Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.1% → 90.5%

Time: 9.9s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+185}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.05e+185)
   (- (+ x (* y (/ z t))) (* a (/ y t)))
   (+ x (* y (+ (/ (- z t) (- t a)) 1.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+185) {
		tmp = (x + (y * (z / t))) - (a * (y / t));
	} else {
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.05d+185)) then
        tmp = (x + (y * (z / t))) - (a * (y / t))
    else
        tmp = x + (y * (((z - t) / (t - a)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.05e+185) {
		tmp = (x + (y * (z / t))) - (a * (y / t));
	} else {
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.05e+185:
		tmp = (x + (y * (z / t))) - (a * (y / t))
	else:
		tmp = x + (y * (((z - t) / (t - a)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.05e+185)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) - Float64(a * Float64(y / t)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.05e+185)
		tmp = (x + (y * (z / t))) - (a * (y / t));
	else
		tmp = x + (y * (((z - t) / (t - a)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.05e+185], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.05e185

   1. Initial program 45.0%

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

      1. sub-neg 45.0%

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

      2. +-commutative 45.0%

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

      3. distribute-frac-neg 45.0%

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

      4. distribute-rgt-neg-out 45.0%

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

      5. associate-/l* 45.1%

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

      6. fma-define 45.3%

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

      7. distribute-frac-neg 45.3%

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

      8. distribute-neg-frac2 45.3%

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

      9. sub-neg 45.3%

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

      10. distribute-neg-in 45.3%

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

      11. remove-double-neg 45.3%

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

      12. +-commutative 45.3%

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

      13. sub-neg 45.3%

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

   3. Simplified 45.3%

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

   5. Taylor expanded in t around inf 76.0%

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

      1. associate-+r+ 86.4%

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

      2. distribute-rgt1-in 86.4%

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

      3. metadata-eval 86.4%

         \[\leadsto \left(x + \left(\color{blue}{0} \cdot y + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      4. mul0-lft 86.4%

         \[\leadsto \left(x + \left(\color{blue}{0} + \frac{y \cdot z}{t}\right)\right) - \frac{a \cdot y}{t} \]

      5. associate-+r+ 86.4%

         \[\leadsto \color{blue}{\left(\left(x + 0\right) + \frac{y \cdot z}{t}\right)} - \frac{a \cdot y}{t} \]

      6. associate-/l* 89.7%

         \[\leadsto \left(\left(x + 0\right) + \color{blue}{y \cdot \frac{z}{t}}\right) - \frac{a \cdot y}{t} \]

      7. associate-/l* 93.2%

         \[\leadsto \left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   7. Simplified 93.2%

      \[\leadsto \color{blue}{\left(\left(x + 0\right) + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}} \]

