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

Percentage Accurate: 76.9% → 88.3%

Time: 10.8s

Alternatives: 15

Speedup: 0.7×

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: 76.9% 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: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\left(x + y\right) + \frac{1}{\frac{\frac{a - t}{t - z}}{y}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -1e-149)
     (+ (+ x y) (/ 1.0 (/ (/ (- a t) (- t z)) y)))
     (if (<= t_1 0.0)
       (+ x (/ (* y (- z a)) t))
       (- (+ x y) (/ 1.0 (/ (/ (- a t) y) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-149) {
		tmp = (x + y) + (1.0 / (((a - t) / (t - z)) / y));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	}
	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) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-1d-149)) then
        tmp = (x + y) + (1.0d0 / (((a - t) / (t - z)) / y))
    else if (t_1 <= 0.0d0) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = (x + y) - (1.0d0 / (((a - t) / y) / z))
    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) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-149) {
		tmp = (x + y) + (1.0 / (((a - t) / (t - z)) / y));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -1e-149:
		tmp = (x + y) + (1.0 / (((a - t) / (t - z)) / y))
	elif t_1 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = (x + y) - (1.0 / (((a - t) / y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-149)
		tmp = Float64(Float64(x + y) + Float64(1.0 / Float64(Float64(Float64(a - t) / Float64(t - z)) / y)));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(1.0 / Float64(Float64(Float64(a - t) / y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -1e-149)
		tmp = (x + y) + (1.0 / (((a - t) / (t - z)) / y));
	elseif (t_1 <= 0.0)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-149], N[(N[(x + y), $MachinePrecision] + N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.99999999999999979e-150

   1. Initial program 78.3%

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

      1. clear-num 78.3%

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

      2. inv-pow 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-/r* 92.4%

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

   4. Applied egg-rr 92.4%

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

      1. unpow-1 92.4%

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

      2. associate-/l/ 78.3%

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

      3. *-commutative 78.3%

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

   6. Simplified 78.3%

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

      1. associate-/r* 92.4%

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

      2. div-inv 92.4%

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

   8. Applied egg-rr 92.4%

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

      1. associate-*l/ 93.4%

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

      2. un-div-inv 93.4%

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

   10. Applied egg-rr 93.4%

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

   if -9.99999999999999979e-150 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 18.5%

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

   3. Taylor expanded in t around inf 96.1%

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

      1. associate--l+ 96.1%

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

      2. distribute-lft-out-- 96.1%

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

      3. div-sub 96.1%

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

      4. mul-1-neg 96.1%

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

      5. unsub-neg 96.1%

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

      6. *-commutative 96.1%

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

      7. distribute-lft-out-- 96.1%

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

   5. Simplified 96.1%

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

   if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 89.1%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-/r* 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. unpow-1 92.8%

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

      2. associate-/l/ 89.1%

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

      3. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in z around inf 91.3%

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

      1. associate-/r* 92.9%

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

   9. Simplified 92.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\left(x + y\right) + \frac{1}{\frac{\frac{a - t}{t - z}}{y}}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\left(x + y\right) + y \cdot \left(\frac{1}{a - t} \cdot \left(t - z\right)\right)\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -1e-149)
     (+ (+ x y) (* y (* (/ 1.0 (- a t)) (- t z))))
     (if (<= t_1 0.0)
       (+ x (/ (* y (- z a)) t))
       (- (+ x y) (/ 1.0 (/ (/ (- a t) y) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-149) {
		tmp = (x + y) + (y * ((1.0 / (a - t)) * (t - z)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	}
	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) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-1d-149)) then
        tmp = (x + y) + (y * ((1.0d0 / (a - t)) * (t - z)))
    else if (t_1 <= 0.0d0) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = (x + y) - (1.0d0 / (((a - t) / y) / z))
    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) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -1e-149) {
		tmp = (x + y) + (y * ((1.0 / (a - t)) * (t - z)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -1e-149:
		tmp = (x + y) + (y * ((1.0 / (a - t)) * (t - z)))
	elif t_1 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = (x + y) - (1.0 / (((a - t) / y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e-149)
		tmp = Float64(Float64(x + y) + Float64(y * Float64(Float64(1.0 / Float64(a - t)) * Float64(t - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(1.0 / Float64(Float64(Float64(a - t) / y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -1e-149)
		tmp = (x + y) + (y * ((1.0 / (a - t)) * (t - z)));
	elseif (t_1 <= 0.0)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-149], N[(N[(x + y), $MachinePrecision] + N[(y * N[(N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.99999999999999979e-150

   1. Initial program 78.3%

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

      1. div-inv 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-*l* 93.4%

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

   4. Applied egg-rr 93.4%

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

   if -9.99999999999999979e-150 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 18.5%

