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

Percentage Accurate: 92.5% → 97.7%

Time: 8.1s

Alternatives: 9

Speedup: 1.0×

• 25.0% 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: 92.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× 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 95.0%

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

   1. associate-*l/ 97.8%

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

3. Simplified 97.8%

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

4. Final simplification 97.8%

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

Alternative 2: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-\frac{x}{t}\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+167}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -85000000:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -8.1 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-98}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- (/ x t)))))
   (if (<= t -9.2e+167)
     x
     (if (<= t -85000000.0)
       (* y (/ z t))
       (if (<= t -8.1e-75)
         t_1
         (if (<= t -1.25e-98)
           (/ (* y z) t)
           (if (<= t 1.75e-193) t_1 (if (<= t 6e-20) (* (/ y t) z) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -(x / t);
	double tmp;
	if (t <= -9.2e+167) {
		tmp = x;
	} else if (t <= -85000000.0) {
		tmp = y * (z / t);
	} else if (t <= -8.1e-75) {
		tmp = t_1;
	} else if (t <= -1.25e-98) {
		tmp = (y * z) / t;
	} else if (t <= 1.75e-193) {
		tmp = t_1;
	} else if (t <= 6e-20) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * -(x / t)
    if (t <= (-9.2d+167)) then
        tmp = x
    else if (t <= (-85000000.0d0)) then
        tmp = y * (z / t)
    else if (t <= (-8.1d-75)) then
        tmp = t_1
    else if (t <= (-1.25d-98)) then
        tmp = (y * z) / t
    else if (t <= 1.75d-193) then
        tmp = t_1
    else if (t <= 6d-20) 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 t_1 = y * -(x / t);
	double tmp;
	if (t <= -9.2e+167) {
		tmp = x;
	} else if (t <= -85000000.0) {
		tmp = y * (z / t);
	} else if (t <= -8.1e-75) {
		tmp = t_1;
	} else if (t <= -1.25e-98) {
		tmp = (y * z) / t;
	} else if (t <= 1.75e-193) {
		tmp = t_1;
	} else if (t <= 6e-20) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -(x / t)
	tmp = 0
	if t <= -9.2e+167:
		tmp = x
	elif t <= -85000000.0:
		tmp = y * (z / t)
	elif t <= -8.1e-75:
		tmp = t_1
	elif t <= -1.25e-98:
		tmp = (y * z) / t
	elif t <= 1.75e-193:
		tmp = t_1
	elif t <= 6e-20:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-Float64(x / t)))
	tmp = 0.0
	if (t <= -9.2e+167)
		tmp = x;
	elseif (t <= -85000000.0)
		tmp = Float64(y * Float64(z / t));
	elseif (t <= -8.1e-75)
		tmp = t_1;
	elseif (t <= -1.25e-98)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 1.75e-193)
		tmp = t_1;
	elseif (t <= 6e-20)
		tmp = Float64(Float64(y / t) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -(x / t);
	tmp = 0.0;
	if (t <= -9.2e+167)
		tmp = x;
	elseif (t <= -85000000.0)
		tmp = y * (z / t);
	elseif (t <= -8.1e-75)
		tmp = t_1;
	elseif (t <= -1.25e-98)
		tmp = (y * z) / t;
	elseif (t <= 1.75e-193)
		tmp = t_1;
	elseif (t <= 6e-20)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-N[(x / t), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[t, -9.2e+167], x, If[LessEqual[t, -85000000.0], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.1e-75], t$95$1, If[LessEqual[t, -1.25e-98], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.75e-193], t$95$1, If[LessEqual[t, 6e-20], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -9.19999999999999952e167 or 6.00000000000000057e-20 < t

   1. Initial program 91.7%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 64.1%

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

   if -9.19999999999999952e167 < t < -8.5e7

   1. Initial program 90.7%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 67.5%

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

   5. Taylor expanded in z around inf 48.9%

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

   if -8.5e7 < t < -8.10000000000000034e-75 or -1.25000000000000005e-98 < t < 1.75000000000000002e-193

   1. Initial program 98.5%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in y around inf 75.6%

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

   5. Taylor expanded in z around 0 65.1%

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

      1. associate-*r/ 65.1%

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

      2. neg-mul-1 65.1%

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

   7. Simplified 65.1%

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

   if -8.10000000000000034e-75 < t < -1.25000000000000005e-98

   1. Initial program 99.3%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in y around inf 72.2%

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

      1. sub-div 72.0%

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

      2. div-inv 72.2%

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

   6. Applied egg-rr 72.2%

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

   7. Taylor expanded in z around inf 85.4%

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

   if 1.75000000000000002e-193 < t < 6.00000000000000057e-20

   1. Initial program 99.8%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 84.5%

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

      1. *-commutative 84.5%

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

      2. sub-div 84.5%

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

      3. associate-/r/ 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around inf 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*r/ 73.6%

