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

Percentage Accurate: 92.2% → 97.9%

Time: 10.5s

Alternatives: 12

Speedup: 1.0×

• 24.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.2% 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: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.6%

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

   1. +-commutative 91.6%

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

   2. associate-*l/ 96.9%

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

   3. fma-def 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 2: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot z}{t}\\ t_2 := \frac{y}{t} \cdot \left(-x\right)\\ \mathbf{if}\;t \leq -4.6 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* y z) t)) (t_2 (* (/ y t) (- x))))
   (if (<= t -4.6e+179)
     x
     (if (<= t -1.1e+53)
       (/ y (/ t z))
       (if (<= t -3.4e-33)
         x
         (if (<= t -1.15e-176)
           t_1
           (if (<= t -5e-308)
             t_2
             (if (<= t 3.2e-141) t_1 (if (<= t 3.5e+18) t_2 x)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / t;
	double t_2 = (y / t) * -x;
	double tmp;
	if (t <= -4.6e+179) {
		tmp = x;
	} else if (t <= -1.1e+53) {
		tmp = y / (t / z);
	} else if (t <= -3.4e-33) {
		tmp = x;
	} else if (t <= -1.15e-176) {
		tmp = t_1;
	} else if (t <= -5e-308) {
		tmp = t_2;
	} else if (t <= 3.2e-141) {
		tmp = t_1;
	} else if (t <= 3.5e+18) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / t
    t_2 = (y / t) * -x
    if (t <= (-4.6d+179)) then
        tmp = x
    else if (t <= (-1.1d+53)) then
        tmp = y / (t / z)
    else if (t <= (-3.4d-33)) then
        tmp = x
    else if (t <= (-1.15d-176)) then
        tmp = t_1
    else if (t <= (-5d-308)) then
        tmp = t_2
    else if (t <= 3.2d-141) then
        tmp = t_1
    else if (t <= 3.5d+18) then
        tmp = t_2
    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 * z) / t;
	double t_2 = (y / t) * -x;
	double tmp;
	if (t <= -4.6e+179) {
		tmp = x;
	} else if (t <= -1.1e+53) {
		tmp = y / (t / z);
	} else if (t <= -3.4e-33) {
		tmp = x;
	} else if (t <= -1.15e-176) {
		tmp = t_1;
	} else if (t <= -5e-308) {
		tmp = t_2;
	} else if (t <= 3.2e-141) {
		tmp = t_1;
	} else if (t <= 3.5e+18) {
		tmp = t_2;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / t
	t_2 = (y / t) * -x
	tmp = 0
	if t <= -4.6e+179:
		tmp = x
	elif t <= -1.1e+53:
		tmp = y / (t / z)
	elif t <= -3.4e-33:
		tmp = x
	elif t <= -1.15e-176:
		tmp = t_1
	elif t <= -5e-308:
		tmp = t_2
	elif t <= 3.2e-141:
		tmp = t_1
	elif t <= 3.5e+18:
		tmp = t_2
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / t)
	t_2 = Float64(Float64(y / t) * Float64(-x))
	tmp = 0.0
	if (t <= -4.6e+179)
		tmp = x;
	elseif (t <= -1.1e+53)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= -3.4e-33)
		tmp = x;
	elseif (t <= -1.15e-176)
		tmp = t_1;
	elseif (t <= -5e-308)
		tmp = t_2;
	elseif (t <= 3.2e-141)
		tmp = t_1;
	elseif (t <= 3.5e+18)
		tmp = t_2;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / t;
	t_2 = (y / t) * -x;
	tmp = 0.0;
	if (t <= -4.6e+179)
		tmp = x;
	elseif (t <= -1.1e+53)
		tmp = y / (t / z);
	elseif (t <= -3.4e-33)
		tmp = x;
	elseif (t <= -1.15e-176)
		tmp = t_1;
	elseif (t <= -5e-308)
		tmp = t_2;
	elseif (t <= 3.2e-141)
		tmp = t_1;
	elseif (t <= 3.5e+18)
		tmp = t_2;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / t), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[t, -4.6e+179], x, If[LessEqual[t, -1.1e+53], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.4e-33], x, If[LessEqual[t, -1.15e-176], t$95$1, If[LessEqual[t, -5e-308], t$95$2, If[LessEqual[t, 3.2e-141], t$95$1, If[LessEqual[t, 3.5e+18], t$95$2, x]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.59999999999999988e179 or -1.09999999999999999e53 < t < -3.4000000000000001e-33 or 3.5e18 < t

