. Taylor expanded in z around 0 66.9%

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

      1. associate-*r/ 66.9%

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

      2. mul-1-neg 66.9%

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

      3. distribute-lft-neg-out 66.9%

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

      4. *-commutative 66.9%

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

   8. Simplified 66.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-114} \lor \neg \left(x \leq 9.5 \cdot 10^{-180}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.1e-114) (not (<= x 9.5e-180)))
   (* x (- 1.0 (/ y t)))
   (/ y (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.1e-114) || !(x <= 9.5e-180)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y / (t / z);
	}
	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 <= (-4.1d-114)) .or. (.not. (x <= 9.5d-180))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = y / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.1e-114) || !(x <= 9.5e-180)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.1e-114) or not (x <= 9.5e-180):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.1e-114) || !(x <= 9.5e-180))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.1e-114) || ~((x <= 9.5e-180)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = y / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.1e-114], N[Not[LessEqual[x, 9.5e-180]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.0999999999999997e-114 or 9.49999999999999934e-180 < x

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-/l* 93.4%

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

      3. fma-define 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around 0 78.8%

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

      1. *-rgt-identity 78.8%

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

      2. mul-1-neg 78.8%

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

      3. associate-/l* 79.9%

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

      4. distribute-rgt-neg-in 79.9%

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

      5. mul-1-neg 79.9%

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

      6. distribute-lft-in 79.8%

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

      7. mul-1-neg 79.8%

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

      8. unsub-neg 79.8%

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

   7. Simplified 79.8%

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

   if -4.0999999999999997e-114 < x < 9.49999999999999934e-180

   1. Initial program 94.4%

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

      1. +-commutative 94.4%

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

      2. associate-/l* 93.3%

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

      3. fma-define 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around -inf 70.2%

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

   6. Taylor expanded in z around inf 66.2%

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

      1. associate-/l* 66.3%

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

   8. Simplified 66.3%

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

      1. clear-num 66.3%

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

      2. un-div-inv 66.4%

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

   10. Applied egg-rr 66.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{-114} \lor \neg \left(x \leq 9.5 \cdot 10^{-180}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-42} \lor \neg \left(z \leq 2.32 \cdot 10^{-125}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e-42) (not (<= z 2.32e-125)))
   (+ x (* y (/ z t)))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-42) || !(z <= 2.32e-125)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (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 ((z <= (-9d-42)) .or. (.not. (z <= 2.32d-125))) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e-42) || !(z <= 2.32e-125)) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e-42) or not (z <= 2.32e-125):
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e-42) || !(z <= 2.32e-125))
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e-42) || ~((z <= 2.32e-125)))
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e-42], N[Not[LessEqual[z, 2.32e-125]], $MachinePrecision]], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e-42 or 2.3199999999999999e-125 < z

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 86.3%

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

      1. associate-/l* 55.7%

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

   5. Simplified 86.3%

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

   if -9e-42 < z < 2.3199999999999999e-125

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-/l* 93.4%

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

      3. fma-define 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around 0 90.0%

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

      1. *-rgt-identity 90.0%

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

      2. mul-1-neg 90.0%

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

      3. associate-/l* 89.0%

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

      4. distribute-rgt-neg-in 89.0%

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

      5. mul-1-neg 89.0%

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

      6. distribute-lft-in 89.0%

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

      7. mul-1-neg 89.0%

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

      8. unsub-neg 89.0%

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

   7. Simplified 89.0%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-42} \lor \neg \left(z \leq 2.32 \cdot 10^{-125}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+55} \lor \neg \left(x \leq 6.5 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5e+55) (not (<= x 6.5e+86)))
   (* x (- 1.0 (/ y t)))
   (+ x (* z (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e+55) || !(x <= 6.5e+86)) {
		tmp = x * (1.0 - (y / 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 ((x <= (-5d+55)) .or. (.not. (x <= 6.5d+86))) then
        tmp = x * (1.0d0 - (y / 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 ((x <= -5e+55) || !(x <= 6.5e+86)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5e+55) or not (x <= 6.5e+86):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5e+55) || !(x <= 6.5e+86))
		tmp = Float64(x * Float64(1.0 - Float64(y / 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 ((x <= -5e+55) || ~((x <= 6.5e+86)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5e+55], N[Not[LessEqual[x, 6.5e+86]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000046e55 or 6.49999999999999996e86 < x

