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

Percentage Accurate: 92.8% → 99.1%

Time: 11.4s

Alternatives: 17

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+308}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- z x) y) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+308)))
     (+ x (* y (/ (- z x) t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+308)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((z - x) * y) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+308)) {
		tmp = x + (y * ((z - x) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((z - x) * y) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+308):
		tmp = x + (y * ((z - x) / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(z - x) * y) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+308))
		tmp = Float64(x + Float64(y * Float64(Float64(z - x) / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((z - x) * y) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+308)))
		tmp = x + (y * ((z - x) / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+308]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 1e308 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 76.2%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 1e308

   1. Initial program 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - x\right) \cdot y}{t} \leq -\infty \lor \neg \left(x + \frac{\left(z - x\right) \cdot y}{t} \leq 10^{+308}\right):\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - x\right) \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot y}{t}\\ \mathbf{if}\;t \leq -8.1 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-264}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z y) t)))
   (if (<= t -8.1e+30)
     x
     (if (<= t -9.2e-82)
       (* z (/ y t))
       (if (<= t -7.2e-264)
         (* (- y) (/ x t))
         (if (<= t 3.1e-267)
           t_1
           (if (<= t 2.05e-156)
             (* x (/ y (- t)))
             (if (<= t 1.4e+32) t_1 x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * y) / t;
	double tmp;
	if (t <= -8.1e+30) {
		tmp = x;
	} else if (t <= -9.2e-82) {
		tmp = z * (y / t);
	} else if (t <= -7.2e-264) {
		tmp = -y * (x / t);
	} else if (t <= 3.1e-267) {
		tmp = t_1;
	} else if (t <= 2.05e-156) {
		tmp = x * (y / -t);
	} else if (t <= 1.4e+32) {
		tmp = t_1;
	} 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 = (z * y) / t
    if (t <= (-8.1d+30)) then
        tmp = x
    else if (t <= (-9.2d-82)) then
        tmp = z * (y / t)
    else if (t <= (-7.2d-264)) then
        tmp = -y * (x / t)
    else if (t <= 3.1d-267) then
        tmp = t_1
    else if (t <= 2.05d-156) then
        tmp = x * (y / -t)
    else if (t <= 1.4d+32) then
        tmp = t_1
    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 = (z * y) / t;
	double tmp;
	if (t <= -8.1e+30) {
		tmp = x;
	} else if (t <= -9.2e-82) {
		tmp = z * (y / t);
	} else if (t <= -7.2e-264) {
		tmp = -y * (x / t);
	} else if (t <= 3.1e-267) {
		tmp = t_1;
	} else if (t <= 2.05e-156) {
		tmp = x * (y / -t);
	} else if (t <= 1.4e+32) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * y) / t
	tmp = 0
	if t <= -8.1e+30:
		tmp = x
	elif t <= -9.2e-82:
		tmp = z * (y / t)
	elif t <= -7.2e-264:
		tmp = -y * (x / t)
	elif t <= 3.1e-267:
		tmp = t_1
	elif t <= 2.05e-156:
		tmp = x * (y / -t)
	elif t <= 1.4e+32:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * y) / t)
	tmp = 0.0
	if (t <= -8.1e+30)
		tmp = x;
	elseif (t <= -9.2e-82)
		tmp = Float64(z * Float64(y / t));
	elseif (t <= -7.2e-264)
		tmp = Float64(Float64(-y) * Float64(x / t));
	elseif (t <= 3.1e-267)
		tmp = t_1;
	elseif (t <= 2.05e-156)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif (t <= 1.4e+32)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * y) / t;
	tmp = 0.0;
	if (t <= -8.1e+30)
		tmp = x;
	elseif (t <= -9.2e-82)
		tmp = z * (y / t);
	elseif (t <= -7.2e-264)
		tmp = -y * (x / t);
	elseif (t <= 3.1e-267)
		tmp = t_1;
	elseif (t <= 2.05e-156)
		tmp = x * (y / -t);
	elseif (t <= 1.4e+32)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t, -8.1e+30], x, If[LessEqual[t, -9.2e-82], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-264], N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-267], t$95$1, If[LessEqual[t, 2.05e-156], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+32], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -8.0999999999999996e30 or 1.4e32 < t

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 68.1%

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

   if -8.0999999999999996e30 < t < -9.19999999999999988e-82

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-/l* 85.7%

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

      3. fma-define 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in y around -inf 75.8%

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

   6. Taylor expanded in z around inf 56.2%

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

      1. associate-/l* 46.8%

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

   8. Simplified 46.8%

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

      1. *-commutative 46.8%

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

      2. associate-*l/ 56.2%

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

   10. Applied egg-rr 56.2%

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

       1. associate-*r/ 56.4%

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

       2. *-commutative 56.4%

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

   12. Applied egg-rr 56.4%

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

   if -9.19999999999999988e-82 < t < -7.2000000000000004e-264

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 97.0%

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

      3. fma-define 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around -inf 88.0%