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

   3. Taylor expanded in t around inf 96.1%

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

      1. associate--l+ 96.1%

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

      2. distribute-lft-out-- 96.1%

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

      3. div-sub 96.1%

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

      4. mul-1-neg 96.1%

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

      5. unsub-neg 96.1%

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

      6. *-commutative 96.1%

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

      7. distribute-lft-out-- 96.1%

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

   5. Simplified 96.1%

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

   if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 89.1%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-/r* 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. unpow-1 92.8%

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

      2. associate-/l/ 89.1%

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

      3. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in z around inf 91.3%

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

      1. associate-/r* 92.9%

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

   9. Simplified 92.9%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-149}:\\ \;\;\;\;\left(x + y\right) + y \cdot \left(\frac{1}{a - t} \cdot \left(t - z\right)\right)\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-117}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* y (- z t)) (- a t)))))
   (if (<= t_1 -5e-117)
     (+ (+ x y) (* (- z t) (/ y (- t a))))
     (if (<= t_1 0.0)
       (+ x (/ (* y (- z a)) t))
       (- (+ x y) (/ 1.0 (/ (/ (- a t) y) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -5e-117) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	}
	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) - ((y * (z - t)) / (a - t))
    if (t_1 <= (-5d-117)) then
        tmp = (x + y) + ((z - t) * (y / (t - a)))
    else if (t_1 <= 0.0d0) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = (x + y) - (1.0d0 / (((a - t) / y) / z))
    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) - ((y * (z - t)) / (a - t));
	double tmp;
	if (t_1 <= -5e-117) {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	} else if (t_1 <= 0.0) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - ((y * (z - t)) / (a - t))
	tmp = 0
	if t_1 <= -5e-117:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	elif t_1 <= 0.0:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = (x + y) - (1.0 / (((a - t) / y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -5e-117)
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	elseif (t_1 <= 0.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(1.0 / Float64(Float64(Float64(a - t) / y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -5e-117)
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	elseif (t_1 <= 0.0)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = (x + y) - (1.0 / (((a - t) / y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-117], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(1.0 / N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5e-117

   1. Initial program 78.4%

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

   3. Taylor expanded in y around 0 78.4%

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

      1. associate-*l/ 93.2%

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

   5. Simplified 93.2%

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

   if -5e-117 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 20.5%

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

   3. Taylor expanded in t around inf 94.3%

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

      1. associate--l+ 94.3%

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

      2. distribute-lft-out-- 94.3%

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

      3. div-sub 94.3%

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

      4. mul-1-neg 94.3%

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

      5. unsub-neg 94.3%

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

      6. *-commutative 94.3%

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

      7. distribute-lft-out-- 94.3%

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

   5. Simplified 94.3%

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

   if 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 89.1%

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

      1. clear-num 89.1%

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

      2. inv-pow 89.1%

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

      3. *-commutative 89.1%

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

      4. associate-/r* 92.8%

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

   4. Applied egg-rr 92.8%

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

      1. unpow-1 92.8%

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

      2. associate-/l/ 89.1%

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

      3. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in z around inf 91.3%

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

      1. associate-/r* 92.9%

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

   9. Simplified 92.9%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq -5 \cdot 10^{-117}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \mathbf{elif}\;\left(x + y\right) - \frac{y \cdot \left(z - t\right)}{a - t} \leq 0:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{1}{\frac{\frac{a - t}{y}}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-183}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+33)
   (+ x y)
   (if (<= a -1.7e-20)
     (/ z (/ (- t a) y))
     (if (<= a -2.75e-82)
       x
       (if (<= a -6.6e-183)
         (* z (/ y (- t a)))
         (if (<= a 3.8e+59) (+ x (/ (* y (- z a)) t)) (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = z / ((t - a) / y);
	} else if (a <= -2.75e-82) {
		tmp = x;
	} else if (a <= -6.6e-183) {
		tmp = z * (y / (t - a));
	} else if (a <= 3.8e+59) {
		tmp = x + ((y * (z - a)) / 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 (a <= (-4.8d+33)) then
        tmp = x + y
    else if (a <= (-1.7d-20)) then
        tmp = z / ((t - a) / y)
    else if (a <= (-2.75d-82)) then
        tmp = x
    else if (a <= (-6.6d-183)) then
        tmp = z * (y / (t - a))
    else if (a <= 3.8d+59) then
        tmp = x + ((y * (z - a)) / 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 (a <= -4.8e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = z / ((t - a) / y);
	} else if (a <= -2.75e-82) {
		tmp = x;
	} else if (a <= -6.6e-183) {
		tmp = z * (y / (t - a));
	} else if (a <= 3.8e+59) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+33:
		tmp = x + y
	elif a <= -1.7e-20:
		tmp = z / ((t - a) / y)
	elif a <= -2.75e-82:
		tmp = x
	elif a <= -6.6e-183:
		tmp = z * (y / (t - a))
	elif a <= 3.8e+59:
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+33)
		tmp = Float64(x + y);
	elseif (a <= -1.7e-20)
		tmp = Float64(z / Float64(Float64(t - a) / y));
	elseif (a <= -2.75e-82)
		tmp = x;
	elseif (a <= -6.6e-183)
		tmp = Float64(z * Float64(y / Float64(t - a)));
	elseif (a <= 3.8e+59)
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e+33)
		tmp = x + y;
	elseif (a <= -1.7e-20)
		tmp = z / ((t - a) / y);
	elseif (a <= -2.75e-82)
		tmp = x;
	elseif (a <= -6.6e-183)
		tmp = z * (y / (t - a));
	elseif (a <= 3.8e+59)
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+33], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.7e-20], N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.75e-82], x, If[LessEqual[a, -6.6e-183], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+59], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.8e33 or 3.8000000000000001e59 < a