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-/l* 90.5%

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

      3. fma-define 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around 0 91.3%

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

      1. *-rgt-identity 91.3%

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

      2. mul-1-neg 91.3%

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

      3. associate-/l* 93.4%

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

      4. distribute-rgt-neg-in 93.4%

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

      5. mul-1-neg 93.4%

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

      6. distribute-lft-in 93.4%

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

      7. mul-1-neg 93.4%

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

      8. unsub-neg 93.4%

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

   7. Simplified 93.4%

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

   if -5.00000000000000046e55 < x < 6.49999999999999996e86

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf 84.4%

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

      1. associate-/l* 48.0%

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

   5. Simplified 83.4%

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

      1. clear-num 47.9%

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

      2. un-div-inv 48.0%

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

   7. Applied egg-rr 83.4%

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

      1. associate-/r/ 87.7%

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

   9. Applied egg-rr 87.7%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+55} \lor \neg \left(x \leq 6.5 \cdot 10^{+86}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;x - \frac{x \cdot y}{t}\\ \mathbf{elif}\;x \leq 10^{+86}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.2e+56)
   (- x (/ (* x y) t))
   (if (<= x 1e+86) (+ x (* z (/ y t))) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e+56) {
		tmp = x - ((x * y) / t);
	} else if (x <= 1e+86) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (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 (x <= (-3.2d+56)) then
        tmp = x - ((x * y) / t)
    else if (x <= 1d+86) then
        tmp = x + (z * (y / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.2e+56) {
		tmp = x - ((x * y) / t);
	} else if (x <= 1e+86) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.2e+56:
		tmp = x - ((x * y) / t)
	elif x <= 1e+86:
		tmp = x + (z * (y / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.2e+56)
		tmp = Float64(x - Float64(Float64(x * y) / t));
	elseif (x <= 1e+86)
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.2e+56)
		tmp = x - ((x * y) / t);
	elseif (x <= 1e+86)
		tmp = x + (z * (y / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.2e+56], N[(x - N[(N[(x * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+86], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.20000000000000003e56

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 90.6%

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

      1. associate-*r/ 43.5%

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

      2. mul-1-neg 43.5%

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

      3. distribute-lft-neg-out 43.5%

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

      4. *-commutative 43.5%

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

   5. Simplified 90.6%

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

      1. div-inv 90.6%

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

      2. add-sqr-sqrt 90.5%

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

      3. sqrt-unprod 65.8%

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

      4. sqr-neg 65.8%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 51.9%

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

      7. remove-double-neg 51.9%

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

      8. distribute-rgt-neg-out 51.9%

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

      9. cancel-sign-sub-inv 51.9%

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

      10. div-inv 51.9%

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

      11. associate-/l* 49.2%

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

      12. add-sqr-sqrt 49.2%

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

      13. sqrt-unprod 27.9%

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

      14. sqr-neg 27.9%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 86.5%

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

   7. Applied egg-rr 86.5%

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

   8. Taylor expanded in y around 0 90.6%

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

   if -3.20000000000000003e56 < x < 1e86

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf 84.4%

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

      1. associate-/l* 48.0%

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

   5. Simplified 83.4%

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

      1. clear-num 47.9%

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

      2. un-div-inv 48.0%

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

   7. Applied egg-rr 83.4%

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

      1. associate-/r/ 87.7%

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

   9. Applied egg-rr 87.7%

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

   if 1e86 < x

   1. Initial program 91.0%

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

      1. +-commutative 91.0%

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

      2. associate-/l* 91.4%

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

      3. fma-define 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in z around 0 92.0%