   if -1.05e185 < t

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0 84.7%

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

      1. associate--l+ 86.8%

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

      2. sub-neg 86.8%

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

      3. *-rgt-identity 86.8%

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

      4. associate-*r/ 93.2%

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

      5. distribute-rgt-neg-in 93.2%

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

      6. mul-1-neg 93.2%

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

      7. distribute-lft-in 93.2%

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

      8. mul-1-neg 93.2%

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

      9. unsub-neg 93.2%

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

   5. Simplified 93.2%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+185}:\\ \;\;\;\;\left(x + y \cdot \frac{z}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{z - t}{t - a} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot \left(a - z\right)}{t}\\ t_2 := \left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{if}\;a \leq -0.022:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-166}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y (- a z)) t))) (t_2 (- (+ x y) (* y (/ z a)))))
   (if (<= a -0.022)
     t_2
     (if (<= a -1.45e-86)
       t_1
       (if (<= a -1.06e-113)
         t_2
         (if (<= a -3.6e-166)
           (+ x (* y (/ z t)))
           (if (<= a 2.35e-267)
             t_1
             (if (<= a 4.8e-229)
               (* z (/ y (- t a)))
               (if (<= a 3.3e+21) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (a - z)) / t);
	double t_2 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -0.022) {
		tmp = t_2;
	} else if (a <= -1.45e-86) {
		tmp = t_1;
	} else if (a <= -1.06e-113) {
		tmp = t_2;
	} else if (a <= -3.6e-166) {
		tmp = x + (y * (z / t));
	} else if (a <= 2.35e-267) {
		tmp = t_1;
	} else if (a <= 4.8e-229) {
		tmp = z * (y / (t - a));
	} else if (a <= 3.3e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((y * (a - z)) / t)
    t_2 = (x + y) - (y * (z / a))
    if (a <= (-0.022d0)) then
        tmp = t_2
    else if (a <= (-1.45d-86)) then
        tmp = t_1
    else if (a <= (-1.06d-113)) then
        tmp = t_2
    else if (a <= (-3.6d-166)) then
        tmp = x + (y * (z / t))
    else if (a <= 2.35d-267) then
        tmp = t_1
    else if (a <= 4.8d-229) then
        tmp = z * (y / (t - a))
    else if (a <= 3.3d+21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (a - z)) / t);
	double t_2 = (x + y) - (y * (z / a));
	double tmp;
	if (a <= -0.022) {
		tmp = t_2;
	} else if (a <= -1.45e-86) {
		tmp = t_1;
	} else if (a <= -1.06e-113) {
		tmp = t_2;
	} else if (a <= -3.6e-166) {
		tmp = x + (y * (z / t));
	} else if (a <= 2.35e-267) {
		tmp = t_1;
	} else if (a <= 4.8e-229) {
		tmp = z * (y / (t - a));
	} else if (a <= 3.3e+21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * (a - z)) / t)
	t_2 = (x + y) - (y * (z / a))
	tmp = 0
	if a <= -0.022:
		tmp = t_2
	elif a <= -1.45e-86:
		tmp = t_1
	elif a <= -1.06e-113:
		tmp = t_2
	elif a <= -3.6e-166:
		tmp = x + (y * (z / t))
	elif a <= 2.35e-267:
		tmp = t_1
	elif a <= 4.8e-229:
		tmp = z * (y / (t - a))
	elif a <= 3.3e+21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * Float64(a - z)) / t))
	t_2 = Float64(Float64(x + y) - Float64(y * Float64(z / a)))
	tmp = 0.0
	if (a <= -0.022)
		tmp = t_2;
	elseif (a <= -1.45e-86)
		tmp = t_1;
	elseif (a <= -1.06e-113)
		tmp = t_2;
	elseif (a <= -3.6e-166)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	elseif (a <= 2.35e-267)
		tmp = t_1;
	elseif (a <= 4.8e-229)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 3.3e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * (a - z)) / t);
	t_2 = (x + y) - (y * (z / a));
	tmp = 0.0;
	if (a <= -0.022)
		tmp = t_2;
	elseif (a <= -1.45e-86)
		tmp = t_1;
	elseif (a <= -1.06e-113)
		tmp = t_2;
	elseif (a <= -3.6e-166)
		tmp = x + (y * (z / t));
	elseif (a <= 2.35e-267)
		tmp = t_1;
	elseif (a <= 4.8e-229)
		tmp = z * (y / (t - a));
	elseif (a <= 3.3e+21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.022], t$95$2, If[LessEqual[a, -1.45e-86], t$95$1, If[LessEqual[a, -1.06e-113], t$95$2, If[LessEqual[a, -3.6e-166], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.35e-267], t$95$1, If[LessEqual[a, 4.8e-229], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+21], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -0.021999999999999999 or -1.45e-86 < a < -1.05999999999999995e-113 or 3.3e21 < a

   1. Initial program 83.7%

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

   3. Taylor expanded in t around 0 81.2%

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

      1. +-commutative 81.2%

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

      2. associate-/l* 85.8%

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

   5. Simplified 85.8%

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

   if -0.021999999999999999 < a < -1.45e-86 or -3.6000000000000001e-166 < a < 2.3500000000000001e-267 or 4.8e-229 < a < 3.3e21

   1. Initial program 77.1%

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

   3. Taylor expanded in t around inf 82.4%

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

      1. associate--l+ 82.4%

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

      2. distribute-lft-out-- 82.4%

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

      3. div-sub 83.6%

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

      4. mul-1-neg 83.6%

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

      5. unsub-neg 83.6%

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

      6. *-commutative 83.6%

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

      7. distribute-lft-out-- 83.6%

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

   5. Simplified 83.6%

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

   if -1.05999999999999995e-113 < a < -3.6000000000000001e-166

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 74.5%

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

      1. associate--l+ 80.4%

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

      2. sub-neg 80.4%

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

      3. *-rgt-identity 80.4%

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

      4. associate-*r/ 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. mul-1-neg 100.0%

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

      7. distribute-lft-in 100.0%

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

      8. mul-1-neg 100.0%

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

      9. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in a around 0 84.7%

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

   if 2.3500000000000001e-267 < a < 4.8e-229

   1. Initial program 67.9%

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

      1. sub-neg 67.9%

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

      2. +-commutative 67.9%

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

      3. distribute-frac-neg 67.9%

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

      4. distribute-rgt-neg-out 67.9%

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

      5. associate-/l* 83.5%

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

      6. fma-define 84.1%

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

      7. distribute-frac-neg 84.1%

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

      8. distribute-neg-frac2 84.1%

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

      9. sub-neg 84.1%

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

      10. distribute-neg-in 84.1%

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

      11. remove-double-neg 84.1%

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

      12. +-commutative 84.1%

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

      13. sub-neg 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in z around inf 84.1%

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

      1. *-commutative 84.1%

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

      2. *-un-lft-identity 84.1%

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

      3. times-frac 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. clear-num 99.7%

