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

Percentage Accurate: 92.8% → 97.5%

Time: 7.7s

Alternatives: 12

Speedup: 1.0×

• 24.5% 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: 92.8% 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: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.2%

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

3. Taylor expanded in z around 0 87.1%

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

   1. +-commutative 87.1%

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

   2. *-commutative 87.1%

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

   3. associate-*r/ 88.5%

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

   4. mul-1-neg 88.5%

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

   5. associate-/l* 94.0%

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

   6. distribute-lft-neg-in 94.0%

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

   7. distribute-rgt-in 98.3%

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

   8. sub-neg 98.3%

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

5. Simplified 98.3%

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

Alternative 2: 48.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq -0.085:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.15e+153)
   x
   (if (<= t -1.52e+106)
     (* x (/ y (- t)))
     (if (<= t -0.085)
       (/ y (/ t z))
       (if (<= t 5.1e-85)
         (/ x (/ (- t) y))
         (if (<= t 1.2e+102) (* y (/ z t)) x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e+153) {
		tmp = x;
	} else if (t <= -1.52e+106) {
		tmp = x * (y / -t);
	} else if (t <= -0.085) {
		tmp = y / (t / z);
	} else if (t <= 5.1e-85) {
		tmp = x / (-t / y);
	} else if (t <= 1.2e+102) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.15d+153)) then
        tmp = x
    else if (t <= (-1.52d+106)) then
        tmp = x * (y / -t)
    else if (t <= (-0.085d0)) then
        tmp = y / (t / z)
    else if (t <= 5.1d-85) then
        tmp = x / (-t / y)
    else if (t <= 1.2d+102) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.15e+153) {
		tmp = x;
	} else if (t <= -1.52e+106) {
		tmp = x * (y / -t);
	} else if (t <= -0.085) {
		tmp = y / (t / z);
	} else if (t <= 5.1e-85) {
		tmp = x / (-t / y);
	} else if (t <= 1.2e+102) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.15e+153:
		tmp = x
	elif t <= -1.52e+106:
		tmp = x * (y / -t)
	elif t <= -0.085:
		tmp = y / (t / z)
	elif t <= 5.1e-85:
		tmp = x / (-t / y)
	elif t <= 1.2e+102:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.15e+153)
		tmp = x;
	elseif (t <= -1.52e+106)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif (t <= -0.085)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= 5.1e-85)
		tmp = Float64(x / Float64(Float64(-t) / y));
	elseif (t <= 1.2e+102)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.15e+153)
		tmp = x;
	elseif (t <= -1.52e+106)
		tmp = x * (y / -t);
	elseif (t <= -0.085)
		tmp = y / (t / z);
	elseif (t <= 5.1e-85)
		tmp = x / (-t / y);
	elseif (t <= 1.2e+102)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.15e+153], x, If[LessEqual[t, -1.52e+106], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.085], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-85], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+102], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.1500000000000001e153 or 1.19999999999999997e102 < t