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

      1. *-rgt-identity 92.0%

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

      2. mul-1-neg 92.0%

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

      3. associate-/l* 96.6%

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

      4. distribute-rgt-neg-in 96.6%

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

      5. mul-1-neg 96.6%

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

      6. distribute-lft-in 96.5%

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

      7. mul-1-neg 96.5%

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

      8. unsub-neg 96.5%

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

   7. Simplified 96.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+56}:\\ \;\;\;\;x - \frac{x \cdot y}{t}\\ \mathbf{elif}\;x \leq 10^{+86}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-32} \lor \neg \left(y \leq 5.1 \cdot 10^{-76}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.2e-32) (not (<= y 5.1e-76))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.2e-32) || !(y <= 5.1e-76)) {
		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 ((y <= (-8.2d-32)) .or. (.not. (y <= 5.1d-76))) 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 ((y <= -8.2e-32) || !(y <= 5.1e-76)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.2e-32) or not (y <= 5.1e-76):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.2e-32) || !(y <= 5.1e-76))
		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 ((y <= -8.2e-32) || ~((y <= 5.1e-76)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.2e-32], N[Not[LessEqual[y, 5.1e-76]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999995e-32 or 5.09999999999999986e-76 < y

   1. Initial program 92.4%

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

      1. +-commutative 92.4%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around -inf 76.8%

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

   6. Taylor expanded in z around inf 47.9%

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

      1. associate-/l* 50.6%

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

   8. Simplified 50.6%

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

   if -8.1999999999999995e-32 < y < 5.09999999999999986e-76

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-/l* 87.9%

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

      3. fma-define 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 67.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-32} \lor \neg \left(y \leq 5.1 \cdot 10^{-76}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-31) (/ y (/ t z)) (if (<= y 1.1e-73) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-31) {
		tmp = y / (t / z);
	} else if (y <= 1.1e-73) {
		tmp = x;
	} 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 (y <= (-1.4d-31)) then
        tmp = y / (t / z)
    else if (y <= 1.1d-73) then
        tmp = x
    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 (y <= -1.4e-31) {
		tmp = y / (t / z);
	} else if (y <= 1.1e-73) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-31:
		tmp = y / (t / z)
	elif y <= 1.1e-73:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-31)
		tmp = Float64(y / Float64(t / z));
	elseif (y <= 1.1e-73)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-31)
		tmp = y / (t / z);
	elseif (y <= 1.1e-73)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-31], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-73], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3999999999999999e-31

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-/l* 96.9%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around -inf 76.6%

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

   6. Taylor expanded in z around inf 42.7%

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

      1. associate-/l* 44.2%

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

   8. Simplified 44.2%

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

      1. clear-num 44.2%

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

      2. un-div-inv 44.2%

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

   10. Applied egg-rr 44.2%

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

   if -1.3999999999999999e-31 < y < 1.1e-73

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-/l* 87.9%

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

      3. fma-define 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in y around 0 67.8%

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

   if 1.1e-73 < y

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 98.7%

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

      3. fma-define 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around -inf 76.9%

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

   6. Taylor expanded in z around inf 52.0%

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

      1. associate-/l* 55.6%

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

   8. Simplified 55.6%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.1% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 95.4%

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

   1. associate-/l* 93.4%

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

   2. *-commutative 93.4%

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

4. Applied egg-rr 93.4%

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

5. Final simplification 93.4%

   \[\leadsto x + y \cdot \frac{z - x}{t} \]
6. Add Preprocessing

Alternative 12: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

   1. +-commutative 95.4%

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

   2. associate-/l* 93.4%

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

   3. fma-define 93.4%

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

3. Simplified 93.4%

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

   1. fma-undefine 93.4%

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

   2. associate-/l* 95.4%

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

   3. *-commutative 95.4%

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

   4. associate-/l* 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

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

Alternative 13: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - x) / (t / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

   1. div-inv 95.4%

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

   2. *-commutative 95.4%

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

   3. associate-*l* 97.6%

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

4. Applied egg-rr 97.6%

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

   1. div-inv 97.6%

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

   2. clear-num 97.2%

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

6. Applied egg-rr 97.2%

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

   1. un-div-inv 97.3%

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

8. Applied egg-rr 97.3%

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

9. Final simplification 97.3%

   \[\leadsto x + \frac{z - x}{\frac{t}{y}} \]
10. Add Preprocessing

Alternative 14: 38.2% 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 95.4%

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

   1. +-commutative 95.4%

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

   2. associate-/l* 93.4%

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

   3. fma-define 93.4%

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

3. Simplified 93.4%

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

5. Taylor expanded in y around 0 41.3%

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

6. Final simplification 41.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 91.2% 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 2024059 
(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)))