   1. Initial program 78.6%

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

   3. Taylor expanded in a around inf 79.7%

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

      1. +-commutative 79.7%

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

   5. Simplified 79.7%

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

   if -4.8e33 < a < -1.6999999999999999e-20

   1. Initial program 74.4%

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

      1. sub-neg 74.4%

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

      2. +-commutative 74.4%

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

      3. distribute-frac-neg 74.4%

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

      4. distribute-rgt-neg-out 74.4%

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

      5. associate-/l* 80.3%

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

      6. fma-define 80.9%

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

      7. distribute-frac-neg 80.9%

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

      8. distribute-neg-frac2 80.9%

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

      9. sub-neg 80.9%

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

      10. distribute-neg-in 80.9%

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

      11. remove-double-neg 80.9%

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

      12. +-commutative 80.9%

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

      13. sub-neg 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in z around inf 55.0%

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

      1. *-commutative 55.0%

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

      2. *-un-lft-identity 55.0%

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

      3. times-frac 73.9%

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

   7. Applied egg-rr 73.9%

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

   8. Taylor expanded in z around 0 55.0%

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

      1. *-commutative 55.0%

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

      2. *-rgt-identity 55.0%

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

      3. times-frac 73.7%

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

      4. /-rgt-identity 73.7%

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

      5. associate-/r/ 73.9%

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

   10. Simplified 73.9%

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

   if -1.6999999999999999e-20 < a < -2.7499999999999999e-82

   1. Initial program 67.7%

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

   3. Taylor expanded in x around inf 91.6%

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

   if -2.7499999999999999e-82 < a < -6.5999999999999999e-183

   1. Initial program 76.1%

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

      1. sub-neg 76.1%

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

      2. +-commutative 76.1%

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

      3. distribute-frac-neg 76.1%

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

      4. distribute-rgt-neg-out 76.1%

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

      5. associate-/l* 80.8%

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

      6. fma-define 80.8%

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

      7. distribute-frac-neg 80.8%

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

      8. distribute-neg-frac2 80.8%

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

      9. sub-neg 80.8%

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

      10. distribute-neg-in 80.8%

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

      11. remove-double-neg 80.8%

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

      12. +-commutative 80.8%

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

      13. sub-neg 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in z around inf 73.1%