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

      1. associate-/l* 97.0%

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

      2. *-commutative 97.0%

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

   7. Applied egg-rr 88.1%

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

   8. Taylor expanded in z around 0 71.9%

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

      1. neg-mul-1 71.9%

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

      2. distribute-neg-frac2 71.9%

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

   10. Simplified 71.9%

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

   if -7.2000000000000004e-264 < t < 3.1000000000000001e-267 or 2.0500000000000001e-156 < t < 1.4e32

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 84.2%

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

      3. fma-define 84.2%

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

   3. Simplified 84.2%

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

   5. Taylor expanded in y around -inf 76.9%

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

   6. Taylor expanded in z around inf 57.1%

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

   if 3.1000000000000001e-267 < t < 2.0500000000000001e-156

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 89.6%

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

      3. fma-define 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in y around -inf 89.5%

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

   6. Taylor expanded in z around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. associate-/l* 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

      4. mul-1-neg 68.0%

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

      5. associate-*r/ 68.0%

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

      6. mul-1-neg 68.0%

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

   8. Simplified 68.0%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.1 \cdot 10^{+30}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-264}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-267}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-156}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+32}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.32 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-259}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-253}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ y t))))
   (if (<= t -1.32e+37)
     x
     (if (<= t -9.2e-82)
       t_1
       (if (<= t -1.12e-259)
         (* (- y) (/ x t))
         (if (<= t 4.4e-253)
           t_1
           (if (<= t 3.7e-155)
             (/ x (/ t (- y)))
             (if (<= t 4.1e+30) (/ (* z y) t) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (t <= -1.32e+37) {
		tmp = x;
	} else if (t <= -9.2e-82) {
		tmp = t_1;
	} else if (t <= -1.12e-259) {
		tmp = -y * (x / t);
	} else if (t <= 4.4e-253) {
		tmp = t_1;
	} else if (t <= 3.7e-155) {
		tmp = x / (t / -y);
	} else if (t <= 4.1e+30) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / t)
    if (t <= (-1.32d+37)) then
        tmp = x
    else if (t <= (-9.2d-82)) then
        tmp = t_1
    else if (t <= (-1.12d-259)) then
        tmp = -y * (x / t)
    else if (t <= 4.4d-253) then
        tmp = t_1
    else if (t <= 3.7d-155) then
        tmp = x / (t / -y)
    else if (t <= 4.1d+30) then
        tmp = (z * y) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (y / t);
	double tmp;
	if (t <= -1.32e+37) {
		tmp = x;
	} else if (t <= -9.2e-82) {
		tmp = t_1;
	} else if (t <= -1.12e-259) {
		tmp = -y * (x / t);
	} else if (t <= 4.4e-253) {
		tmp = t_1;
	} else if (t <= 3.7e-155) {
		tmp = x / (t / -y);
	} else if (t <= 4.1e+30) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (y / t)
	tmp = 0
	if t <= -1.32e+37:
		tmp = x
	elif t <= -9.2e-82:
		tmp = t_1
	elif t <= -1.12e-259:
		tmp = -y * (x / t)
	elif t <= 4.4e-253:
		tmp = t_1
	elif t <= 3.7e-155:
		tmp = x / (t / -y)
	elif t <= 4.1e+30:
		tmp = (z * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (t <= -1.32e+37)
		tmp = x;
	elseif (t <= -9.2e-82)
		tmp = t_1;
	elseif (t <= -1.12e-259)
		tmp = Float64(Float64(-y) * Float64(x / t));
	elseif (t <= 4.4e-253)
		tmp = t_1;
	elseif (t <= 3.7e-155)
		tmp = Float64(x / Float64(t / Float64(-y)));
	elseif (t <= 4.1e+30)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (y / t);
	tmp = 0.0;
	if (t <= -1.32e+37)
		tmp = x;
	elseif (t <= -9.2e-82)
		tmp = t_1;
	elseif (t <= -1.12e-259)
		tmp = -y * (x / t);
	elseif (t <= 4.4e-253)
		tmp = t_1;
	elseif (t <= 3.7e-155)
		tmp = x / (t / -y);
	elseif (t <= 4.1e+30)
		tmp = (z * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.32e+37], x, If[LessEqual[t, -9.2e-82], t$95$1, If[LessEqual[t, -1.12e-259], N[((-y) * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-253], t$95$1, If[LessEqual[t, 3.7e-155], N[(x / N[(t / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.1e+30], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.3199999999999999e37 or 4.10000000000000005e30 < t

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 68.1%

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

   if -1.3199999999999999e37 < t < -9.19999999999999988e-82 or -1.1199999999999999e-259 < t < 4.39999999999999992e-253