   1. Initial program 74.2%

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

   3. Taylor expanded in y around 0 65.8%

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

   if -1.1500000000000001e153 < t < -1.52e106

   1. Initial program 85.4%

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

   3. Taylor expanded in y around -inf 63.4%

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

   4. Taylor expanded in z around 0 41.1%

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

      1. mul-1-neg 41.1%

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

      2. associate-/l* 55.6%

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

      3. distribute-rgt-neg-in 55.6%

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

      4. distribute-neg-frac2 55.6%

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

   6. Simplified 55.6%

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

   if -1.52e106 < t < -0.0850000000000000061

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 61.5%

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

   4. Taylor expanded in z around inf 52.3%

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

      1. associate-/l* 90.7%

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

   6. Simplified 52.1%

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

      1. clear-num 90.8%

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

      2. un-div-inv 90.9%

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

   8. Applied egg-rr 52.3%

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

   if -0.0850000000000000061 < t < 5.1000000000000002e-85

   1. Initial program 98.8%

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

   3. Taylor expanded in y around -inf 86.9%

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

   4. Taylor expanded in z around 0 55.6%

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

      1. associate-*r/ 55.6%

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

      2. mul-1-neg 55.6%

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

      3. distribute-lft-neg-out 55.6%

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

      4. *-commutative 55.6%

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

      5. associate-/l* 53.8%

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

   6. Simplified 53.8%

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

      1. *-commutative 53.8%

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

      2. div-inv 53.8%

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

      3. associate-*l* 59.2%

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

      4. add-sqr-sqrt 30.4%

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

      5. sqrt-unprod 26.9%

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

      6. sqr-neg 26.9%

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

      7. sqrt-unprod 2.6%

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

      8. add-sqr-sqrt 5.6%

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

      9. associate-/r/ 5.6%

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

      10. div-inv 5.6%

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

      11. frac-2neg 5.6%

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

      12. add-sqr-sqrt 3.0%

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

      13. sqrt-unprod 28.8%

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

      14. sqr-neg 28.8%

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

      15. sqrt-unprod 28.8%

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

      16. add-sqr-sqrt 59.2%

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

      17. distribute-neg-frac2 59.2%

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

   8. Applied egg-rr 59.2%

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

   if 5.1000000000000002e-85 < t < 1.19999999999999997e102

   1. Initial program 97.5%

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

   3. Taylor expanded in y around -inf 75.2%

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

   4. Taylor expanded in z around inf 64.0%

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

      1. associate-/l* 87.4%

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

   6. Simplified 66.4%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq -0.085:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{-t}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.029:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (/ y (- t)))))
   (if (<= t -1.15e+153)
     x
     (if (<= t -8e+105)
       t_1
       (if (<= t -0.029)
         (/ y (/ t z))
         (if (<= t 6.2e-80) t_1 (if (<= t 8.6e+106) (* y (/ z t)) x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y / -t);
	double tmp;
	if (t <= -1.15e+153) {
		tmp = x;
	} else if (t <= -8e+105) {
		tmp = t_1;
	} else if (t <= -0.029) {
		tmp = y / (t / z);
	} else if (t <= 6.2e-80) {
		tmp = t_1;
	} else if (t <= 8.6e+106) {
		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) :: t_1
    real(8) :: tmp
    t_1 = x * (y / -t)
    if (t <= (-1.15d+153)) then
        tmp = x
    else if (t <= (-8d+105)) then
        tmp = t_1
    else if (t <= (-0.029d0)) then
        tmp = y / (t / z)
    else if (t <= 6.2d-80) then
        tmp = t_1
    else if (t <= 8.6d+106) 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 t_1 = x * (y / -t);
	double tmp;
	if (t <= -1.15e+153) {
		tmp = x;
	} else if (t <= -8e+105) {
		tmp = t_1;
	} else if (t <= -0.029) {
		tmp = y / (t / z);
	} else if (t <= 6.2e-80) {
		tmp = t_1;
	} else if (t <= 8.6e+106) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y / -t)
	tmp = 0
	if t <= -1.15e+153:
		tmp = x
	elif t <= -8e+105:
		tmp = t_1
	elif t <= -0.029:
		tmp = y / (t / z)
	elif t <= 6.2e-80:
		tmp = t_1
	elif t <= 8.6e+106:
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y / Float64(-t)))
	tmp = 0.0
	if (t <= -1.15e+153)
		tmp = x;
	elseif (t <= -8e+105)
		tmp = t_1;
	elseif (t <= -0.029)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= 6.2e-80)
		tmp = t_1;
	elseif (t <= 8.6e+106)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y / -t);
	tmp = 0.0;
	if (t <= -1.15e+153)
		tmp = x;
	elseif (t <= -8e+105)
		tmp = t_1;
	elseif (t <= -0.029)
		tmp = y / (t / z);
	elseif (t <= 6.2e-80)
		tmp = t_1;
	elseif (t <= 8.6e+106)
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+153], x, If[LessEqual[t, -8e+105], t$95$1, If[LessEqual[t, -0.029], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-80], t$95$1, If[LessEqual[t, 8.6e+106], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1500000000000001e153 or 8.5999999999999999e106 < t

   1. Initial program 74.2%

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

   3. Taylor expanded in y around 0 65.8%

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

   if -1.1500000000000001e153 < t < -7.9999999999999995e105 or -0.0290000000000000015 < t < 6.20000000000000032e-80