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

      1. *-commutative 73.1%

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

      2. *-un-lft-identity 73.1%

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

      3. times-frac 77.9%

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

   7. Applied egg-rr 77.9%

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

   if -6.5999999999999999e-183 < a < 3.8000000000000001e59

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf 85.3%

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

      1. associate--l+ 85.3%

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

      2. distribute-lft-out-- 85.3%

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

      3. div-sub 85.3%

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

      4. mul-1-neg 85.3%

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

      5. unsub-neg 85.3%

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

      6. *-commutative 85.3%

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

      7. distribute-lft-out-- 86.2%

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

   5. Simplified 86.2%

      \[\leadsto \color{blue}{x - \frac{y \cdot \left(a - z\right)}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq -2.75 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-183}:\\ \;\;\;\;z \cdot \frac{y}{t - a}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t - a}{y}}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ (- t a) y))))
   (if (<= a -4.8e+33)
     (+ x y)
     (if (<= a -1.7e-20)
       t_1
       (if (<= a -2.6e-82)
         x
         (if (<= a -1.25e-299) t_1 (if (<= a 5.1e-201) x (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / ((t - a) / y);
	double tmp;
	if (a <= -4.8e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = t_1;
	} else if (a <= -2.6e-82) {
		tmp = x;
	} else if (a <= -1.25e-299) {
		tmp = t_1;
	} else if (a <= 5.1e-201) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z / ((t - a) / y)
    if (a <= (-4.8d+33)) then
        tmp = x + y
    else if (a <= (-1.7d-20)) then
        tmp = t_1
    else if (a <= (-2.6d-82)) then
        tmp = x
    else if (a <= (-1.25d-299)) then
        tmp = t_1
    else if (a <= 5.1d-201) 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 t_1 = z / ((t - a) / y);
	double tmp;
	if (a <= -4.8e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = t_1;
	} else if (a <= -2.6e-82) {
		tmp = x;
	} else if (a <= -1.25e-299) {
		tmp = t_1;
	} else if (a <= 5.1e-201) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / ((t - a) / y)
	tmp = 0
	if a <= -4.8e+33:
		tmp = x + y
	elif a <= -1.7e-20:
		tmp = t_1
	elif a <= -2.6e-82:
		tmp = x
	elif a <= -1.25e-299:
		tmp = t_1
	elif a <= 5.1e-201:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(Float64(t - a) / y))
	tmp = 0.0
	if (a <= -4.8e+33)
		tmp = Float64(x + y);
	elseif (a <= -1.7e-20)
		tmp = t_1;
	elseif (a <= -2.6e-82)
		tmp = x;
	elseif (a <= -1.25e-299)
		tmp = t_1;
	elseif (a <= 5.1e-201)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / ((t - a) / y);
	tmp = 0.0;
	if (a <= -4.8e+33)
		tmp = x + y;
	elseif (a <= -1.7e-20)
		tmp = t_1;
	elseif (a <= -2.6e-82)
		tmp = x;
	elseif (a <= -1.25e-299)
		tmp = t_1;
	elseif (a <= 5.1e-201)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+33], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.7e-20], t$95$1, If[LessEqual[a, -2.6e-82], x, If[LessEqual[a, -1.25e-299], t$95$1, If[LessEqual[a, 5.1e-201], x, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.8e33 or 5.1000000000000001e-201 < a

   1. Initial program 78.8%

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

   3. Taylor expanded in a around inf 73.4%

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

      1. +-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -4.8e33 < a < -1.6999999999999999e-20 or -2.6e-82 < a < -1.24999999999999989e-299

   1. Initial program 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

      3. distribute-frac-neg 76.5%

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

      4. distribute-rgt-neg-out 76.5%

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

      5. associate-/l* 81.3%

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

      6. fma-define 81.4%

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

      7. distribute-frac-neg 81.4%

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

      8. distribute-neg-frac2 81.4%

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

      9. sub-neg 81.4%

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

      10. distribute-neg-in 81.4%

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

      11. remove-double-neg 81.4%

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

      12. +-commutative 81.4%

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

      13. sub-neg 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. *-commutative 65.0%

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

      2. *-un-lft-identity 65.0%

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

      3. times-frac 71.6%

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

   7. Applied egg-rr 71.6%

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

   8. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

      2. *-rgt-identity 65.0%

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

      3. times-frac 66.5%

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

      4. /-rgt-identity 66.5%

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

      5. associate-/r/ 71.7%

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

   10. Simplified 71.7%

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

   if -1.6999999999999999e-20 < a < -2.6e-82 or -1.24999999999999989e-299 < a < 5.1000000000000001e-201