   1. Initial program 90.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 69.6%

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

   if -4.59999999999999988e179 < t < -1.09999999999999999e53

   1. Initial program 65.1%

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

   5. Taylor expanded in y around inf 64.1%

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

   6. Taylor expanded in z around inf 53.2%

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

      1. clear-num 53.2%

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

      2. un-div-inv 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -3.4000000000000001e-33 < t < -1.1500000000000001e-176 or -4.99999999999999955e-308 < t < 3.2000000000000001e-141

   1. Initial program 99.7%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in y around inf 75.0%

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

   6. Taylor expanded in z around inf 61.8%

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

   7. Taylor expanded in y around 0 72.0%

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

   if -1.1500000000000001e-176 < t < -4.99999999999999955e-308 or 3.2000000000000001e-141 < t < 3.5e18

   1. Initial program 97.4%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in y around inf 73.3%

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

   6. Taylor expanded in z around 0 54.5%

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

      1. associate-*r/ 54.5%

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

      2. neg-mul-1 54.5%

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

   8. Simplified 54.5%

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

      1. distribute-frac-neg 54.5%

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

      2. distribute-rgt-neg-in 54.5%

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

      3. *-commutative 54.5%

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

      4. div-inv 54.5%

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

      5. associate-*l* 60.1%

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

      6. associate-/r/ 60.1%

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

      7. clear-num 60.2%

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

   10. Applied egg-rr 60.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-176}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-308}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{t} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -1.04 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-151}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-97} \lor \neg \left(x \leq 2.1 \cdot 10^{-5}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= x -1.04e-25)
     t_1
     (if (<= x -2.7e-142)
       (/ z (/ t y))
       (if (<= x -7.5e-204)
         t_1
         (if (<= x 1.8e-151)
           (/ y (/ t z))
           (if (or (<= x 1.2e-97) (not (<= x 2.1e-5))) t_1 (/ (* y z) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -1.04e-25) {
		tmp = t_1;
	} else if (x <= -2.7e-142) {
		tmp = z / (t / y);
	} else if (x <= -7.5e-204) {
		tmp = t_1;
	} else if (x <= 1.8e-151) {
		tmp = y / (t / z);
	} else if ((x <= 1.2e-97) || !(x <= 2.1e-5)) {
		tmp = t_1;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (x <= (-1.04d-25)) then
        tmp = t_1
    else if (x <= (-2.7d-142)) then
        tmp = z / (t / y)
    else if (x <= (-7.5d-204)) then
        tmp = t_1
    else if (x <= 1.8d-151) then
        tmp = y / (t / z)
    else if ((x <= 1.2d-97) .or. (.not. (x <= 2.1d-5))) then
        tmp = t_1
    else
        tmp = (y * z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -1.04e-25) {
		tmp = t_1;
	} else if (x <= -2.7e-142) {
		tmp = z / (t / y);
	} else if (x <= -7.5e-204) {
		tmp = t_1;
	} else if (x <= 1.8e-151) {
		tmp = y / (t / z);
	} else if ((x <= 1.2e-97) || !(x <= 2.1e-5)) {
		tmp = t_1;
	} else {
		tmp = (y * z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -1.04e-25:
		tmp = t_1
	elif x <= -2.7e-142:
		tmp = z / (t / y)
	elif x <= -7.5e-204:
		tmp = t_1
	elif x <= 1.8e-151:
		tmp = y / (t / z)
	elif (x <= 1.2e-97) or not (x <= 2.1e-5):
		tmp = t_1
	else:
		tmp = (y * z) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -1.04e-25)
		tmp = t_1;
	elseif (x <= -2.7e-142)
		tmp = Float64(z / Float64(t / y));
	elseif (x <= -7.5e-204)
		tmp = t_1;
	elseif (x <= 1.8e-151)
		tmp = Float64(y / Float64(t / z));
	elseif ((x <= 1.2e-97) || !(x <= 2.1e-5))
		tmp = t_1;
	else
		tmp = Float64(Float64(y * z) / t);
	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 <= -1.04e-25)
		tmp = t_1;
	elseif (x <= -2.7e-142)
		tmp = z / (t / y);
	elseif (x <= -7.5e-204)
		tmp = t_1;
	elseif (x <= 1.8e-151)
		tmp = y / (t / z);
	elseif ((x <= 1.2e-97) || ~((x <= 2.1e-5)))
		tmp = t_1;
	else
		tmp = (y * z) / t;
	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, -1.04e-25], t$95$1, If[LessEqual[x, -2.7e-142], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.5e-204], t$95$1, If[LessEqual[x, 1.8e-151], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.2e-97], N[Not[LessEqual[x, 2.1e-5]], $MachinePrecision]], t$95$1, N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.04000000000000004e-25 or -2.6999999999999998e-142 < x < -7.5000000000000003e-204 or 1.80000000000000016e-151 < x < 1.2e-97 or 2.09999999999999988e-5 < x