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

   9. Simplified 73.6%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+167}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -85000000:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -8.1 \cdot 10^{-75}:\\ \;\;\;\;y \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-98}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-193}:\\ \;\;\;\;y \cdot \left(-\frac{x}{t}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(-y\right)}{t}\\ \mathbf{if}\;t \leq -1.06 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -45000000:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-100}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y)) t)))
   (if (<= t -1.06e+169)
     x
     (if (<= t -45000000.0)
       (* y (/ z t))
       (if (<= t -3.5e-75)
         t_1
         (if (<= t -9e-100)
           (/ (* y z) t)
           (if (<= t 3.25e-193) t_1 (if (<= t 6.5e-20) (* (/ y t) z) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * -y) / t;
	double tmp;
	if (t <= -1.06e+169) {
		tmp = x;
	} else if (t <= -45000000.0) {
		tmp = y * (z / t);
	} else if (t <= -3.5e-75) {
		tmp = t_1;
	} else if (t <= -9e-100) {
		tmp = (y * z) / t;
	} else if (t <= 3.25e-193) {
		tmp = t_1;
	} else if (t <= 6.5e-20) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (x * -y) / t
    if (t <= (-1.06d+169)) then
        tmp = x
    else if (t <= (-45000000.0d0)) then
        tmp = y * (z / t)
    else if (t <= (-3.5d-75)) then
        tmp = t_1
    else if (t <= (-9d-100)) then
        tmp = (y * z) / t
    else if (t <= 3.25d-193) then
        tmp = t_1
    else if (t <= 6.5d-20) 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 t_1 = (x * -y) / t;
	double tmp;
	if (t <= -1.06e+169) {
		tmp = x;
	} else if (t <= -45000000.0) {
		tmp = y * (z / t);
	} else if (t <= -3.5e-75) {
		tmp = t_1;
	} else if (t <= -9e-100) {
		tmp = (y * z) / t;
	} else if (t <= 3.25e-193) {
		tmp = t_1;
	} else if (t <= 6.5e-20) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * -y) / t
	tmp = 0
	if t <= -1.06e+169:
		tmp = x
	elif t <= -45000000.0:
		tmp = y * (z / t)
	elif t <= -3.5e-75:
		tmp = t_1
	elif t <= -9e-100:
		tmp = (y * z) / t
	elif t <= 3.25e-193:
		tmp = t_1
	elif t <= 6.5e-20:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(-y)) / t)
	tmp = 0.0
	if (t <= -1.06e+169)
		tmp = x;
	elseif (t <= -45000000.0)
		tmp = Float64(y * Float64(z / t));
	elseif (t <= -3.5e-75)
		tmp = t_1;
	elseif (t <= -9e-100)
		tmp = Float64(Float64(y * z) / t);
	elseif (t <= 3.25e-193)
		tmp = t_1;
	elseif (t <= 6.5e-20)
		tmp = Float64(Float64(y / t) * z);
	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 <= -1.06e+169)
		tmp = x;
	elseif (t <= -45000000.0)
		tmp = y * (z / t);
	elseif (t <= -3.5e-75)
		tmp = t_1;
	elseif (t <= -9e-100)
		tmp = (y * z) / t;
	elseif (t <= 3.25e-193)
		tmp = t_1;
	elseif (t <= 6.5e-20)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * (-y)), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -1.06e+169], x, If[LessEqual[t, -45000000.0], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-75], t$95$1, If[LessEqual[t, -9e-100], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 3.25e-193], t$95$1, If[LessEqual[t, 6.5e-20], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.05999999999999995e169 or 6.50000000000000032e-20 < t

   1. Initial program 91.7%

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

      1. associate-*l/ 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 64.1%

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

   if -1.05999999999999995e169 < t < -4.5e7

   1. Initial program 90.7%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 67.5%

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

   5. Taylor expanded in z around inf 48.9%

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

   if -4.5e7 < t < -3.49999999999999985e-75 or -9.0000000000000002e-100 < t < 3.2500000000000002e-193