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 77.7%

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

      3. fma-define 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around -inf 84.6%

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

   6. Taylor expanded in z around inf 58.8%

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

      1. associate-/l* 46.5%

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

   8. Simplified 46.5%

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

      1. *-commutative 46.5%

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

      2. associate-*l/ 58.8%

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

   10. Applied egg-rr 58.8%

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

       1. associate-*r/ 59.0%

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

       2. *-commutative 59.0%

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

   12. Applied egg-rr 59.0%

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

   if -9.19999999999999988e-82 < t < -1.1199999999999999e-259

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 97.0%

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

      3. fma-define 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around -inf 88.0%

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

      1. associate-/l* 97.0%

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

      2. *-commutative 97.0%

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

   7. Applied egg-rr 88.1%

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

   8. Taylor expanded in z around 0 71.9%

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

      1. neg-mul-1 71.9%

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

      2. distribute-neg-frac2 71.9%

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

   10. Simplified 71.9%

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

   if 4.39999999999999992e-253 < t < 3.7e-155

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 90.9%

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

      3. fma-define 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in y around -inf 91.2%

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

   6. Taylor expanded in z around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. associate-/l* 72.7%

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

      3. distribute-rgt-neg-in 72.7%

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

      4. mul-1-neg 72.7%

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

      5. associate-*r/ 72.7%

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

      6. mul-1-neg 72.7%

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

   8. Simplified 72.7%

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

      1. add-sqr-sqrt 29.7%

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

      2. sqrt-unprod 30.1%

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

      3. distribute-frac-neg 30.1%

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

      4. distribute-frac-neg 30.1%

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

      5. sqr-neg 30.1%

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

      6. sqrt-unprod 0.4%

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

      7. add-sqr-sqrt 5.5%

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

      8. clear-num 5.5%

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

      9. div-inv 5.5%

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

      10. frac-2neg 5.5%

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

      11. distribute-frac-neg2 5.5%

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

      12. add-sqr-sqrt 5.1%

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

      13. sqrt-unprod 43.6%

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

      14. sqr-neg 43.6%

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

      15. sqrt-unprod 42.9%

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

      16. add-sqr-sqrt 72.8%

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

   10. Applied egg-rr 72.8%

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

   if 3.7e-155 < t < 4.10000000000000005e30

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 90.1%

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

      3. fma-define 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around -inf 71.1%

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

   6. Taylor expanded in z around inf 54.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-259}:\\ \;\;\;\;\left(-y\right) \cdot \frac{x}{t}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{\frac{t}{-y}}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot \left(-y\right)}{t}\\ t_2 := z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -1.58 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-251}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* x (- y)) t)) (t_2 (* z (/ y t))))
   (if (<= t -1.58e+31)
     x
     (if (<= t -1.45e-81)
       t_2
       (if (<= t -2.25e-276)
         t_1
         (if (<= t 1.2e-251)
           t_2
           (if (<= t 1.3e-155) t_1 (if (<= t 2.2e+35) (/ (* z y) t) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * -y) / t;
	double t_2 = z * (y / t);
	double tmp;
	if (t <= -1.58e+31) {
		tmp = x;
	} else if (t <= -1.45e-81) {
		tmp = t_2;
	} else if (t <= -2.25e-276) {
		tmp = t_1;
	} else if (t <= 1.2e-251) {
		tmp = t_2;
	} else if (t <= 1.3e-155) {
		tmp = t_1;
	} else if (t <= 2.2e+35) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * -y) / t
    t_2 = z * (y / t)
    if (t <= (-1.58d+31)) then
        tmp = x
    else if (t <= (-1.45d-81)) then
        tmp = t_2
    else if (t <= (-2.25d-276)) then
        tmp = t_1
    else if (t <= 1.2d-251) then
        tmp = t_2
    else if (t <= 1.3d-155) then
        tmp = t_1
    else if (t <= 2.2d+35) then
        tmp = (z * y) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * -y) / t;
	double t_2 = z * (y / t);
	double tmp;
	if (t <= -1.58e+31) {
		tmp = x;
	} else if (t <= -1.45e-81) {
		tmp = t_2;
	} else if (t <= -2.25e-276) {
		tmp = t_1;
	} else if (t <= 1.2e-251) {
		tmp = t_2;
	} else if (t <= 1.3e-155) {
		tmp = t_1;
	} else if (t <= 2.2e+35) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * -y) / t
	t_2 = z * (y / t)
	tmp = 0
	if t <= -1.58e+31:
		tmp = x
	elif t <= -1.45e-81:
		tmp = t_2
	elif t <= -2.25e-276:
		tmp = t_1
	elif t <= 1.2e-251:
		tmp = t_2
	elif t <= 1.3e-155:
		tmp = t_1
	elif t <= 2.2e+35:
		tmp = (z * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(-y)) / t)
	t_2 = Float64(z * Float64(y / t))
	tmp = 0.0
	if (t <= -1.58e+31)
		tmp = x;
	elseif (t <= -1.45e-81)
		tmp = t_2;
	elseif (t <= -2.25e-276)
		tmp = t_1;
	elseif (t <= 1.2e-251)
		tmp = t_2;
	elseif (t <= 1.3e-155)
		tmp = t_1;
	elseif (t <= 2.2e+35)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * -y) / t;
	t_2 = z * (y / t);
	tmp = 0.0;
	if (t <= -1.58e+31)
		tmp = x;
	elseif (t <= -1.45e-81)
		tmp = t_2;
	elseif (t <= -2.25e-276)
		tmp = t_1;
	elseif (t <= 1.2e-251)
		tmp = t_2;
	elseif (t <= 1.3e-155)
		tmp = t_1;
	elseif (t <= 2.2e+35)
		tmp = (z * y) / t;
	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]}, Block[{t$95$2 = N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.58e+31], x, If[LessEqual[t, -1.45e-81], t$95$2, If[LessEqual[t, -2.25e-276], t$95$1, If[LessEqual[t, 1.2e-251], t$95$2, If[LessEqual[t, 1.3e-155], t$95$1, If[LessEqual[t, 2.2e+35], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.57999999999999992e31 or 2.1999999999999999e35 < t