   1. Initial program 73.3%

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

   3. Taylor expanded in x around inf 79.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-299}:\\ \;\;\;\;\frac{z}{\frac{t - a}{y}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{t - a}\\ \mathbf{if}\;a \leq -5 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- t a)))))
   (if (<= a -5e+33)
     (+ x y)
     (if (<= a -1.7e-20)
       t_1
       (if (<= a -5.5e-82)
         x
         (if (<= a -1.6e-299) t_1 (if (<= a 5.4e-201) x (+ x y))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (t - a));
	double tmp;
	if (a <= -5e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = t_1;
	} else if (a <= -5.5e-82) {
		tmp = x;
	} else if (a <= -1.6e-299) {
		tmp = t_1;
	} else if (a <= 5.4e-201) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (t - a))
    if (a <= (-5d+33)) then
        tmp = x + y
    else if (a <= (-1.7d-20)) then
        tmp = t_1
    else if (a <= (-5.5d-82)) then
        tmp = x
    else if (a <= (-1.6d-299)) then
        tmp = t_1
    else if (a <= 5.4d-201) 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 t_1 = y * (z / (t - a));
	double tmp;
	if (a <= -5e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = t_1;
	} else if (a <= -5.5e-82) {
		tmp = x;
	} else if (a <= -1.6e-299) {
		tmp = t_1;
	} else if (a <= 5.4e-201) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (t - a))
	tmp = 0
	if a <= -5e+33:
		tmp = x + y
	elif a <= -1.7e-20:
		tmp = t_1
	elif a <= -5.5e-82:
		tmp = x
	elif a <= -1.6e-299:
		tmp = t_1
	elif a <= 5.4e-201:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(t - a)))
	tmp = 0.0
	if (a <= -5e+33)
		tmp = Float64(x + y);
	elseif (a <= -1.7e-20)
		tmp = t_1;
	elseif (a <= -5.5e-82)
		tmp = x;
	elseif (a <= -1.6e-299)
		tmp = t_1;
	elseif (a <= 5.4e-201)
		tmp = x;
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (t - a));
	tmp = 0.0;
	if (a <= -5e+33)
		tmp = x + y;
	elseif (a <= -1.7e-20)
		tmp = t_1;
	elseif (a <= -5.5e-82)
		tmp = x;
	elseif (a <= -1.6e-299)
		tmp = t_1;
	elseif (a <= 5.4e-201)
		tmp = x;
	else
		tmp = x + y;
	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[a, -5e+33], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.7e-20], t$95$1, If[LessEqual[a, -5.5e-82], x, If[LessEqual[a, -1.6e-299], t$95$1, If[LessEqual[a, 5.4e-201], x, N[(x + y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.99999999999999973e33 or 5.40000000000000011e-201 < a

   1. Initial program 78.8%

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

   3. Taylor expanded in a around inf 73.4%

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

      1. +-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -4.99999999999999973e33 < a < -1.6999999999999999e-20 or -5.4999999999999998e-82 < a < -1.60000000000000004e-299

   1. Initial program 76.5%

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

      1. sub-neg 76.5%

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

      2. +-commutative 76.5%

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

      3. distribute-frac-neg 76.5%

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

      4. distribute-rgt-neg-out 76.5%

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

      5. associate-/l* 81.3%

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

      6. fma-define 81.4%

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

      7. distribute-frac-neg 81.4%

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

      8. distribute-neg-frac2 81.4%

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

      9. sub-neg 81.4%

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

      10. distribute-neg-in 81.4%

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

      11. remove-double-neg 81.4%

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

      12. +-commutative 81.4%

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

      13. sub-neg 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in z around inf 65.0%

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

      1. associate-/l* 66.5%

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

   7. Simplified 66.5%

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

   if -1.6999999999999999e-20 < a < -5.4999999999999998e-82 or -1.60000000000000004e-299 < a < 5.40000000000000011e-201

   1. Initial program 73.3%

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

   3. Taylor expanded in x around inf 79.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{z}{t - a}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-300}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+33)
   (+ x y)
   (if (<= a -1.7e-20)
     (* y (/ z (- a)))
     (if (<= a -2.5e-108)
       x
       (if (<= a -4e-300) (/ (* y z) t) (if (<= a 4.5e-201) x (+ x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = y * (z / -a);
	} else if (a <= -2.5e-108) {
		tmp = x;
	} else if (a <= -4e-300) {
		tmp = (y * z) / t;
	} else if (a <= 4.5e-201) {
		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 (a <= (-4.8d+33)) then
        tmp = x + y
    else if (a <= (-1.7d-20)) then
        tmp = y * (z / -a)
    else if (a <= (-2.5d-108)) then
        tmp = x
    else if (a <= (-4d-300)) then
        tmp = (y * z) / t
    else if (a <= 4.5d-201) 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 (a <= -4.8e+33) {
		tmp = x + y;
	} else if (a <= -1.7e-20) {
		tmp = y * (z / -a);
	} else if (a <= -2.5e-108) {
		tmp = x;
	} else if (a <= -4e-300) {
		tmp = (y * z) / t;
	} else if (a <= 4.5e-201) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+33:
		tmp = x + y
	elif a <= -1.7e-20:
		tmp = y * (z / -a)
	elif a <= -2.5e-108:
		tmp = x
	elif a <= -4e-300:
		tmp = (y * z) / t
	elif a <= 4.5e-201:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+33)
		tmp = Float64(x + y);
	elseif (a <= -1.7e-20)
		tmp = Float64(y * Float64(z / Float64(-a)));
	elseif (a <= -2.5e-108)
		tmp = x;
	elseif (a <= -4e-300)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 4.5e-201)
		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 (a <= -4.8e+33)
		tmp = x + y;
	elseif (a <= -1.7e-20)
		tmp = y * (z / -a);
	elseif (a <= -2.5e-108)
		tmp = x;
	elseif (a <= -4e-300)
		tmp = (y * z) / t;
	elseif (a <= 4.5e-201)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+33], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.7e-20], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.5e-108], x, If[LessEqual[a, -4e-300], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 4.5e-201], x, N[(x + y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.8e33 or 4.5000000000000002e-201 < a