   1. Initial program 98.5%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in x around inf 80.1%

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

      1. *-commutative 80.1%

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

      2. distribute-lft-in 80.1%

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

      3. *-rgt-identity 80.1%

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

      4. mul-1-neg 80.1%

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

      5. distribute-rgt-neg-in 80.1%

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

      6. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in x around 0 80.2%

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

   8. Taylor expanded in y around inf 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

      3. distribute-rgt-neg-in 71.1%

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

   10. Simplified 71.1%

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

   if -3.49999999999999985e-75 < t < -9.0000000000000002e-100

   1. Initial program 99.3%

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

      1. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in y around inf 72.2%

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

      1. sub-div 72.0%

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

      2. div-inv 72.2%

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

   6. Applied egg-rr 72.2%

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

   7. Taylor expanded in z around inf 85.4%

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

   if 3.2500000000000002e-193 < t < 6.50000000000000032e-20

   1. Initial program 99.8%

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

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 84.5%

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

      1. *-commutative 84.5%

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

      2. sub-div 84.5%

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

      3. associate-/r/ 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around inf 71.2%

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

      1. *-commutative 71.2%

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

      2. associate-*r/ 73.6%

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

   9. Simplified 73.6%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.06 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -45000000:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-100}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-193}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-111} \lor \neg \left(t \leq 2.4 \cdot 10^{-194}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e-111) (not (<= t 2.4e-194)))
   (+ x (* (/ y t) z))
   (/ (* x (- y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e-111) || !(t <= 2.4e-194)) {
		tmp = x + ((y / t) * z);
	} 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 ((t <= (-2.2d-111)) .or. (.not. (t <= 2.4d-194))) then
        tmp = x + ((y / t) * z)
    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 ((t <= -2.2e-111) || !(t <= 2.4e-194)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = (x * -y) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.2e-111) or not (t <= 2.4e-194):
		tmp = x + ((y / t) * z)
	else:
		tmp = (x * -y) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e-111) || !(t <= 2.4e-194))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(Float64(x * Float64(-y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.2e-111) || ~((t <= 2.4e-194)))
		tmp = x + ((y / t) * z);
	else
		tmp = (x * -y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e-111], N[Not[LessEqual[t, 2.4e-194]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * (-y)), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e-111 or 2.4e-194 < t

   1. Initial program 93.9%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around inf 80.0%

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

      1. associate-*l/ 81.3%

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

      2. *-commutative 81.3%

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

   6. Simplified 81.3%

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

   if -2.2e-111 < t < 2.4e-194

   1. Initial program 98.2%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 78.7%

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

      1. *-commutative 78.7%

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

      2. distribute-lft-in 78.7%

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

      3. *-rgt-identity 78.7%

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

      4. mul-1-neg 78.7%

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

      5. distribute-rgt-neg-in 78.7%

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

      6. unsub-neg 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in x around 0 78.9%

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

   8. Taylor expanded in y around inf 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

      3. distribute-rgt-neg-in 74.0%

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

   10. Simplified 74.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-111} \lor \neg \left(t \leq 2.4 \cdot 10^{-194}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \end{array} \]

Alternative 5: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-7} \lor \neg \left(z \leq 2.9 \cdot 10^{+17}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-7) (not (<= z 2.9e+17)))
   (+ x (* (/ y t) z))
   (- x (* x (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-7) || !(z <= 2.9e+17)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (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 ((z <= (-1.65d-7)) .or. (.not. (z <= 2.9d+17))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x - (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 ((z <= -1.65e-7) || !(z <= 2.9e+17)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (x * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e-7) or not (z <= 2.9e+17):
		tmp = x + ((y / t) * z)
	else:
		tmp = x - (x * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-7) || !(z <= 2.9e+17))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x - Float64(x * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e-7) || ~((z <= 2.9e+17)))
		tmp = x + ((y / t) * z);
	else
		tmp = x - (x * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-7], N[Not[LessEqual[z, 2.9e+17]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6500000000000001e-7 or 2.9e17 < z