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 68.1%

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

   if -1.57999999999999992e31 < t < -1.44999999999999994e-81 or -2.24999999999999981e-276 < t < 1.19999999999999998e-251

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 81.7%

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

      3. fma-define 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in y around -inf 83.8%

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

   6. Taylor expanded in z around inf 59.2%

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

      1. associate-/l* 48.9%

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

   8. Simplified 48.9%

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

      1. *-commutative 48.9%

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

      2. associate-*l/ 59.2%

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

   10. Applied egg-rr 59.2%

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

       1. associate-*r/ 59.4%

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

       2. *-commutative 59.4%

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

   12. Applied egg-rr 59.4%

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

   if -1.44999999999999994e-81 < t < -2.24999999999999981e-276 or 1.19999999999999998e-251 < t < 1.30000000000000004e-155

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 91.4%

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

      3. fma-define 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in y around -inf 89.6%

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

   6. Taylor expanded in z around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. mul-1-neg 73.1%

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

      3. distribute-lft-neg-out 73.1%

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

      4. *-commutative 73.1%

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

   8. Simplified 73.1%

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

   if 1.30000000000000004e-155 < t < 2.1999999999999999e35

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 90.1%

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

      3. fma-define 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around -inf 71.1%

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

   6. Taylor expanded in z around inf 54.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+31}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-251}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-155}:\\ \;\;\;\;\frac{x \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+36}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9.2e+34)
   x
   (if (<= t -5.4e-82)
     (* z (/ y t))
     (if (<= t 9.5e-157)
       (* x (/ y (- t)))
       (if (<= t 4.9e+36) (/ (* z y) t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9.2e+34) {
		tmp = x;
	} else if (t <= -5.4e-82) {
		tmp = z * (y / t);
	} else if (t <= 9.5e-157) {
		tmp = x * (y / -t);
	} else if (t <= 4.9e+36) {
		tmp = (z * y) / 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 <= (-9.2d+34)) then
        tmp = x
    else if (t <= (-5.4d-82)) then
        tmp = z * (y / t)
    else if (t <= 9.5d-157) then
        tmp = x * (y / -t)
    else if (t <= 4.9d+36) then
        tmp = (z * y) / 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 <= -9.2e+34) {
		tmp = x;
	} else if (t <= -5.4e-82) {
		tmp = z * (y / t);
	} else if (t <= 9.5e-157) {
		tmp = x * (y / -t);
	} else if (t <= 4.9e+36) {
		tmp = (z * y) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9.2e+34:
		tmp = x
	elif t <= -5.4e-82:
		tmp = z * (y / t)
	elif t <= 9.5e-157:
		tmp = x * (y / -t)
	elif t <= 4.9e+36:
		tmp = (z * y) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9.2e+34)
		tmp = x;
	elseif (t <= -5.4e-82)
		tmp = Float64(z * Float64(y / t));
	elseif (t <= 9.5e-157)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif (t <= 4.9e+36)
		tmp = Float64(Float64(z * y) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9.2e+34)
		tmp = x;
	elseif (t <= -5.4e-82)
		tmp = z * (y / t);
	elseif (t <= 9.5e-157)
		tmp = x * (y / -t);
	elseif (t <= 4.9e+36)
		tmp = (z * y) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9.2e+34], x, If[LessEqual[t, -5.4e-82], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-157], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e+36], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.1999999999999993e34 or 4.89999999999999981e36 < t