   1. Initial program 97.3%

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

   3. Taylor expanded in y around -inf 84.2%

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

   4. Taylor expanded in z around 0 53.9%

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

      1. mul-1-neg 53.9%

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

      2. associate-/l* 58.8%

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

      3. distribute-rgt-neg-in 58.8%

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

      4. distribute-neg-frac2 58.8%

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

   6. Simplified 58.8%

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

   if -7.9999999999999995e105 < t < -0.0290000000000000015

   1. Initial program 99.9%

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

   3. Taylor expanded in y around -inf 61.5%

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

   4. Taylor expanded in z around inf 52.3%

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

      1. associate-/l* 90.7%

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

   6. Simplified 52.1%

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

      1. clear-num 90.8%

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

      2. un-div-inv 90.9%

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

   8. Applied egg-rr 52.3%

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

   if 6.20000000000000032e-80 < t < 8.5999999999999999e106

   1. Initial program 97.5%

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

   3. Taylor expanded in y around -inf 75.2%

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

   4. Taylor expanded in z around inf 64.0%

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

      1. associate-/l* 87.4%

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

   6. Simplified 66.4%

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

Alternative 4: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+189}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-10} \lor \neg \left(t \leq 2.4 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.6e+189)
   (+ x (* (/ y t) z))
   (if (<= t -3.25e+105)
     (* x (- 1.0 (/ y t)))
     (if (or (<= t -5.6e-10) (not (<= t 2.4e-27)))
       (+ x (/ y (/ t z)))
       (/ (* y (- z x)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.6e+189) {
		tmp = x + ((y / t) * z);
	} else if (t <= -3.25e+105) {
		tmp = x * (1.0 - (y / t));
	} else if ((t <= -5.6e-10) || !(t <= 2.4e-27)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y * (z - x)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8.6d+189)) then
        tmp = x + ((y / t) * z)
    else if (t <= (-3.25d+105)) then
        tmp = x * (1.0d0 - (y / t))
    else if ((t <= (-5.6d-10)) .or. (.not. (t <= 2.4d-27))) then
        tmp = x + (y / (t / z))
    else
        tmp = (y * (z - x)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.6e+189) {
		tmp = x + ((y / t) * z);
	} else if (t <= -3.25e+105) {
		tmp = x * (1.0 - (y / t));
	} else if ((t <= -5.6e-10) || !(t <= 2.4e-27)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y * (z - x)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.6e+189:
		tmp = x + ((y / t) * z)
	elif t <= -3.25e+105:
		tmp = x * (1.0 - (y / t))
	elif (t <= -5.6e-10) or not (t <= 2.4e-27):
		tmp = x + (y / (t / z))
	else:
		tmp = (y * (z - x)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.6e+189)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	elseif (t <= -3.25e+105)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif ((t <= -5.6e-10) || !(t <= 2.4e-27))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(Float64(y * Float64(z - x)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.6e+189)
		tmp = x + ((y / t) * z);
	elseif (t <= -3.25e+105)
		tmp = x * (1.0 - (y / t));
	elseif ((t <= -5.6e-10) || ~((t <= 2.4e-27)))
		tmp = x + (y / (t / z));
	else
		tmp = (y * (z - x)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.6e+189], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.25e+105], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -5.6e-10], N[Not[LessEqual[t, 2.4e-27]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.59999999999999995e189

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*r/ 99.5%

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

   5. Simplified 99.5%

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

   if -8.59999999999999995e189 < t < -3.25000000000000024e105

   1. Initial program 81.2%

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

   3. Taylor expanded in x around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   5. Simplified 85.7%

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

   if -3.25000000000000024e105 < t < -5.60000000000000031e-10 or 2.40000000000000002e-27 < t