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

      2. frac-times 68.1%

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

      3. *-un-lft-identity 68.1%

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

   9. Applied egg-rr 68.1%

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

       1. associate-*l/ 68.4%

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

       2. *-un-lft-identity 68.4%

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

       3. associate-/r/ 100.0%

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

   11. Applied egg-rr 100.0%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.022:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-86}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq -1.06 \cdot 10^{-113}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-166}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-267}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+21}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(\frac{y}{x} + 1\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))))
   (if (<= a -1.15e-8)
     (+ x y)
     (if (<= a -1.35e-86)
       t_1
       (if (<= a -2.15e-103)
         (* x (+ (/ y x) 1.0))
         (if (<= a -3e-115)
           (* z (/ y (- t a)))
           (if (<= a 2.3e+24) t_1 (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (a <= -1.15e-8) {
		tmp = x + y;
	} else if (a <= -1.35e-86) {
		tmp = t_1;
	} else if (a <= -2.15e-103) {
		tmp = x * ((y / x) + 1.0);
	} else if (a <= -3e-115) {
		tmp = z * (y / (t - a));
	} else if (a <= 2.3e+24) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    if (a <= (-1.15d-8)) then
        tmp = x + y
    else if (a <= (-1.35d-86)) then
        tmp = t_1
    else if (a <= (-2.15d-103)) then
        tmp = x * ((y / x) + 1.0d0)
    else if (a <= (-3d-115)) then
        tmp = z * (y / (t - a))
    else if (a <= 2.3d+24) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (z / t));
	double tmp;
	if (a <= -1.15e-8) {
		tmp = x + y;
	} else if (a <= -1.35e-86) {
		tmp = t_1;
	} else if (a <= -2.15e-103) {
		tmp = x * ((y / x) + 1.0);
	} else if (a <= -3e-115) {
		tmp = z * (y / (t - a));
	} else if (a <= 2.3e+24) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (z / t))
	tmp = 0
	if a <= -1.15e-8:
		tmp = x + y
	elif a <= -1.35e-86:
		tmp = t_1
	elif a <= -2.15e-103:
		tmp = x * ((y / x) + 1.0)
	elif a <= -3e-115:
		tmp = z * (y / (t - a))
	elif a <= 2.3e+24:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	tmp = 0.0
	if (a <= -1.15e-8)
		tmp = Float64(x + y);
	elseif (a <= -1.35e-86)
		tmp = t_1;
	elseif (a <= -2.15e-103)
		tmp = Float64(x * Float64(Float64(y / x) + 1.0));
	elseif (a <= -3e-115)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 2.3e+24)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (z / t));
	tmp = 0.0;
	if (a <= -1.15e-8)
		tmp = x + y;
	elseif (a <= -1.35e-86)
		tmp = t_1;
	elseif (a <= -2.15e-103)
		tmp = x * ((y / x) + 1.0);
	elseif (a <= -3e-115)
		tmp = z * (y / (t - a));
	elseif (a <= 2.3e+24)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-8], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.35e-86], t$95$1, If[LessEqual[a, -2.15e-103], N[(x * N[(N[(y / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3e-115], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e+24], t$95$1, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.15e-8 or 2.2999999999999999e24 < a

   1. Initial program 82.6%

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

   3. Taylor expanded in a around inf 77.4%

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

      1. +-commutative 77.4%

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

   5. Simplified 77.4%

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

   if -1.15e-8 < a < -1.34999999999999996e-86 or -3.0000000000000002e-115 < a < 2.2999999999999999e24

   1. Initial program 76.4%

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

   3. Taylor expanded in x around 0 76.4%

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

      1. associate--l+ 80.0%

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

      2. sub-neg 80.0%

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

      3. *-rgt-identity 80.0%

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

      4. associate-*r/ 86.4%

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

      5. distribute-rgt-neg-in 86.4%

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

      6. mul-1-neg 86.4%

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

      7. distribute-lft-in 86.4%

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

      8. mul-1-neg 86.4%

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

      9. unsub-neg 86.4%

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

   5. Simplified 86.4%

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

   6. Taylor expanded in a around 0 75.6%

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

   if -1.34999999999999996e-86 < a < -2.15000000000000011e-103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in a around inf 96.2%

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

   if -2.15000000000000011e-103 < a < -3.0000000000000002e-115

   1. Initial program 99.4%

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

      1. sub-neg 99.4%

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

      2. +-commutative 99.4%

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

      3. distribute-frac-neg 99.4%

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

      4. distribute-rgt-neg-out 99.4%

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

      5. associate-/l* 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg 100.0%

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

      8. distribute-neg-frac2 100.0%

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

      9. sub-neg 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. remove-double-neg 100.0%