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 98.3%

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

      3. fma-define 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 68.1%

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

   if -9.1999999999999993e34 < t < -5.4000000000000003e-82

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-/l* 85.7%

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

      3. fma-define 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in y around -inf 75.8%

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

   6. Taylor expanded in z around inf 56.2%

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

      1. associate-/l* 46.8%

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

   8. Simplified 46.8%

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

      1. *-commutative 46.8%

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

      2. associate-*l/ 56.2%

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

   10. Applied egg-rr 56.2%

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

       1. associate-*r/ 56.4%

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

       2. *-commutative 56.4%

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

   12. Applied egg-rr 56.4%

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

   if -5.4000000000000003e-82 < t < 9.50000000000000019e-157

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-/l* 88.1%

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

      3. fma-define 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around -inf 90.6%

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

   6. Taylor expanded in z around 0 64.0%

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

      1. mul-1-neg 64.0%

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

      2. associate-/l* 61.7%

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

      3. distribute-rgt-neg-in 61.7%

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

      4. mul-1-neg 61.7%

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

      5. associate-*r/ 61.7%

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

      6. mul-1-neg 61.7%

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

   8. Simplified 61.7%

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

   if 9.50000000000000019e-157 < t < 4.89999999999999981e36

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 90.1%

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

      3. fma-define 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in y around -inf 71.1%

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

   6. Taylor expanded in z around inf 54.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-157}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+36}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-147} \lor \neg \left(x \leq 9.2 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.95e-147) (not (<= x 9.2e-61)))
   (* x (- 1.0 (/ y t)))
   (* z (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e-147) || !(x <= 9.2e-61)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.95d-147)) .or. (.not. (x <= 9.2d-61))) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = z * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e-147) || !(x <= 9.2e-61)) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = z * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.95e-147) or not (x <= 9.2e-61):
		tmp = x * (1.0 - (y / t))
	else:
		tmp = z * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.95e-147) || !(x <= 9.2e-61))
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(z * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.95e-147) || ~((x <= 9.2e-61)))
		tmp = x * (1.0 - (y / t));
	else
		tmp = z * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.95e-147], N[Not[LessEqual[x, 9.2e-61]], $MachinePrecision]], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9499999999999999e-147 or 9.19999999999999967e-61 < x

   1. Initial program 90.8%

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

      1. +-commutative 90.8%

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

      2. associate-/l* 92.5%

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

      3. fma-define 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in z around 0 77.9%

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

      1. *-rgt-identity 77.9%

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

      2. mul-1-neg 77.9%

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

      3. associate-/l* 84.4%

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

      4. distribute-rgt-neg-in 84.4%

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

      5. mul-1-neg 84.4%

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

      6. distribute-lft-in 84.4%

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

      7. mul-1-neg 84.4%

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

      8. unsub-neg 84.4%

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

   7. Simplified 84.4%

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

   if -1.9499999999999999e-147 < x < 9.19999999999999967e-61

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-/l* 93.9%

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

      3. fma-define 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in y around -inf 68.3%

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

   6. Taylor expanded in z around inf 61.1%

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

      1. associate-/l* 61.2%

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

   8. Simplified 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-*l/ 61.1%

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

   10. Applied egg-rr 61.1%

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

       1. associate-*r/ 66.3%

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

       2. *-commutative 66.3%

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

   12. Applied egg-rr 66.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-147} \lor \neg \left(x \leq 9.2 \cdot 10^{-61}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+18} \lor \neg \left(y \leq 9 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1e+18) (not (<= y 9e+102)))
   (* y (/ (- z x) t))
   (* x (/ (- t y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e+18) || !(y <= 9e+102)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1d+18)) .or. (.not. (y <= 9d+102))) then
        tmp = y * ((z - x) / t)
    else
        tmp = x * ((t - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e+18) || !(y <= 9e+102)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1e+18) or not (y <= 9e+102):
		tmp = y * ((z - x) / t)
	else:
		tmp = x * ((t - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1e+18) || !(y <= 9e+102))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = Float64(x * Float64(Float64(t - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1e+18) || ~((y <= 9e+102)))
		tmp = y * ((z - x) / t);
	else
		tmp = x * ((t - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1e+18], N[Not[LessEqual[y, 9e+102]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1e18 or 9.00000000000000042e102 < y