   1. Initial program 78.8%

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

   3. Taylor expanded in a around inf 73.4%

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

      1. +-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -4.8e33 < a < -1.6999999999999999e-20

   1. Initial program 74.4%

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

   3. Taylor expanded in x around 0 54.9%

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

      1. sub-neg 54.9%

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

      2. *-rgt-identity 54.9%

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

      3. associate-*r/ 60.9%

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

      4. distribute-rgt-neg-in 60.9%

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

      5. mul-1-neg 60.9%

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

      6. distribute-lft-in 60.9%

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

      7. mul-1-neg 60.9%

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

      8. unsub-neg 60.9%

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

   5. Simplified 60.9%

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

   6. Taylor expanded in t around 0 54.0%

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

   7. Taylor expanded in z around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. associate-/l* 54.3%

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

      3. distribute-rgt-neg-in 54.3%

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

      4. distribute-frac-neg 54.3%

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

   9. Simplified 54.3%

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

   if -1.6999999999999999e-20 < a < -2.5e-108 or -4.0000000000000001e-300 < a < 4.5000000000000002e-201

   1. Initial program 75.8%

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

   3. Taylor expanded in x around inf 74.5%

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

   if -2.5e-108 < a < -4.0000000000000001e-300

   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* 79.2%

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

      6. fma-define 79.2%

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

      7. distribute-frac-neg 79.2%

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

      8. distribute-neg-frac2 79.2%

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

      9. sub-neg 79.2%

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

      10. distribute-neg-in 79.2%

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

      11. remove-double-neg 79.2%

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

      12. +-commutative 79.2%

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

      13. sub-neg 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in z around inf 68.5%

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

   6. Taylor expanded in t around inf 60.7%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-300}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+114} \lor \neg \left(t \leq 2.35 \cdot 10^{+213}\right):\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.35e+114) (not (<= t 2.35e+213)))
   (+ x (/ (* y (- z a)) t))
   (+ (+ x y) (* (- z t) (/ y (- t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.35e+114) || !(t <= 2.35e+213)) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) + ((z - t) * (y / (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) :: tmp
    if ((t <= (-1.35d+114)) .or. (.not. (t <= 2.35d+213))) then
        tmp = x + ((y * (z - a)) / t)
    else
        tmp = (x + y) + ((z - t) * (y / (t - a)))
    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 <= -1.35e+114) || !(t <= 2.35e+213)) {
		tmp = x + ((y * (z - a)) / t);
	} else {
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.35e+114) or not (t <= 2.35e+213):
		tmp = x + ((y * (z - a)) / t)
	else:
		tmp = (x + y) + ((z - t) * (y / (t - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.35e+114) || !(t <= 2.35e+213))
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	else
		tmp = Float64(Float64(x + y) + Float64(Float64(z - t) * Float64(y / Float64(t - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.35e+114) || ~((t <= 2.35e+213)))
		tmp = x + ((y * (z - a)) / t);
	else
		tmp = (x + y) + ((z - t) * (y / (t - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.35e+114], N[Not[LessEqual[t, 2.35e+213]], $MachinePrecision]], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] + N[(N[(z - t), $MachinePrecision] * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e114 or 2.3499999999999999e213 < t

   1. Initial program 48.6%

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

   3. Taylor expanded in t around inf 85.8%

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

      1. associate--l+ 85.8%

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

      2. distribute-lft-out-- 85.8%

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

      3. div-sub 85.8%

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

      4. mul-1-neg 85.8%

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

      5. unsub-neg 85.8%

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

      6. *-commutative 85.8%

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

      7. distribute-lft-out-- 85.9%

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

   5. Simplified 85.9%

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

   if -1.35e114 < t < 2.3499999999999999e213

   1. Initial program 85.2%

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

   3. Taylor expanded in y around 0 85.2%

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

      1. associate-*l/ 92.1%

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

   5. Simplified 92.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{+114} \lor \neg \left(t \leq 2.35 \cdot 10^{+213}\right):\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) + \left(z - t\right) \cdot \frac{y}{t - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-99} \lor \neg \left(a \leq 5.1 \cdot 10^{-61}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.5e-99) (not (<= a 5.1e-61)))
   (- (+ x y) (* y (/ z a)))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.5e-99) || !(a <= 5.1e-61)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * (z - a)) / 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 ((a <= (-3.5d-99)) .or. (.not. (a <= 5.1d-61))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x + ((y * (z - a)) / 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 ((a <= -3.5e-99) || !(a <= 5.1e-61)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.5e-99) or not (a <= 5.1e-61):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.5e-99) || !(a <= 5.1e-61))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.5e-99) || ~((a <= 5.1e-61)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.5e-99], N[Not[LessEqual[a, 5.1e-61]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4999999999999999e-99 or 5.09999999999999968e-61 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in t around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-/l* 82.9%