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

      12. +-commutative 100.0%

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

      13. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 95.2%

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

      1. *-commutative 95.2%

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

      2. *-un-lft-identity 95.2%

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

      3. times-frac 95.8%

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

   7. Applied egg-rr 95.8%

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

      1. clear-num 95.5%

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

      2. frac-times 95.5%

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

      3. *-un-lft-identity 95.5%

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

   9. Applied egg-rr 95.5%

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

       1. associate-*l/ 95.8%

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

       2. *-un-lft-identity 95.8%

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

       3. associate-/r/ 95.8%

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

   11. Applied egg-rr 95.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-8}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-86}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(\frac{y}{x} + 1\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-115}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+24}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{if}\;a \leq -0.32:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-267}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (* y (- a z)) t))))
   (if (<= a -0.32)
     (+ x y)
     (if (<= a 2.35e-267)
       t_1
       (if (<= a 4.8e-229)
         (* z (/ y (- t a)))
         (if (<= a 4.3e+24) t_1 (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (a - z)) / t);
	double tmp;
	if (a <= -0.32) {
		tmp = x + y;
	} else if (a <= 2.35e-267) {
		tmp = t_1;
	} else if (a <= 4.8e-229) {
		tmp = z * (y / (t - a));
	} else if (a <= 4.3e+24) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y * (a - z)) / t)
    if (a <= (-0.32d0)) then
        tmp = x + y
    else if (a <= 2.35d-267) then
        tmp = t_1
    else if (a <= 4.8d-229) then
        tmp = z * (y / (t - a))
    else if (a <= 4.3d+24) then
        tmp = t_1
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y * (a - z)) / t);
	double tmp;
	if (a <= -0.32) {
		tmp = x + y;
	} else if (a <= 2.35e-267) {
		tmp = t_1;
	} else if (a <= 4.8e-229) {
		tmp = z * (y / (t - a));
	} else if (a <= 4.3e+24) {
		tmp = t_1;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y * (a - z)) / t)
	tmp = 0
	if a <= -0.32:
		tmp = x + y
	elif a <= 2.35e-267:
		tmp = t_1
	elif a <= 4.8e-229:
		tmp = z * (y / (t - a))
	elif a <= 4.3e+24:
		tmp = t_1
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y * Float64(a - z)) / t))
	tmp = 0.0
	if (a <= -0.32)
		tmp = Float64(x + y);
	elseif (a <= 2.35e-267)
		tmp = t_1;
	elseif (a <= 4.8e-229)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 4.3e+24)
		tmp = t_1;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y * (a - z)) / t);
	tmp = 0.0;
	if (a <= -0.32)
		tmp = x + y;
	elseif (a <= 2.35e-267)
		tmp = t_1;
	elseif (a <= 4.8e-229)
		tmp = z * (y / (t - a));
	elseif (a <= 4.3e+24)
		tmp = t_1;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -0.32], N[(x + y), $MachinePrecision], If[LessEqual[a, 2.35e-267], t$95$1, If[LessEqual[a, 4.8e-229], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.3e+24], t$95$1, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -0.320000000000000007 or 4.29999999999999987e24 < a

   1. Initial program 83.2%

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

   3. Taylor expanded in a around inf 78.0%

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

      1. +-commutative 78.0%

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

   5. Simplified 78.0%

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

   if -0.320000000000000007 < a < 2.3500000000000001e-267 or 4.8e-229 < a < 4.29999999999999987e24

   1. Initial program 77.9%

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

   3. Taylor expanded in t around inf 77.7%

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

      1. associate--l+ 77.7%

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

      2. distribute-lft-out-- 77.7%

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

      3. div-sub 78.7%

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

      4. mul-1-neg 78.7%

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

      5. unsub-neg 78.7%

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

      6. *-commutative 78.7%

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

      7. distribute-lft-out-- 78.7%

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

   5. Simplified 78.7%

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

   if 2.3500000000000001e-267 < a < 4.8e-229

   1. Initial program 67.9%

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

      1. sub-neg 67.9%

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

      2. +-commutative 67.9%

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

      3. distribute-frac-neg 67.9%

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

      4. distribute-rgt-neg-out 67.9%

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

      5. associate-/l* 83.5%

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

      6. fma-define 84.1%

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

      7. distribute-frac-neg 84.1%

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

      8. distribute-neg-frac2 84.1%

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

      9. sub-neg 84.1%

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

      10. distribute-neg-in 84.1%

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

      11. remove-double-neg 84.1%

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

      12. +-commutative 84.1%

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

      13. sub-neg 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in z around inf 84.1%