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around -inf 73.6%

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

      1. associate-/l* 97.9%

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

      2. *-commutative 97.9%

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

   7. Applied egg-rr 83.4%

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

   if -1e18 < y < 9.00000000000000042e102

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-/l* 89.9%

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

      3. fma-define 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 76.3%

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

      1. *-rgt-identity 76.3%

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

      2. mul-1-neg 76.3%

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

      3. associate-/l* 78.8%

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

      4. distribute-rgt-neg-in 78.8%

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

      5. mul-1-neg 78.8%

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

      6. distribute-lft-in 78.8%

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

      7. mul-1-neg 78.8%

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

      8. unsub-neg 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in t around 0 78.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+18} \lor \neg \left(y \leq 9 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.9e+110)
   (* x (/ (- t y) t))
   (if (<= x 2.7e-58) (+ x (* y (/ z t))) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+110) {
		tmp = x * ((t - y) / t);
	} else if (x <= 2.7e-58) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.9d+110)) then
        tmp = x * ((t - y) / t)
    else if (x <= 2.7d-58) then
        tmp = x + (y * (z / t))
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.9e+110) {
		tmp = x * ((t - y) / t);
	} else if (x <= 2.7e-58) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.9e+110:
		tmp = x * ((t - y) / t)
	elif x <= 2.7e-58:
		tmp = x + (y * (z / t))
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.9e+110)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 2.7e-58)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.9e+110)
		tmp = x * ((t - y) / t);
	elseif (x <= 2.7e-58)
		tmp = x + (y * (z / t));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.9e+110], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-58], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.9e110

   1. Initial program 87.0%

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

      1. +-commutative 87.0%

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

      2. associate-/l* 88.8%

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

      3. fma-define 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 83.5%

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

      1. *-rgt-identity 83.5%

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

      2. mul-1-neg 83.5%

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

      3. associate-/l* 94.6%

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

      4. distribute-rgt-neg-in 94.6%

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

      5. mul-1-neg 94.6%

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

      6. distribute-lft-in 94.6%

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

      7. mul-1-neg 94.6%

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

      8. unsub-neg 94.6%

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

   7. Simplified 94.6%

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

   8. Taylor expanded in t around 0 94.6%

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

   if -2.9e110 < x < 2.6999999999999999e-58

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. associate-/l* 50.9%

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

   5. Simplified 83.8%

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

   if 2.6999999999999999e-58 < x

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-/l* 92.3%

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

      3. fma-define 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 80.9%

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

      1. *-rgt-identity 80.9%

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

      2. mul-1-neg 80.9%

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

      3. associate-/l* 88.8%

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

      4. distribute-rgt-neg-in 88.8%

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

      5. mul-1-neg 88.8%

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

      6. distribute-lft-in 88.8%

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

      7. mul-1-neg 88.8%

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

      8. unsub-neg 88.8%

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

   7. Simplified 88.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+110}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e+109)
   (* x (/ (- t y) t))
   (if (<= x 2.7e-58) (+ x (/ y (/ t z))) (* x (- 1.0 (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e+109) {
		tmp = x * ((t - y) / t);
	} else if (x <= 2.7e-58) {
		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 (x <= (-9.5d+109)) then
        tmp = x * ((t - y) / t)
    else if (x <= 2.7d-58) 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 (x <= -9.5e+109) {
		tmp = x * ((t - y) / t);
	} else if (x <= 2.7e-58) {
		tmp = x + (y / (t / z));
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e+109:
		tmp = x * ((t - y) / t)
	elif x <= 2.7e-58:
		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 (x <= -9.5e+109)
		tmp = Float64(x * Float64(Float64(t - y) / t));
	elseif (x <= 2.7e-58)
		tmp = Float64(x + Float64(y / Float64(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 (x <= -9.5e+109)
		tmp = x * ((t - y) / t);
	elseif (x <= 2.7e-58)
		tmp = x + (y / (t / z));
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e+109], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e-58], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.49999999999999972e109