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

   5. Simplified 82.9%

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

   if -3.4999999999999999e-99 < a < 5.09999999999999968e-61

   1. Initial program 76.3%

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

   3. Taylor expanded in t around inf 91.4%

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

      1. associate--l+ 91.4%

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

      2. distribute-lft-out-- 91.4%

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

      3. div-sub 91.4%

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

      4. mul-1-neg 91.4%

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

      5. unsub-neg 91.4%

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

      6. *-commutative 91.4%

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

      7. distribute-lft-out-- 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-99} \lor \neg \left(a \leq 5.1 \cdot 10^{-61}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-99} \lor \neg \left(a \leq 5.4 \cdot 10^{-61}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.5e-99) (not (<= a 5.4e-61)))
   (- (+ x y) (/ (* y z) a))
   (+ x (/ (* y (- z a)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.5e-99) || !(a <= 5.4e-61)) {
		tmp = (x + y) - ((y * z) / a);
	} else {
		tmp = x + ((y * (z - a)) / 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 ((a <= (-2.5d-99)) .or. (.not. (a <= 5.4d-61))) then
        tmp = (x + y) - ((y * z) / a)
    else
        tmp = x + ((y * (z - a)) / 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 ((a <= -2.5e-99) || !(a <= 5.4e-61)) {
		tmp = (x + y) - ((y * z) / a);
	} else {
		tmp = x + ((y * (z - a)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.5e-99) or not (a <= 5.4e-61):
		tmp = (x + y) - ((y * z) / a)
	else:
		tmp = x + ((y * (z - a)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.5e-99) || !(a <= 5.4e-61))
		tmp = Float64(Float64(x + y) - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - a)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.5e-99) || ~((a <= 5.4e-61)))
		tmp = (x + y) - ((y * z) / a);
	else
		tmp = x + ((y * (z - a)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.5e-99], N[Not[LessEqual[a, 5.4e-61]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - a), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.49999999999999985e-99 or 5.39999999999999987e-61 < a

   1. Initial program 77.8%

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

   3. Taylor expanded in t around 0 79.1%

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

   if -2.49999999999999985e-99 < a < 5.39999999999999987e-61

   1. Initial program 76.3%

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

   3. Taylor expanded in t around inf 91.4%

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

      1. associate--l+ 91.4%

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

      2. distribute-lft-out-- 91.4%

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

      3. div-sub 91.4%

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

      4. mul-1-neg 91.4%

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

      5. unsub-neg 91.4%

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

      6. *-commutative 91.4%

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

      7. distribute-lft-out-- 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-99} \lor \neg \left(a \leq 5.4 \cdot 10^{-61}\right):\\ \;\;\;\;\left(x + y\right) - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - a\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-106}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-300}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e-106)
   (+ x y)
   (if (<= a -3.3e-300) (/ (* y z) t) (if (<= a 5.6e-201) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e-106) {
		tmp = x + y;
	} else if (a <= -3.3e-300) {
		tmp = (y * z) / t;
	} else if (a <= 5.6e-201) {
		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 (a <= (-4.8d-106)) then
        tmp = x + y
    else if (a <= (-3.3d-300)) then
        tmp = (y * z) / t
    else if (a <= 5.6d-201) 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 (a <= -4.8e-106) {
		tmp = x + y;
	} else if (a <= -3.3e-300) {
		tmp = (y * z) / t;
	} else if (a <= 5.6e-201) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e-106:
		tmp = x + y
	elif a <= -3.3e-300:
		tmp = (y * z) / t
	elif a <= 5.6e-201:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e-106)
		tmp = Float64(x + y);
	elseif (a <= -3.3e-300)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 5.6e-201)
		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 (a <= -4.8e-106)
		tmp = x + y;
	elseif (a <= -3.3e-300)
		tmp = (y * z) / t;
	elseif (a <= 5.6e-201)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e-106], N[(x + y), $MachinePrecision], If[LessEqual[a, -3.3e-300], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 5.6e-201], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.7999999999999995e-106 or 5.5999999999999998e-201 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 67.9%

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

      1. +-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -4.7999999999999995e-106 < a < -3.3000000000000002e-300