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

      1. *-commutative 84.1%

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

      2. *-un-lft-identity 84.1%

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

      3. times-frac 100.0%

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

   7. Applied egg-rr 100.0%

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

      1. clear-num 99.7%

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

      2. frac-times 68.1%

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

      3. *-un-lft-identity 68.1%

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

   9. Applied egg-rr 68.1%

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

       1. associate-*l/ 68.4%

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

       2. *-un-lft-identity 68.4%

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

       3. associate-/r/ 100.0%

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

   11. Applied egg-rr 100.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.32:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-267}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{+24}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+97} \lor \neg \left(z \leq 4.7 \cdot 10^{+271}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{x} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= z -3.4e+119)
     t_1
     (if (<= z 1.72e+44)
       (+ x y)
       (if (or (<= z 2e+97) (not (<= z 4.7e+271)))
         t_1
         (* x (+ (/ y x) 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -3.4e+119) {
		tmp = t_1;
	} else if (z <= 1.72e+44) {
		tmp = x + y;
	} else if ((z <= 2e+97) || !(z <= 4.7e+271)) {
		tmp = t_1;
	} else {
		tmp = x * ((y / x) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (z <= (-3.4d+119)) then
        tmp = t_1
    else if (z <= 1.72d+44) then
        tmp = x + y
    else if ((z <= 2d+97) .or. (.not. (z <= 4.7d+271))) then
        tmp = t_1
    else
        tmp = x * ((y / x) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (z <= -3.4e+119) {
		tmp = t_1;
	} else if (z <= 1.72e+44) {
		tmp = x + y;
	} else if ((z <= 2e+97) || !(z <= 4.7e+271)) {
		tmp = t_1;
	} else {
		tmp = x * ((y / x) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if z <= -3.4e+119:
		tmp = t_1
	elif z <= 1.72e+44:
		tmp = x + y
	elif (z <= 2e+97) or not (z <= 4.7e+271):
		tmp = t_1
	else:
		tmp = x * ((y / x) + 1.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (z <= -3.4e+119)
		tmp = t_1;
	elseif (z <= 1.72e+44)
		tmp = Float64(x + y);
	elseif ((z <= 2e+97) || !(z <= 4.7e+271))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(y / x) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (z <= -3.4e+119)
		tmp = t_1;
	elseif (z <= 1.72e+44)
		tmp = x + y;
	elseif ((z <= 2e+97) || ~((z <= 4.7e+271)))
		tmp = t_1;
	else
		tmp = x * ((y / x) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+119], t$95$1, If[LessEqual[z, 1.72e+44], N[(x + y), $MachinePrecision], If[Or[LessEqual[z, 2e+97], N[Not[LessEqual[z, 4.7e+271]], $MachinePrecision]], t$95$1, N[(x * N[(N[(y / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000013e119 or 1.72e44 < z < 2.0000000000000001e97 or 4.6999999999999998e271 < z

   1. Initial program 74.1%

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

      1. sub-neg 74.1%

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

      2. +-commutative 74.1%

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

      3. distribute-frac-neg 74.1%

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

      4. distribute-rgt-neg-out 74.1%

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

      5. associate-/l* 89.5%

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

      6. fma-define 89.7%

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

      7. distribute-frac-neg 89.7%

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

      8. distribute-neg-frac2 89.7%

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

      9. sub-neg 89.7%

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

      10. distribute-neg-in 89.7%

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

      11. remove-double-neg 89.7%

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

      12. +-commutative 89.7%

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

      13. sub-neg 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around inf 57.2%