   1. Initial program 87.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. unsub-neg 88.5%

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

   7. Simplified 88.5%

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

   if -1.04000000000000004e-25 < x < -2.6999999999999998e-142

   1. Initial program 99.8%

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

   5. Taylor expanded in y around inf 55.5%

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

   6. Taylor expanded in z around inf 39.7%

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

   7. Taylor expanded in y around 0 61.7%

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

      1. associate-*l/ 61.6%

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

      2. *-commutative 61.6%

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

   9. Simplified 61.6%

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

       1. clear-num 61.6%

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

       2. un-div-inv 61.7%

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

   11. Applied egg-rr 61.7%

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

   if -7.5000000000000003e-204 < x < 1.80000000000000016e-151

   1. Initial program 98.0%

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

      1. associate-*l/ 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in y around inf 87.1%

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

   6. Taylor expanded in z around inf 80.1%

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

      1. clear-num 80.0%

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

      2. un-div-inv 80.3%

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

   8. Applied egg-rr 80.3%

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

   if 1.2e-97 < x < 2.09999999999999988e-5

   1. Initial program 99.9%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 75.5%

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

   6. Taylor expanded in z around inf 62.2%

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

   7. Taylor expanded in y around 0 73.8%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-142}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-204}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-151}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-97} \lor \neg \left(x \leq 2.1 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-139}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-203} \lor \neg \left(x \leq 2600\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- 1.0 (/ y t)))))
   (if (<= x -1.8e-23)
     t_1
     (if (<= x -2.25e-139)
       (/ z (/ t y))
       (if (or (<= x -6e-203) (not (<= x 2600.0))) t_1 (* y (/ (- z x) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -1.8e-23) {
		tmp = t_1;
	} else if (x <= -2.25e-139) {
		tmp = z / (t / y);
	} else if ((x <= -6e-203) || !(x <= 2600.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * (1.0d0 - (y / t))
    if (x <= (-1.8d-23)) then
        tmp = t_1
    else if (x <= (-2.25d-139)) then
        tmp = z / (t / y)
    else if ((x <= (-6d-203)) .or. (.not. (x <= 2600.0d0))) then
        tmp = t_1
    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 t_1 = x * (1.0 - (y / t));
	double tmp;
	if (x <= -1.8e-23) {
		tmp = t_1;
	} else if (x <= -2.25e-139) {
		tmp = z / (t / y);
	} else if ((x <= -6e-203) || !(x <= 2600.0)) {
		tmp = t_1;
	} else {
		tmp = y * ((z - x) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (1.0 - (y / t))
	tmp = 0
	if x <= -1.8e-23:
		tmp = t_1
	elif x <= -2.25e-139:
		tmp = z / (t / y)
	elif (x <= -6e-203) or not (x <= 2600.0):
		tmp = t_1
	else:
		tmp = y * ((z - x) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(1.0 - Float64(y / t)))
	tmp = 0.0
	if (x <= -1.8e-23)
		tmp = t_1;
	elseif (x <= -2.25e-139)
		tmp = Float64(z / Float64(t / y));
	elseif ((x <= -6e-203) || !(x <= 2600.0))
		tmp = t_1;
	else
		tmp = Float64(y * Float64(Float64(z - x) / t));
	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 <= -1.8e-23)
		tmp = t_1;
	elseif (x <= -2.25e-139)
		tmp = z / (t / y);
	elseif ((x <= -6e-203) || ~((x <= 2600.0)))
		tmp = t_1;
	else
		tmp = y * ((z - x) / t);
	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, -1.8e-23], t$95$1, If[LessEqual[x, -2.25e-139], N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -6e-203], N[Not[LessEqual[x, 2600.0]], $MachinePrecision]], t$95$1, N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7999999999999999e-23 or -2.25000000000000011e-139 < x < -6.0000000000000002e-203 or 2600 < x