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf 88.2%

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

      1. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.3%

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

   7. Applied egg-rr 92.3%

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

   if -5.60000000000000031e-10 < t < 2.40000000000000002e-27

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 88.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+189}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-10} \lor \neg \left(t \leq 2.4 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+195}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-10} \lor \neg \left(t \leq 6 \cdot 10^{-20}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8e+195)
   (+ x (* (/ y t) z))
   (if (<= t -1.16e+106)
     (* x (- 1.0 (/ y t)))
     (if (or (<= t -3.9e-10) (not (<= t 6e-20)))
       (+ x (/ y (/ t z)))
       (* (/ y t) (- z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e+195) {
		tmp = x + ((y / t) * z);
	} else if (t <= -1.16e+106) {
		tmp = x * (1.0 - (y / t));
	} else if ((t <= -3.9e-10) || !(t <= 6e-20)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8d+195)) then
        tmp = x + ((y / t) * z)
    else if (t <= (-1.16d+106)) then
        tmp = x * (1.0d0 - (y / t))
    else if ((t <= (-3.9d-10)) .or. (.not. (t <= 6d-20))) then
        tmp = x + (y / (t / z))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8e+195) {
		tmp = x + ((y / t) * z);
	} else if (t <= -1.16e+106) {
		tmp = x * (1.0 - (y / t));
	} else if ((t <= -3.9e-10) || !(t <= 6e-20)) {
		tmp = x + (y / (t / z));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8e+195:
		tmp = x + ((y / t) * z)
	elif t <= -1.16e+106:
		tmp = x * (1.0 - (y / t))
	elif (t <= -3.9e-10) or not (t <= 6e-20):
		tmp = x + (y / (t / z))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8e+195)
		tmp = Float64(x + Float64(Float64(y / t) * z));
	elseif (t <= -1.16e+106)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif ((t <= -3.9e-10) || !(t <= 6e-20))
		tmp = Float64(x + Float64(y / Float64(t / z)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8e+195)
		tmp = x + ((y / t) * z);
	elseif (t <= -1.16e+106)
		tmp = x * (1.0 - (y / t));
	elseif ((t <= -3.9e-10) || ~((t <= 6e-20)))
		tmp = x + (y / (t / z));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8e+195], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.16e+106], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3.9e-10], N[Not[LessEqual[t, 6e-20]], $MachinePrecision]], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.99999999999999982e195

   1. Initial program 68.7%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*r/ 99.5%

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

   5. Simplified 99.5%

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

   if -7.99999999999999982e195 < t < -1.16000000000000004e106

   1. Initial program 81.2%

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

   3. Taylor expanded in x around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   5. Simplified 85.7%

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

   if -1.16000000000000004e106 < t < -3.9e-10 or 6.00000000000000057e-20 < t

   1. Initial program 88.3%

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

   3. Taylor expanded in z around inf 88.2%

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

      1. associate-/l* 92.3%

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

   5. Simplified 92.3%

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

      1. clear-num 92.3%

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

      2. un-div-inv 92.3%

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

   7. Applied egg-rr 92.3%

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

   if -3.9e-10 < t < 6.00000000000000057e-20

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 88.8%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*r/ 90.8%

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

      4. mul-1-neg 90.8%

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

      5. associate-/l* 89.8%

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

      6. distribute-lft-neg-in 89.8%

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

      7. distribute-rgt-in 98.9%

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

      8. sub-neg 98.9%

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

   6. Simplified 88.8%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+195}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq -1.16 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-10} \lor \neg \left(t \leq 6 \cdot 10^{-20}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+189}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-9} \lor \neg \left(t \leq 2.3 \cdot 10^{-26}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= t -3.5e+189)
     t_1
     (if (<= t -1.4e+106)
       (* x (- 1.0 (/ y t)))
       (if (or (<= t -3e-9) (not (<= t 2.3e-26))) t_1 (* (/ y t) (- z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (t <= -3.5e+189) {
		tmp = t_1;
	} else if (t <= -1.4e+106) {
		tmp = x * (1.0 - (y / t));
	} else if ((t <= -3e-9) || !(t <= 2.3e-26)) {
		tmp = t_1;
	} else {
		tmp = (y / t) * (z - 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) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (t <= (-3.5d+189)) then
        tmp = t_1
    else if (t <= (-1.4d+106)) then
        tmp = x * (1.0d0 - (y / t))
    else if ((t <= (-3d-9)) .or. (.not. (t <= 2.3d-26))) then
        tmp = t_1
    else
        tmp = (y / t) * (z - x)
    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 / t));
	double tmp;
	if (t <= -3.5e+189) {
		tmp = t_1;
	} else if (t <= -1.4e+106) {
		tmp = x * (1.0 - (y / t));
	} else if ((t <= -3e-9) || !(t <= 2.3e-26)) {
		tmp = t_1;
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (z / t))
	tmp = 0
	if t <= -3.5e+189:
		tmp = t_1
	elif t <= -1.4e+106:
		tmp = x * (1.0 - (y / t))
	elif (t <= -3e-9) or not (t <= 2.3e-26):
		tmp = t_1
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (t <= -3.5e+189)
		tmp = t_1;
	elseif (t <= -1.4e+106)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif ((t <= -3e-9) || !(t <= 2.3e-26))
		tmp = t_1;
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (t <= -3.5e+189)
		tmp = t_1;
	elseif (t <= -1.4e+106)
		tmp = x * (1.0 - (y / t));
	elseif ((t <= -3e-9) || ~((t <= 2.3e-26)))
		tmp = t_1;
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.5e+189], t$95$1, If[LessEqual[t, -1.4e+106], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -3e-9], N[Not[LessEqual[t, 2.3e-26]], $MachinePrecision]], t$95$1, N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.49999999999999996e189 or -1.39999999999999996e106 < t < -2.99999999999999998e-9 or 2.30000000000000009e-26 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in z around inf 86.9%