   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* 79.2%

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

      6. fma-define 79.2%

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

      7. distribute-frac-neg 79.2%

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

      8. distribute-neg-frac2 79.2%

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

      9. sub-neg 79.2%

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

      10. distribute-neg-in 79.2%

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

      11. remove-double-neg 79.2%

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

      12. +-commutative 79.2%

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

      13. sub-neg 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in z around inf 68.5%

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

   6. Taylor expanded in t around inf 60.7%

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

   if -3.3000000000000002e-300 < a < 5.5999999999999998e-201

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 75.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-106}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-300}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5e-108)
   (+ x y)
   (if (<= a -1.62e-299) (* y (/ z t)) (if (<= a 2.3e-201) x (+ x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5e-108) {
		tmp = x + y;
	} else if (a <= -1.62e-299) {
		tmp = y * (z / t);
	} else if (a <= 2.3e-201) {
		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 (a <= (-5d-108)) then
        tmp = x + y
    else if (a <= (-1.62d-299)) then
        tmp = y * (z / t)
    else if (a <= 2.3d-201) 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 (a <= -5e-108) {
		tmp = x + y;
	} else if (a <= -1.62e-299) {
		tmp = y * (z / t);
	} else if (a <= 2.3e-201) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5e-108:
		tmp = x + y
	elif a <= -1.62e-299:
		tmp = y * (z / t)
	elif a <= 2.3e-201:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5e-108)
		tmp = Float64(x + y);
	elseif (a <= -1.62e-299)
		tmp = Float64(y * Float64(z / t));
	elseif (a <= 2.3e-201)
		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 (a <= -5e-108)
		tmp = x + y;
	elseif (a <= -1.62e-299)
		tmp = y * (z / t);
	elseif (a <= 2.3e-201)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5e-108], N[(x + y), $MachinePrecision], If[LessEqual[a, -1.62e-299], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.3e-201], x, N[(x + y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5e-108 or 2.29999999999999986e-201 < a

   1. Initial program 78.1%

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

   3. Taylor expanded in a around inf 67.9%

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

      1. +-commutative 67.9%

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

   5. Simplified 67.9%

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

   if -5e-108 < a < -1.6199999999999999e-299

   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* 79.2%

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

      6. fma-define 79.2%

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

      7. distribute-frac-neg 79.2%

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

      8. distribute-neg-frac2 79.2%

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

      9. sub-neg 79.2%

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

      10. distribute-neg-in 79.2%

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

      11. remove-double-neg 79.2%

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

      12. +-commutative 79.2%

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

      13. sub-neg 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in z around inf 68.5%

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

   6. Taylor expanded in t around inf 60.7%

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

      1. associate-/l* 58.1%

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

   8. Simplified 58.1%

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

   if -1.6199999999999999e-299 < a < 2.29999999999999986e-201

   1. Initial program 75.5%

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

   3. Taylor expanded in x around inf 75.2%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-108}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;a \leq -1.62 \cdot 10^{-299}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-201}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t -1e+154) x (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1e+154) {
		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 <= (-1d+154)) 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 <= -1e+154) {
		tmp = x;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1e+154:
		tmp = x
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1e+154)
		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 <= -1e+154)
		tmp = x;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1e+154], x, N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000004e154

   1. Initial program 57.4%

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

   3. Taylor expanded in x around inf 84.6%

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

   if -1.00000000000000004e154 < t

   1. Initial program 80.4%

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

   3. Taylor expanded in a around inf 59.6%

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

      1. +-commutative 59.6%

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

   5. Simplified 59.6%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.9 \cdot 10^{+218}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 2.9e+218) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.9e+218) {
		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 <= 2.9d+218) 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 <= 2.9e+218) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.9e+218:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.9e+218)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.9e+218)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.9e+218], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.8999999999999999e218

   1. Initial program 78.1%

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

   3. Taylor expanded in x around inf 58.5%

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

   if 2.8999999999999999e218 < y

   1. Initial program 64.0%

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

   3. Taylor expanded in x around 0 64.0%

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

      1. sub-neg 64.0%

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

      2. *-rgt-identity 64.0%

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

      3. associate-*r/ 88.1%

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

      4. distribute-rgt-neg-in 88.1%

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

      5. mul-1-neg 88.1%

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

      6. distribute-lft-in 88.1%

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

      7. mul-1-neg 88.1%

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

      8. unsub-neg 88.1%

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

   5. Simplified 88.1%

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

   6. Taylor expanded in a around inf 35.1%

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

Alternative 15: 51.4% 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 77.2%

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

3. Taylor expanded in x around inf 55.4%

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

Developer target: 88.4% 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 2024108 
(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))))