   1. Initial program 86.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. unsub-neg 88.5%

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

   7. Simplified 88.5%

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

   if -1.7999999999999999e-23 < x < -2.25000000000000011e-139

   1. Initial program 99.8%

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

   5. Taylor expanded in y around inf 55.5%

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

   6. Taylor expanded in z around inf 39.7%

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

   7. Taylor expanded in y around 0 61.7%

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

      1. associate-*l/ 61.6%

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

      2. *-commutative 61.6%

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

   9. Simplified 61.6%

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

       1. clear-num 61.6%

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

       2. un-div-inv 61.7%

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

   11. Applied egg-rr 61.7%

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

   if -6.0000000000000002e-203 < x < 2600

   1. Initial program 98.6%

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

      1. associate-*l/ 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around inf 80.0%

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

   6. Taylor expanded in z around 0 79.8%

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

      1. associate-*l/ 78.5%

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

      2. associate-*r* 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*r/ 77.4%

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

      5. distribute-lft-out 80.0%

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

      6. +-commutative 80.0%

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

      7. mul-1-neg 80.0%

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

      8. sub-neg 80.0%

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

      9. div-sub 80.0%

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

   8. Simplified 80.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-139}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-203} \lor \neg \left(x \leq 2600\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -5e+179)
   x
   (if (<= t -1.15e+53)
     (* y (/ z t))
     (if (<= t -2.6e-33) x (if (<= t 3.9e+18) (* (/ y t) z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5e+179) {
		tmp = x;
	} else if (t <= -1.15e+53) {
		tmp = y * (z / t);
	} else if (t <= -2.6e-33) {
		tmp = x;
	} else if (t <= 3.9e+18) {
		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 (t <= (-5d+179)) then
        tmp = x
    else if (t <= (-1.15d+53)) then
        tmp = y * (z / t)
    else if (t <= (-2.6d-33)) then
        tmp = x
    else if (t <= 3.9d+18) 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 (t <= -5e+179) {
		tmp = x;
	} else if (t <= -1.15e+53) {
		tmp = y * (z / t);
	} else if (t <= -2.6e-33) {
		tmp = x;
	} else if (t <= 3.9e+18) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -5e+179:
		tmp = x
	elif t <= -1.15e+53:
		tmp = y * (z / t)
	elif t <= -2.6e-33:
		tmp = x
	elif t <= 3.9e+18:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5e+179)
		tmp = x;
	elseif (t <= -1.15e+53)
		tmp = Float64(y * Float64(z / t));
	elseif (t <= -2.6e-33)
		tmp = x;
	elseif (t <= 3.9e+18)
		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 (t <= -5e+179)
		tmp = x;
	elseif (t <= -1.15e+53)
		tmp = y * (z / t);
	elseif (t <= -2.6e-33)
		tmp = x;
	elseif (t <= 3.9e+18)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -5e+179], x, If[LessEqual[t, -1.15e+53], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-33], x, If[LessEqual[t, 3.9e+18], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5e179 or -1.1500000000000001e53 < t < -2.59999999999999994e-33 or 3.9e18 < t