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

      1. associate-/l* 69.7%

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

   7. Simplified 69.7%

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

   if -3.40000000000000013e119 < z < 1.72e44

   1. Initial program 81.6%

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

   3. Taylor expanded in a around inf 74.1%

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

      1. +-commutative 74.1%

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

   5. Simplified 74.1%

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

   if 2.0000000000000001e97 < z < 4.6999999999999998e271

   1. Initial program 85.0%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. associate-/l* 73.2%

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

      2. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in a around inf 58.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;z \leq 1.72 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+97} \lor \neg \left(z \leq 4.7 \cdot 10^{+271}\right):\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{x} + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{t - a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+271}:\\ \;\;\;\;x \cdot \left(\frac{y}{x} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- t a)))))
   (if (<= z -3.4e+119)
     t_1
     (if (<= z 2.45e+44)
       (+ x y)
       (if (<= z 3.7e+170)
         t_1
         (if (<= z 4.7e+271) (* x (+ (/ y x) 1.0)) (* y (/ z (- t a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (t - a));
	double tmp;
	if (z <= -3.4e+119) {
		tmp = t_1;
	} else if (z <= 2.45e+44) {
		tmp = x + y;
	} else if (z <= 3.7e+170) {
		tmp = t_1;
	} else if (z <= 4.7e+271) {
		tmp = x * ((y / x) + 1.0);
	} else {
		tmp = y * (z / (t - a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / (t - a))
    if (z <= (-3.4d+119)) then
        tmp = t_1
    else if (z <= 2.45d+44) then
        tmp = x + y
    else if (z <= 3.7d+170) then
        tmp = t_1
    else if (z <= 4.7d+271) then
        tmp = x * ((y / x) + 1.0d0)
    else
        tmp = y * (z / (t - a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (t - a));
	double tmp;
	if (z <= -3.4e+119) {
		tmp = t_1;
	} else if (z <= 2.45e+44) {
		tmp = x + y;
	} else if (z <= 3.7e+170) {
		tmp = t_1;
	} else if (z <= 4.7e+271) {
		tmp = x * ((y / x) + 1.0);
	} else {
		tmp = y * (z / (t - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (t - a))
	tmp = 0
	if z <= -3.4e+119:
		tmp = t_1
	elif z <= 2.45e+44:
		tmp = x + y
	elif z <= 3.7e+170:
		tmp = t_1
	elif z <= 4.7e+271:
		tmp = x * ((y / x) + 1.0)
	else:
		tmp = y * (z / (t - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(t - a)))
	tmp = 0.0
	if (z <= -3.4e+119)
		tmp = t_1;
	elseif (z <= 2.45e+44)
		tmp = Float64(x + y);
	elseif (z <= 3.7e+170)
		tmp = t_1;
	elseif (z <= 4.7e+271)
		tmp = Float64(x * Float64(Float64(y / x) + 1.0));
	else
		tmp = Float64(y * Float64(z / Float64(t - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (t - a));
	tmp = 0.0;
	if (z <= -3.4e+119)
		tmp = t_1;
	elseif (z <= 2.45e+44)
		tmp = x + y;
	elseif (z <= 3.7e+170)
		tmp = t_1;
	elseif (z <= 4.7e+271)
		tmp = x * ((y / x) + 1.0);
	else
		tmp = y * (z / (t - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+119], t$95$1, If[LessEqual[z, 2.45e+44], N[(x + y), $MachinePrecision], If[LessEqual[z, 3.7e+170], t$95$1, If[LessEqual[z, 4.7e+271], N[(x * N[(N[(y / x), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000013e119 or 2.45000000000000018e44 < z < 3.69999999999999987e170

   1. Initial program 81.6%

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

      1. sub-neg 81.6%

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

      2. +-commutative 81.6%

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

      3. distribute-frac-neg 81.6%

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

      4. distribute-rgt-neg-out 81.6%

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

      5. associate-/l* 91.7%

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

      6. fma-define 91.9%

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

      7. distribute-frac-neg 91.9%

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

      8. distribute-neg-frac2 91.9%

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

      9. sub-neg 91.9%

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

      10. distribute-neg-in 91.9%

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

      11. remove-double-neg 91.9%

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

      12. +-commutative 91.9%

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

      13. sub-neg 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in z around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. *-un-lft-identity 59.7%

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

      3. times-frac 65.6%

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

   7. Applied egg-rr 65.6%

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

      1. clear-num 65.5%

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

      2. frac-times 63.3%

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

      3. *-un-lft-identity 63.3%

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

   9. Applied egg-rr 63.3%

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

       1. associate-*l/ 63.4%

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

       2. *-un-lft-identity 63.4%

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

       3. associate-/r/ 65.6%

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

   11. Applied egg-rr 65.6%

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

   if -3.40000000000000013e119 < z < 2.45000000000000018e44

   1. Initial program 81.6%

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

   3. Taylor expanded in a around inf 74.1%

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

      1. +-commutative 74.1%

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

   5. Simplified 74.1%

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

   if 3.69999999999999987e170 < z < 4.6999999999999998e271

   1. Initial program 76.1%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. associate-/l* 76.0%

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

      2. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in a around inf 66.7%

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

   if 4.6999999999999998e271 < z

   1. Initial program 53.8%

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

      1. sub-neg 53.8%

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

      2. +-commutative 53.8%

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

      3. distribute-frac-neg 53.8%

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

      4. distribute-rgt-neg-out 53.8%

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

      5. associate-/l* 87.8%

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

      6. fma-define 87.8%

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

      7. distribute-frac-neg 87.8%

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

      8. distribute-neg-frac2 87.8%

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

      9. sub-neg 87.8%

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

      10. distribute-neg-in 87.8%

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

      11. remove-double-neg 87.8%

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

      12. +-commutative 87.8%

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

      13. sub-neg 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around inf 41.5%