   1. Initial program 87.0%

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

      1. +-commutative 87.0%

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

      2. associate-/l* 88.8%

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

      3. fma-define 88.8%

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

   3. Simplified 88.8%

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

   5. Taylor expanded in z around 0 83.5%

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

      1. *-rgt-identity 83.5%

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

      2. mul-1-neg 83.5%

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

      3. associate-/l* 94.6%

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

      4. distribute-rgt-neg-in 94.6%

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

      5. mul-1-neg 94.6%

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

      6. distribute-lft-in 94.6%

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

      7. mul-1-neg 94.6%

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

      8. unsub-neg 94.6%

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

   7. Simplified 94.6%

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

   8. Taylor expanded in t around 0 94.6%

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

   if -9.49999999999999972e109 < x < 2.6999999999999999e-58

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf 82.3%

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

      1. associate-/l* 50.9%

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

   5. Simplified 83.8%

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

      1. clear-num 83.7%

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

      2. un-div-inv 83.8%

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

   7. Applied egg-rr 83.8%

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

   if 2.6999999999999999e-58 < x

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. associate-/l* 92.3%

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

      3. fma-define 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 80.9%

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

      1. *-rgt-identity 80.9%

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

      2. mul-1-neg 80.9%

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

      3. associate-/l* 88.8%

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

      4. distribute-rgt-neg-in 88.8%

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

      5. mul-1-neg 88.8%

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

      6. distribute-lft-in 88.8%

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

      7. mul-1-neg 88.8%

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

      8. unsub-neg 88.8%

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

   7. Simplified 88.8%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-58}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 84.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-138}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.65e-138)
   (+ x (/ y (/ t z)))
   (if (<= z 7.2e-78) (* x (- 1.0 (/ y t))) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.65e-138) {
		tmp = x + (y / (t / z));
	} else if (z <= 7.2e-78) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.65d-138)) then
        tmp = x + (y / (t / z))
    else if (z <= 7.2d-78) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.65e-138) {
		tmp = x + (y / (t / z));
	} else if (z <= 7.2e-78) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.65e-138:
		tmp = x + (y / (t / z))
	elif z <= 7.2e-78:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.65e-138)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 7.2e-78)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.65e-138)
		tmp = x + (y / (t / z));
	elseif (z <= 7.2e-78)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.65e-138], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-78], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.65000000000000013e-138

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. associate-/l* 43.3%

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

   5. Simplified 85.4%

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

      1. clear-num 85.4%

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

      2. un-div-inv 85.4%

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

   7. Applied egg-rr 85.4%

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

   if -2.65000000000000013e-138 < z < 7.2000000000000005e-78

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-/l* 93.2%

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

      3. fma-define 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 90.2%

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

      1. *-rgt-identity 90.2%

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

      2. mul-1-neg 90.2%

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

      3. associate-/l* 93.3%

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

      4. distribute-rgt-neg-in 93.3%

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

      5. mul-1-neg 93.3%

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

      6. distribute-lft-in 93.3%

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

      7. mul-1-neg 93.3%

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

      8. unsub-neg 93.3%

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

   7. Simplified 93.3%

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

   if 7.2000000000000005e-78 < z

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-/l* 92.8%

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

      3. fma-define 92.8%

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

   3. Simplified 92.8%

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

      1. fma-undefine 92.8%

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

      2. associate-/l* 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 75.9%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

   9. Simplified 84.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-138}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.2e-136)
   (+ x (/ y (/ t z)))
   (if (<= z 3.5e-75) (* x (- 1.0 (/ y t))) (+ x (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.2e-136) {
		tmp = x + (y / (t / z));
	} else if (z <= 3.5e-75) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (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 <= (-2.2d-136)) then
        tmp = x + (y / (t / z))
    else if (z <= 3.5d-75) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = x + (z / (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 <= -2.2e-136) {
		tmp = x + (y / (t / z));
	} else if (z <= 3.5e-75) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = x + (z / (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.2e-136:
		tmp = x + (y / (t / z))
	elif z <= 3.5e-75:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = x + (z / (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.2e-136)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (z <= 3.5e-75)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(x + Float64(z / Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.2e-136)
		tmp = x + (y / (t / z));
	elseif (z <= 3.5e-75)
		tmp = x * (1.0 - (y / t));
	else
		tmp = x + (z / (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.2e-136], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e-75], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e-136

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. associate-/l* 43.3%

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

   5. Simplified 85.4%

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

      1. clear-num 85.4%

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

      2. un-div-inv 85.4%

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

   7. Applied egg-rr 85.4%

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

   if -2.2000000000000001e-136 < z < 3.49999999999999985e-75

   1. Initial program 94.1%

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

      1. +-commutative 94.1%

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

      2. associate-/l* 93.2%

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

      3. fma-define 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around 0 90.2%

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

      1. *-rgt-identity 90.2%

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

      2. mul-1-neg 90.2%

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

      3. associate-/l* 93.3%

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

      4. distribute-rgt-neg-in 93.3%

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

      5. mul-1-neg 93.3%

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

      6. distribute-lft-in 93.3%

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

      7. mul-1-neg 93.3%

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

      8. unsub-neg 93.3%

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

   7. Simplified 93.3%

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

   if 3.49999999999999985e-75 < z

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-/l* 92.8%

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

      3. fma-define 92.8%

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

   3. Simplified 92.8%

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

      1. fma-undefine 92.8%

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

      2. associate-/l* 88.1%

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

      3. *-commutative 88.1%

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

      4. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 75.9%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

   9. Simplified 84.1%

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

       1. clear-num 84.0%

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

       2. un-div-inv 84.1%

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

   11. Applied egg-rr 84.1%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-136}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.45e-20)
   (+ x (/ y (/ t z)))
   (if (<= t 2e-74) (/ (* (- z x) y) t) (+ x (* z (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e-20) {
		tmp = x + (y / (t / z));
	} else if (t <= 2e-74) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.45d-20)) then
        tmp = x + (y / (t / z))
    else if (t <= 2d-74) then
        tmp = ((z - x) * y) / t
    else
        tmp = x + (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.45e-20) {
		tmp = x + (y / (t / z));
	} else if (t <= 2e-74) {
		tmp = ((z - x) * y) / t;
	} else {
		tmp = x + (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.45e-20:
		tmp = x + (y / (t / z))
	elif t <= 2e-74:
		tmp = ((z - x) * y) / t
	else:
		tmp = x + (z * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.45e-20)
		tmp = Float64(x + Float64(y / Float64(t / z)));
	elseif (t <= 2e-74)
		tmp = Float64(Float64(Float64(z - x) * y) / t);
	else
		tmp = Float64(x + Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.45e-20)
		tmp = x + (y / (t / z));
	elseif (t <= 2e-74)
		tmp = ((z - x) * y) / t;
	else
		tmp = x + (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.45e-20], N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-74], N[(N[(N[(z - x), $MachinePrecision] * y), $MachinePrecision] / t), $MachinePrecision], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.45e-20