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

      1. associate-/l* 92.6%

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

   5. Simplified 92.6%

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

   if -3.49999999999999996e189 < t < -1.39999999999999996e106

   1. Initial program 81.2%

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

   3. Taylor expanded in x around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   5. Simplified 85.7%

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

   if -2.99999999999999998e-9 < t < 2.30000000000000009e-26

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 88.8%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*r/ 90.8%

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

      4. mul-1-neg 90.8%

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

      5. associate-/l* 89.8%

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

      6. distribute-lft-neg-in 89.8%

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

      7. distribute-rgt-in 98.9%

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

      8. sub-neg 98.9%

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

   6. Simplified 88.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{+189}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-9} \lor \neg \left(t \leq 2.3 \cdot 10^{-26}\right):\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-177} \lor \neg \left(x \leq 2.55 \cdot 10^{-59}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= x -1.95e-33)
     t_1
     (if (<= x -4.3e-151)
       (/ y (/ t z))
       (if (or (<= x -7e-177) (not (<= x 2.55e-59))) t_1 (* (/ y t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -1.95e-33) {
		tmp = t_1;
	} else if (x <= -4.3e-151) {
		tmp = y / (t / z);
	} else if ((x <= -7e-177) || !(x <= 2.55e-59)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (x <= (-1.95d-33)) then
        tmp = t_1
    else if (x <= (-4.3d-151)) then
        tmp = y / (t / z)
    else if ((x <= (-7d-177)) .or. (.not. (x <= 2.55d-59))) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -1.95e-33) {
		tmp = t_1;
	} else if (x <= -4.3e-151) {
		tmp = y / (t / z);
	} else if ((x <= -7e-177) || !(x <= 2.55e-59)) {
		tmp = t_1;
	} else {
		tmp = (y / t) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -1.95e-33:
		tmp = t_1
	elif x <= -4.3e-151:
		tmp = y / (t / z)
	elif (x <= -7e-177) or not (x <= 2.55e-59):
		tmp = t_1
	else:
		tmp = (y / t) * z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -1.95e-33)
		tmp = t_1;
	elseif (x <= -4.3e-151)
		tmp = Float64(y / Float64(t / z));
	elseif ((x <= -7e-177) || !(x <= 2.55e-59))
		tmp = t_1;
	else
		tmp = Float64(Float64(y / t) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (1.0 - (y / t));
	tmp = 0.0;
	if (x <= -1.95e-33)
		tmp = t_1;
	elseif (x <= -4.3e-151)
		tmp = y / (t / z);
	elseif ((x <= -7e-177) || ~((x <= 2.55e-59)))
		tmp = t_1;
	else
		tmp = (y / t) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e-33], t$95$1, If[LessEqual[x, -4.3e-151], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -7e-177], N[Not[LessEqual[x, 2.55e-59]], $MachinePrecision]], t$95$1, N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.94999999999999987e-33 or -4.30000000000000018e-151 < x < -7.0000000000000003e-177 or 2.5499999999999998e-59 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf 86.8%