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

      1. associate-/l* 87.5%

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

   7. Simplified 87.5%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+119}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+44}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+170}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+271}:\\ \;\;\;\;x \cdot \left(\frac{y}{x} + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+224}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+108}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.65e+224)
   (- x (/ (* y (- a z)) t))
   (if (<= t 1.12e+108) (+ (+ x y) (* y (/ z (- t a)))) (+ x (* y (/ z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+224) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t <= 1.12e+108) {
		tmp = (x + y) + (y * (z / (t - a)));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.65d+224)) then
        tmp = x - ((y * (a - z)) / t)
    else if (t <= 1.12d+108) then
        tmp = (x + y) + (y * (z / (t - a)))
    else
        tmp = x + (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.65e+224) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t <= 1.12e+108) {
		tmp = (x + y) + (y * (z / (t - a)));
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.65e+224:
		tmp = x - ((y * (a - z)) / t)
	elif t <= 1.12e+108:
		tmp = (x + y) + (y * (z / (t - a)))
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.65e+224)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	elseif (t <= 1.12e+108)
		tmp = Float64(Float64(x + y) + Float64(y * Float64(z / Float64(t - a))));
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.65e+224)
		tmp = x - ((y * (a - z)) / t);
	elseif (t <= 1.12e+108)
		tmp = (x + y) + (y * (z / (t - a)));
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.65e+224], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+108], N[(N[(x + y), $MachinePrecision] + N[(y * N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.64999999999999998e224

   1. Initial program 30.6%

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

   3. Taylor expanded in t around inf 94.6%

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

      1. associate--l+ 94.6%

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

      2. distribute-lft-out-- 94.6%

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

      3. div-sub 94.6%

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

      4. mul-1-neg 94.6%

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

      5. unsub-neg 94.6%

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

      6. *-commutative 94.6%

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

      7. distribute-lft-out-- 94.6%

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

   5. Simplified 94.6%

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

   if -1.64999999999999998e224 < t < 1.11999999999999994e108

   1. Initial program 88.8%

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

   3. Taylor expanded in z around inf 87.2%

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

      1. associate-/l* 89.2%

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

   5. Simplified 89.2%

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

   if 1.11999999999999994e108 < t

   1. Initial program 63.3%

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

   3. Taylor expanded in x around 0 63.3%

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

      1. associate--l+ 69.1%

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

      2. sub-neg 69.1%

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

      3. *-rgt-identity 69.1%

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

      4. associate-*r/ 88.3%

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

      5. distribute-rgt-neg-in 88.3%

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

      6. mul-1-neg 88.3%

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

      7. distribute-lft-in 88.4%

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

      8. mul-1-neg 88.4%

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

      9. unsub-neg 88.4%

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

   5. Simplified 88.4%

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

   6. Taylor expanded in a around 0 88.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+224}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+108}:\\ \;\;\;\;\left(x + y\right) + y \cdot \frac{z}{t - a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(\frac{z - t}{t - a} + 1\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ x (* y (+ (/ (- z t) (- t a)) 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * (((z - t) / (t - a)) + 1.0));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * (((z - t) / (t - a)) + 1.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * (((z - t) / (t - a)) + 1.0));
}

Python

def code(x, y, z, t, a):
	return x + (y * (((z - t) / (t - a)) + 1.0))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(Float64(z - t) / Float64(t - a)) + 1.0)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * (((z - t) / (t - a)) + 1.0));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(N[(z - t), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 80.3%

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

3. Taylor expanded in x around 0 80.3%

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

   1. associate--l+ 83.7%

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

   2. sub-neg 83.7%

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

   3. *-rgt-identity 83.7%

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

   4. associate-*r/ 91.3%

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

   5. distribute-rgt-neg-in 91.3%

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

   6. mul-1-neg 91.3%

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

   7. distribute-lft-in 91.3%

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

   8. mul-1-neg 91.3%

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

   9. unsub-neg 91.3%

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

5. Simplified 91.3%

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

6. Final simplification 91.3%

   \[\leadsto x + y \cdot \left(\frac{z - t}{t - a} + 1\right) \]
7. Add Preprocessing

Alternative 9: 54.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+105}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+178}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.08e+105) y (if (<= y 8e+178) x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.08e+105) {
		tmp = y;
	} else if (y <= 8e+178) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.08d+105)) then
        tmp = y
    else if (y <= 8d+178) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.08e+105) {
		tmp = y;
	} else if (y <= 8e+178) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.08e+105:
		tmp = y
	elif y <= 8e+178:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.08e+105)
		tmp = y;
	elseif (y <= 8e+178)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.08e+105)
		tmp = y;
	elseif (y <= 8e+178)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.08e+105], y, If[LessEqual[y, 8e+178], x, y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.07999999999999994e105 or 8.0000000000000004e178 < y

   1. Initial program 68.8%

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

   3. Taylor expanded in x around inf 36.9%

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

      1. associate-/l* 42.0%

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

      2. *-commutative 42.0%

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

   5. Simplified 42.0%

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

   6. Taylor expanded in a around inf 27.0%

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

   7. Taylor expanded in x around 0 42.8%

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

   if -1.07999999999999994e105 < y < 8.0000000000000004e178

   1. Initial program 84.3%

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

   3. Taylor expanded in x around inf 63.9%

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

Alternative 10: 60.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+246}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e+246) (/ y (/ a (- z))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+246) {
		tmp = y / (a / -z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.1d+246)) then
        tmp = y / (a / -z)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+246) {
		tmp = y / (a / -z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+246:
		tmp = y / (a / -z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+246)
		tmp = Float64(y / Float64(a / Float64(-z)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e+246)
		tmp = y / (a / -z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+246], N[(y / N[(a / (-z)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e246