   1. Initial program 92.9%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around inf 86.0%

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

      1. associate-*l/ 88.6%

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

      2. *-commutative 88.6%

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

   6. Simplified 88.6%

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

   if -1.6500000000000001e-7 < z < 2.9e17

   1. Initial program 96.9%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. distribute-lft-in 87.1%

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

      3. *-rgt-identity 87.1%

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

      4. mul-1-neg 87.1%

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

      5. distribute-rgt-neg-in 87.1%

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

      6. unsub-neg 87.1%

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

   6. Simplified 87.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-7} \lor \neg \left(z \leq 2.9 \cdot 10^{+17}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6: 72.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.2e-112)
   (+ x (/ y (/ t z)))
   (if (<= t 7.6e-194) (/ (* x (- y)) t) (+ x (* (/ y t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.2e-112) {
		tmp = x + (y / (t / z));
	} else if (t <= 7.6e-194) {
		tmp = (x * -y) / t;
	} else {
		tmp = x + ((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 (t <= (-1.2d-112)) then
        tmp = x + (y / (t / z))
    else if (t <= 7.6d-194) then
        tmp = (x * -y) / t
    else
        tmp = x + ((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 (t <= -1.2e-112) {
		tmp = x + (y / (t / z));
	} else if (t <= 7.6e-194) {
		tmp = (x * -y) / t;
	} else {
		tmp = x + ((y / t) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.2e-112:
		tmp = x + (y / (t / z))
	elif t <= 7.6e-194:
		tmp = (x * -y) / t
	else:
		tmp = x + ((y / t) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.2e-112)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (t <= 7.6e-194)
		tmp = Float64(Float64(x * Float64(-y)) / t);
	else
		tmp = Float64(x + Float64(Float64(y / t) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.2e-112)
		tmp = x + (y / (t / z));
	elseif (t <= 7.6e-194)
		tmp = (x * -y) / t;
	else
		tmp = x + ((y / t) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.2e-112], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e-194], N[(N[(x * (-y)), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2e-112

   1. Initial program 91.4%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in z around inf 81.4%

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

   if -1.2e-112 < t < 7.6000000000000006e-194

   1. Initial program 98.2%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 78.7%

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

      1. *-commutative 78.7%

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

      2. distribute-lft-in 78.7%

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

      3. *-rgt-identity 78.7%

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

      4. mul-1-neg 78.7%

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

      5. distribute-rgt-neg-in 78.7%

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

      6. unsub-neg 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in x around 0 78.9%

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

   8. Taylor expanded in y around inf 74.0%

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

      1. associate-*r/ 74.0%

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

      2. neg-mul-1 74.0%

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

      3. distribute-rgt-neg-in 74.0%

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

   10. Simplified 74.0%

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

   if 7.6000000000000006e-194 < t

   1. Initial program 95.7%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around inf 79.5%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

   6. Simplified 82.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-112}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \end{array} \]

Alternative 7: 54.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-135} \lor \neg \left(y \leq 0.041\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-135) (not (<= y 0.041))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-135) || !(y <= 0.041)) {
		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 <= (-5.2d-135)) .or. (.not. (y <= 0.041d0))) 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 <= -5.2e-135) || !(y <= 0.041)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-135) or not (y <= 0.041):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e-135) || !(y <= 0.041))
		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 <= -5.2e-135) || ~((y <= 0.041)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e-135], N[Not[LessEqual[y, 0.041]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.20000000000000008e-135 or 0.0410000000000000017 < y

   1. Initial program 92.7%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in y around inf 78.7%

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

   5. Taylor expanded in z around inf 48.6%

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

   if -5.20000000000000008e-135 < y < 0.0410000000000000017

   1. Initial program 98.8%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 65.9%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-135} \lor \neg \left(y \leq 0.041\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 54.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;y \leq 0.24:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.2e-138) (* (/ y t) z) (if (<= y 0.24) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e-138) {
		tmp = (y / t) * z;
	} else if (y <= 0.24) {
		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 <= (-6.2d-138)) then
        tmp = (y / t) * z
    else if (y <= 0.24d0) 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 <= -6.2e-138) {
		tmp = (y / t) * z;
	} else if (y <= 0.24) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.2e-138:
		tmp = (y / t) * z
	elif y <= 0.24:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.2e-138)
		tmp = Float64(Float64(y / t) * z);
	elseif (y <= 0.24)
		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 <= -6.2e-138)
		tmp = (y / t) * z;
	elseif (y <= 0.24)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.2e-138], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[y, 0.24], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1999999999999996e-138

   1. Initial program 91.8%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 72.1%

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

      1. *-commutative 72.1%

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

      2. sub-div 75.2%

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

      3. associate-/r/ 78.4%

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

   6. Applied egg-rr 78.4%

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

   7. Taylor expanded in z around inf 45.8%

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

      1. *-commutative 45.8%

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

      2. associate-*r/ 50.2%

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

   9. Simplified 50.2%

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

   if -6.1999999999999996e-138 < y < 0.23999999999999999

   1. Initial program 98.8%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 65.9%

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

   if 0.23999999999999999 < y

   1. Initial program 94.0%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in y around inf 88.4%

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

   5. Taylor expanded in z around inf 50.1%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-138}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{elif}\;y \leq 0.24:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 9: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-*l/ 97.8%

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

3. Simplified 97.8%

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

4. Taylor expanded in y around 0 35.9%

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

5. Final simplification 35.9%

   \[\leadsto x \]

Developer target: 90.6% 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 2023174 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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