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

      1. mul-1-neg 86.8%

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

      2. unsub-neg 86.8%

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

   5. Simplified 86.8%

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

   if -1.94999999999999987e-33 < x < -4.30000000000000018e-151

   1. Initial program 95.8%

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

   3. Taylor expanded in y around -inf 75.7%

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

   4. Taylor expanded in z around inf 58.5%

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

      1. associate-/l* 82.2%

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

   6. Simplified 62.3%

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

      1. clear-num 82.2%

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

      2. un-div-inv 82.3%

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

   8. Applied egg-rr 62.4%

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

   if -7.0000000000000003e-177 < x < 2.5499999999999998e-59

   1. Initial program 91.0%

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

   3. Taylor expanded in y around -inf 76.1%

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

   4. Taylor expanded in z around inf 69.9%

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

      1. *-commutative 84.5%

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

      2. associate-*r/ 90.9%

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

   6. Simplified 77.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-151}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-177} \lor \neg \left(x \leq 2.55 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{t} \cdot z\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y t) z))))
   (if (<= t -4.2e+188)
     t_1
     (if (<= t -7.4e+105)
       (* x (- 1.0 (/ y t)))
       (if (<= t -3.8e-6)
         t_1
         (if (<= t 1.3e-25) (* (/ y t) (- z x)) (+ x (* y (/ z t)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / t) * z);
	double tmp;
	if (t <= -4.2e+188) {
		tmp = t_1;
	} else if (t <= -7.4e+105) {
		tmp = x * (1.0 - (y / t));
	} else if (t <= -3.8e-6) {
		tmp = t_1;
	} else if (t <= 1.3e-25) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y / t) * z)
    if (t <= (-4.2d+188)) then
        tmp = t_1
    else if (t <= (-7.4d+105)) then
        tmp = x * (1.0d0 - (y / t))
    else if (t <= (-3.8d-6)) then
        tmp = t_1
    else if (t <= 1.3d-25) then
        tmp = (y / t) * (z - x)
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / t) * z);
	double tmp;
	if (t <= -4.2e+188) {
		tmp = t_1;
	} else if (t <= -7.4e+105) {
		tmp = x * (1.0 - (y / t));
	} else if (t <= -3.8e-6) {
		tmp = t_1;
	} else if (t <= 1.3e-25) {
		tmp = (y / t) * (z - x);
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / t) * z)
	tmp = 0
	if t <= -4.2e+188:
		tmp = t_1
	elif t <= -7.4e+105:
		tmp = x * (1.0 - (y / t))
	elif t <= -3.8e-6:
		tmp = t_1
	elif t <= 1.3e-25:
		tmp = (y / t) * (z - x)
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / t) * z))
	tmp = 0.0
	if (t <= -4.2e+188)
		tmp = t_1;
	elseif (t <= -7.4e+105)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (t <= -3.8e-6)
		tmp = t_1;
	elseif (t <= 1.3e-25)
		tmp = Float64(Float64(y / t) * Float64(z - x));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / t) * z);
	tmp = 0.0;
	if (t <= -4.2e+188)
		tmp = t_1;
	elseif (t <= -7.4e+105)
		tmp = x * (1.0 - (y / t));
	elseif (t <= -3.8e-6)
		tmp = t_1;
	elseif (t <= 1.3e-25)
		tmp = (y / t) * (z - x);
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+188], t$95$1, If[LessEqual[t, -7.4e+105], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-6], t$95$1, If[LessEqual[t, 1.3e-25], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.19999999999999973e188 or -7.3999999999999997e105 < t < -3.8e-6

   1. Initial program 82.7%

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

   3. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*r/ 95.8%

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

   5. Simplified 95.8%

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

   if -4.19999999999999973e188 < t < -7.3999999999999997e105

   1. Initial program 81.2%

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

   3. Taylor expanded in x around inf 85.7%

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

      1. mul-1-neg 85.7%

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

      2. unsub-neg 85.7%

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

   5. Simplified 85.7%

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

   if -3.8e-6 < t < 1.3e-25

   1. Initial program 98.9%

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

   3. Taylor expanded in y around -inf 88.8%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. +-commutative 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*r/ 90.8%