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-out 76.6%

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

      5. associate-/l* 92.2%

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

      6. fma-define 92.4%

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

      7. distribute-frac-neg 92.4%

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

      8. distribute-neg-frac2 92.4%

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

      9. sub-neg 92.4%

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

      10. distribute-neg-in 92.4%

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

      11. remove-double-neg 92.4%

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

      12. +-commutative 92.4%

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

      13. sub-neg 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. *-commutative 76.6%

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

      2. *-un-lft-identity 76.6%

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

      3. times-frac 91.6%

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

   7. Applied egg-rr 91.6%

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

      1. clear-num 91.6%

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

      2. frac-times 95.2%

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

      3. *-un-lft-identity 95.2%

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

   9. Applied egg-rr 95.2%

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

   10. Taylor expanded in t around 0 71.9%

       \[\leadsto \frac{y}{\color{blue}{-1 \cdot \frac{a}{z}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 71.9%

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

       2. neg-mul-1 71.9%

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

   12. Simplified 71.9%

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

   if -2.1e246 < z

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+246}:\\ \;\;\;\;\frac{y}{\frac{a}{-z}}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+245}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+245) (* z (/ y (- a))) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+245) {
		tmp = z * (y / -a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9d+245)) then
        tmp = z * (y / -a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+245) {
		tmp = z * (y / -a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+245:
		tmp = z * (y / -a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+245)
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9e+245)
		tmp = z * (y / -a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+245], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e245

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-out 76.6%

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

      5. associate-/l* 92.2%

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

      6. fma-define 92.4%

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

      7. distribute-frac-neg 92.4%

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

      8. distribute-neg-frac2 92.4%

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

      9. sub-neg 92.4%

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

      10. distribute-neg-in 92.4%

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

      11. remove-double-neg 92.4%

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

      12. +-commutative 92.4%

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

      13. sub-neg 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around inf 76.6%

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

   6. Taylor expanded in t around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. *-commutative 68.4%

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

      3. neg-mul-1 68.4%

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

      4. distribute-rgt-neg-in 68.4%

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

   8. Simplified 68.4%

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

   9. Taylor expanded in z around 0 68.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   10. Step-by-step derivation

       1. mul-1-neg 68.4%

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

       2. *-commutative 68.4%

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

       3. associate-*r/ 68.0%

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

       4. distribute-rgt-neg-in 68.0%

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

   11. Simplified 68.0%

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

   if -9e245 < z

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+245}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+247}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e+247) (* y (/ z t)) (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+247) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.6d+247)) then
        tmp = y * (z / t)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e+247) {
		tmp = y * (z / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e+247:
		tmp = y * (z / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e+247)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e+247)
		tmp = y * (z / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e+247], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999991e247

   1. Initial program 76.6%

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

      1. sub-neg 76.6%

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

      2. +-commutative 76.6%

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

      3. distribute-frac-neg 76.6%

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

      4. distribute-rgt-neg-out 76.6%

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

      5. associate-/l* 92.2%

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

      6. fma-define 92.4%

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

      7. distribute-frac-neg 92.4%

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

      8. distribute-neg-frac2 92.4%

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

      9. sub-neg 92.4%

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

      10. distribute-neg-in 92.4%

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

      11. remove-double-neg 92.4%

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

      12. +-commutative 92.4%

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

      13. sub-neg 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around inf 76.6%

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

      1. *-commutative 76.6%

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

      2. *-un-lft-identity 76.6%

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

      3. times-frac 91.6%

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

   7. Applied egg-rr 91.6%

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

   8. Taylor expanded in t around inf 43.2%

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

      1. associate-/l* 58.6%

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

   10. Simplified 58.6%

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

   if -2.59999999999999991e247 < z

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. +-commutative 63.8%

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

   5. Simplified 63.8%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+247}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -1.45e+224) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+224) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.45d+224)) then
        tmp = x
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.45e+224) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.45e+224:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.45e+224)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.45e+224)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.45e+224], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.44999999999999995e224

   1. Initial program 30.6%

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

   3. Taylor expanded in x around inf 73.3%

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

   if -1.44999999999999995e224 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in a around inf 63.3%

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

      1. +-commutative 63.3%

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

   5. Simplified 63.3%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+224}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 80.3%

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

3. Taylor expanded in x around inf 49.2%

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

Developer target: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / Float64(a - t))) * y))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024101 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -1.3664970889390727e-7) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 1.4754293444577233e-239) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y))))

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