   1. Initial program 90.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 69.6%

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

   if -5e179 < t < -1.1500000000000001e53

   1. Initial program 65.1%

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

   5. Taylor expanded in y around inf 64.1%

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

   6. Taylor expanded in z around inf 53.2%

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

   if -2.59999999999999994e-33 < t < 3.9e18

   1. Initial program 98.8%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 74.3%

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

   6. Taylor expanded in z around inf 48.4%

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

   7. Taylor expanded in y around 0 56.6%

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

      1. associate-*l/ 55.9%

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

      2. *-commutative 55.9%

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

   9. Simplified 55.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e+179)
   x
   (if (<= t -1.02e+53)
     (/ y (/ t z))
     (if (<= t -3e-33) x (if (<= t 3.4e+19) (* (/ y t) z) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e+179) {
		tmp = x;
	} else if (t <= -1.02e+53) {
		tmp = y / (t / z);
	} else if (t <= -3e-33) {
		tmp = x;
	} else if (t <= 3.4e+19) {
		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 (t <= (-4.8d+179)) then
        tmp = x
    else if (t <= (-1.02d+53)) then
        tmp = y / (t / z)
    else if (t <= (-3d-33)) then
        tmp = x
    else if (t <= 3.4d+19) 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 (t <= -4.8e+179) {
		tmp = x;
	} else if (t <= -1.02e+53) {
		tmp = y / (t / z);
	} else if (t <= -3e-33) {
		tmp = x;
	} else if (t <= 3.4e+19) {
		tmp = (y / t) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.8e+179:
		tmp = x
	elif t <= -1.02e+53:
		tmp = y / (t / z)
	elif t <= -3e-33:
		tmp = x
	elif t <= 3.4e+19:
		tmp = (y / t) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.8e+179)
		tmp = x;
	elseif (t <= -1.02e+53)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= -3e-33)
		tmp = x;
	elseif (t <= 3.4e+19)
		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 (t <= -4.8e+179)
		tmp = x;
	elseif (t <= -1.02e+53)
		tmp = y / (t / z);
	elseif (t <= -3e-33)
		tmp = x;
	elseif (t <= 3.4e+19)
		tmp = (y / t) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.8e+179], x, If[LessEqual[t, -1.02e+53], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3e-33], x, If[LessEqual[t, 3.4e+19], N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.80000000000000025e179 or -1.01999999999999999e53 < t < -3.0000000000000002e-33 or 3.4e19 < t

   1. Initial program 90.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 69.6%

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

   if -4.80000000000000025e179 < t < -1.01999999999999999e53

   1. Initial program 65.1%

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

   5. Taylor expanded in y around inf 64.1%

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

   6. Taylor expanded in z around inf 53.2%

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

      1. clear-num 53.2%

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

      2. un-div-inv 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -3.0000000000000002e-33 < t < 3.4e19

   1. Initial program 98.8%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 74.3%

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

   6. Taylor expanded in z around inf 48.4%

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

   7. Taylor expanded in y around 0 56.6%

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

      1. associate-*l/ 55.9%

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

      2. *-commutative 55.9%

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

   9. Simplified 55.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.6e+179)
   x
   (if (<= t -1.15e+53)
     (/ y (/ t z))
     (if (<= t -2.5e-33) x (if (<= t 2.7e+17) (/ (* y z) t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e+179) {
		tmp = x;
	} else if (t <= -1.15e+53) {
		tmp = y / (t / z);
	} else if (t <= -2.5e-33) {
		tmp = x;
	} else if (t <= 2.7e+17) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.6d+179)) then
        tmp = x
    else if (t <= (-1.15d+53)) then
        tmp = y / (t / z)
    else if (t <= (-2.5d-33)) then
        tmp = x
    else if (t <= 2.7d+17) then
        tmp = (y * z) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.6e+179) {
		tmp = x;
	} else if (t <= -1.15e+53) {
		tmp = y / (t / z);
	} else if (t <= -2.5e-33) {
		tmp = x;
	} else if (t <= 2.7e+17) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.6e+179:
		tmp = x
	elif t <= -1.15e+53:
		tmp = y / (t / z)
	elif t <= -2.5e-33:
		tmp = x
	elif t <= 2.7e+17:
		tmp = (y * z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.6e+179)
		tmp = x;
	elseif (t <= -1.15e+53)
		tmp = Float64(y / Float64(t / z));
	elseif (t <= -2.5e-33)
		tmp = x;
	elseif (t <= 2.7e+17)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.6e+179)
		tmp = x;
	elseif (t <= -1.15e+53)
		tmp = y / (t / z);
	elseif (t <= -2.5e-33)
		tmp = x;
	elseif (t <= 2.7e+17)
		tmp = (y * z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.6e+179], x, If[LessEqual[t, -1.15e+53], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.5e-33], x, If[LessEqual[t, 2.7e+17], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.59999999999999988e179 or -1.1500000000000001e53 < t < -2.50000000000000014e-33 or 2.7e17 < t

   1. Initial program 90.1%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 69.6%

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

   if -4.59999999999999988e179 < t < -1.1500000000000001e53

   1. Initial program 65.1%

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

   5. Taylor expanded in y around inf 64.1%

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

   6. Taylor expanded in z around inf 53.2%

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

      1. clear-num 53.2%

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

      2. un-div-inv 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -2.50000000000000014e-33 < t < 2.7e17