   1. Initial program 85.4%

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

   3. Taylor expanded in z around inf 84.3%

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

      1. associate-/l* 28.1%

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

   5. Simplified 90.6%

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

      1. clear-num 90.7%

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

      2. un-div-inv 90.7%

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

   7. Applied egg-rr 90.7%

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

   if -1.45e-20 < t < 1.99999999999999992e-74

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-/l* 86.4%

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

      3. fma-define 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in y around -inf 87.8%

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

   if 1.99999999999999992e-74 < t

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. associate-/l* 96.9%

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

      3. fma-define 96.9%

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

   3. Simplified 96.9%

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

      1. fma-undefine 96.9%

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

      2. associate-/l* 86.5%

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

      3. *-commutative 86.5%

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

      4. associate-/l* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 82.9%

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

      1. associate-*l/ 88.1%

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

      2. *-commutative 88.1%

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

   9. Simplified 88.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{\left(z - x\right) \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+17} \lor \neg \left(y \leq 7.2 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e+17) (not (<= y 7.2e+102))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e+17) || !(y <= 7.2e+102)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.5d+17)) .or. (.not. (y <= 7.2d+102))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e+17) || !(y <= 7.2e+102)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e+17) or not (y <= 7.2e+102):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e+17) || !(y <= 7.2e+102))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e+17) || ~((y <= 7.2e+102)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e+17], N[Not[LessEqual[y, 7.2e+102]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e17 or 7.2000000000000003e102 < y

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around -inf 73.6%

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

   6. Taylor expanded in z around inf 47.7%

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

      1. associate-/l* 55.6%

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

   8. Simplified 55.6%

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

   if -2.5e17 < y < 7.2000000000000003e102

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-/l* 89.9%

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

      3. fma-define 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around 0 59.0%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+17} \lor \neg \left(y \leq 7.2 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 54.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+17} \lor \neg \left(y \leq 7.3 \cdot 10^{+102}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.8e+17) (not (<= y 7.3e+102))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.8e+17) || !(y <= 7.3e+102)) {
		tmp = z * (y / 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 <= (-2.8d+17)) .or. (.not. (y <= 7.3d+102))) then
        tmp = z * (y / 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 <= -2.8e+17) || !(y <= 7.3e+102)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.8e+17) or not (y <= 7.3e+102):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.8e+17) || !(y <= 7.3e+102))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.8e+17) || ~((y <= 7.3e+102)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.8e+17], N[Not[LessEqual[y, 7.3e+102]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e17 or 7.29999999999999989e102 < y

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. associate-/l* 97.9%

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

      3. fma-define 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in y around -inf 73.6%

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

   6. Taylor expanded in z around inf 47.7%

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

      1. associate-/l* 55.6%

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

   8. Simplified 55.6%

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

      1. *-commutative 55.6%

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

      2. associate-*l/ 47.7%

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

   10. Applied egg-rr 47.7%

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

       1. associate-*r/ 60.4%

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

       2. *-commutative 60.4%

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

   12. Applied egg-rr 60.4%

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

   if -2.8e17 < y < 7.29999999999999989e102

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-/l* 89.9%

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

      3. fma-define 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in y around 0 59.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+17} \lor \neg \left(y \leq 7.3 \cdot 10^{+102}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 92.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. associate-/l* 92.9%

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

   2. *-commutative 92.9%

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

4. Applied egg-rr 92.9%

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

5. Final simplification 92.9%

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

Alternative 16: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. +-commutative 91.7%

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

   2. associate-/l* 92.9%

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

   3. fma-define 92.9%

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

3. Simplified 92.9%

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

   1. fma-undefine 92.9%

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

   2. associate-/l* 91.7%

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

   3. *-commutative 91.7%

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

   4. associate-/l* 98.0%

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

6. Applied egg-rr 98.0%

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

7. Final simplification 98.0%

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

Alternative 17: 38.1% 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 91.7%

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

   1. +-commutative 91.7%

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

   2. associate-/l* 92.9%

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

   3. fma-define 92.9%

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

3. Simplified 92.9%

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

5. Taylor expanded in y around 0 42.4%

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

6. Final simplification 42.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 90.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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