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

      4. mul-1-neg 90.8%

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

      5. associate-/l* 89.8%

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

      6. distribute-lft-neg-in 89.8%

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

      7. distribute-rgt-in 98.9%

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

      8. sub-neg 98.9%

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

   6. Simplified 88.8%

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

   if 1.3e-25 < t

   1. Initial program 85.0%

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

   3. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 92.6%

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

   5. Simplified 92.6%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+188}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-6}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-20} \lor \neg \left(x \leq 3.5 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5e-20) (not (<= x 3.5e+14)))
   (* x (- 1.0 (/ y t)))
   (* (/ y t) (- z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e-20) || !(x <= 3.5e+14)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - 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 ((x <= (-5d-20)) .or. (.not. (x <= 3.5d+14))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = (y / t) * (z - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5e-20) || !(x <= 3.5e+14)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = (y / t) * (z - x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5e-20) or not (x <= 3.5e+14):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = (y / t) * (z - x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5e-20) || !(x <= 3.5e+14))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(Float64(y / t) * Float64(z - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5e-20) || ~((x <= 3.5e+14)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = (y / t) * (z - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5e-20], N[Not[LessEqual[x, 3.5e+14]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / t), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.9999999999999999e-20 or 3.5e14 < x

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 90.6%

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

      1. mul-1-neg 90.6%

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

      2. unsub-neg 90.6%

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

   5. Simplified 90.6%

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

   if -4.9999999999999999e-20 < x < 3.5e14

   1. Initial program 93.9%

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

   3. Taylor expanded in y around -inf 74.7%

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

   4. Taylor expanded in z around 0 73.9%

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

      1. +-commutative 93.1%

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

      2. *-commutative 93.1%

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

      3. associate-*r/ 94.5%

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

      4. mul-1-neg 94.5%

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

      5. associate-/l* 93.6%

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

      6. distribute-lft-neg-in 93.6%

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

      7. distribute-rgt-in 96.8%

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

      8. sub-neg 96.8%

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

   6. Simplified 78.1%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-20} \lor \neg \left(x \leq 3.5 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13} \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e-13) (not (<= z 1.12e-8))) (* (/ y t) z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-13) || !(z <= 1.12e-8)) {
		tmp = (y / t) * z;
	} 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 ((z <= (-1.45d-13)) .or. (.not. (z <= 1.12d-8))) then
        tmp = (y / t) * z
    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 ((z <= -1.45e-13) || !(z <= 1.12e-8)) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.45e-13) or not (z <= 1.12e-8):
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.45e-13) || !(z <= 1.12e-8))
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.45e-13) || ~((z <= 1.12e-8)))
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.45e-13], N[Not[LessEqual[z, 1.12e-8]], $MachinePrecision]], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e-13 or 1.11999999999999994e-8 < z

   1. Initial program 86.4%

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

   3. Taylor expanded in y around -inf 72.6%

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

   4. Taylor expanded in z around inf 60.3%

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

      1. *-commutative 77.8%

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

      2. associate-*r/ 83.8%

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

   6. Simplified 65.3%

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

   if -1.4499999999999999e-13 < z < 1.11999999999999994e-8

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 47.3%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13} \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-12} \lor \neg \left(z \leq 2.9 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.4e-12) (not (<= z 2.9e-12))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.4e-12) || !(z <= 2.9e-12)) {
		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 ((z <= (-1.4d-12)) .or. (.not. (z <= 2.9d-12))) 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 ((z <= -1.4e-12) || !(z <= 2.9e-12)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.4e-12) or not (z <= 2.9e-12):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.4e-12) || !(z <= 2.9e-12))
		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 ((z <= -1.4e-12) || ~((z <= 2.9e-12)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.4e-12], N[Not[LessEqual[z, 2.9e-12]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4000000000000001e-12 or 2.9000000000000002e-12 < z

   1. Initial program 86.4%

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

   3. Taylor expanded in y around -inf 72.6%

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

   4. Taylor expanded in z around inf 60.3%

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

      1. associate-/l* 82.9%

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

   6. Simplified 63.9%

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

   if -1.4000000000000001e-12 < z < 2.9000000000000002e-12

   1. Initial program 94.0%

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

   3. Taylor expanded in y around 0 47.3%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-12} \lor \neg \left(z \leq 2.9 \cdot 10^{-12}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.8% 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 90.2%

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

3. Taylor expanded in y around 0 34.4%

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

Developer target: 91.1% 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 2024081 
(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)))