   1. Initial program 98.8%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in y around inf 74.3%

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

   6. Taylor expanded in z around inf 48.4%

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

   7. Taylor expanded in y around 0 56.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-20} \lor \neg \left(z \leq 1.06 \cdot 10^{-92}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e-20) (not (<= z 1.06e-92)))
   (+ x (* (/ y t) z))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-20) || !(z <= 1.06e-92)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.8d-20)) .or. (.not. (z <= 1.06d-92))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e-20) || !(z <= 1.06e-92)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e-20) or not (z <= 1.06e-92):
		tmp = x + ((y / t) * z)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e-20) || !(z <= 1.06e-92))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.8e-20) || ~((z <= 1.06e-92)))
		tmp = x + ((y / t) * z);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e-20], N[Not[LessEqual[z, 1.06e-92]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.80000000000000014e-20 or 1.06e-92 < z

   1. Initial program 93.1%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around inf 85.5%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -7.80000000000000014e-20 < z < 1.06e-92

   1. Initial program 89.5%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 88.1%

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

      1. mul-1-neg 88.1%

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

      2. unsub-neg 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-20} \lor \neg \left(z \leq 1.06 \cdot 10^{-92}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.06 \cdot 10^{-20} \lor \neg \left(z \leq 2.5 \cdot 10^{-92}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.06e-20) (not (<= z 2.5e-92)))
   (+ x (* (/ y t) z))
   (- x (/ x (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.06e-20) || !(z <= 2.5e-92)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (x / (t / y));
	}
	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 <= (-2.06d-20)) .or. (.not. (z <= 2.5d-92))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x - (x / (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.06e-20) || !(z <= 2.5e-92)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x - (x / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.06e-20) or not (z <= 2.5e-92):
		tmp = x + ((y / t) * z)
	else:
		tmp = x - (x / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.06e-20) || !(z <= 2.5e-92))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x - Float64(x / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.06e-20) || ~((z <= 2.5e-92)))
		tmp = x + ((y / t) * z);
	else
		tmp = x - (x / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.06e-20], N[Not[LessEqual[z, 2.5e-92]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.06000000000000008e-20 or 2.50000000000000006e-92 < z

   1. Initial program 93.1%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in z around inf 85.5%

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

      1. associate-*l/ 88.4%

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

      2. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   if -2.06000000000000008e-20 < z < 2.50000000000000006e-92

   1. Initial program 89.5%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

   7. Simplified 87.0%

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

      1. frac-2neg 87.0%

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

      2. div-inv 86.6%

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

      3. distribute-frac-neg 86.6%

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

      4. remove-double-neg 86.6%

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

      5. clear-num 86.6%

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

      6. add-sqr-sqrt 41.9%

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

      7. sqrt-unprod 63.8%

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

      8. sqr-neg 63.8%

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

      9. sqrt-unprod 25.9%

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

      10. add-sqr-sqrt 49.2%

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

      11. cancel-sign-sub-inv 49.2%

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

      12. clear-num 49.2%

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

      13. clear-num 49.2%

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

      14. add-sqr-sqrt 25.9%

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

      15. sqrt-unprod 63.8%

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

      16. sqr-neg 63.8%

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

      17. sqrt-unprod 41.9%

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

      18. add-sqr-sqrt 86.6%

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

   9. Applied egg-rr 86.6%

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

   10. Taylor expanded in y around 0 79.9%

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

       1. associate-/l* 89.0%

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

   12. Simplified 89.0%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.06 \cdot 10^{-20} \lor \neg \left(z \leq 2.5 \cdot 10^{-92}\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+81} \lor \neg \left(z \leq 4.5 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.95e+81) (not (<= z 4.5e-31))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.95e+81) || !(z <= 4.5e-31)) {
		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 <= (-2.95d+81)) .or. (.not. (z <= 4.5d-31))) 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 <= -2.95e+81) || !(z <= 4.5e-31)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.95e+81) or not (z <= 4.5e-31):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.95e+81) || !(z <= 4.5e-31))
		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 <= -2.95e+81) || ~((z <= 4.5e-31)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.95e+81], N[Not[LessEqual[z, 4.5e-31]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.9500000000000002e81 or 4.5000000000000004e-31 < z

   1. Initial program 92.0%

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

   5. Taylor expanded in y around inf 66.7%

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

   6. Taylor expanded in z around inf 58.9%

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

   if -2.9500000000000002e81 < z < 4.5000000000000004e-31

   1. Initial program 91.3%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 52.9%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+81} \lor \neg \left(z \leq 4.5 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.9% 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 91.6%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

5. Final simplification 96.9%

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

Alternative 12: 39.5% 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 91.6%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in y around 0 39.1%

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

6. Final simplification 39.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 91.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024041 
(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)))