Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 96.9% → 99.8%

Time: 8.0s

Alternatives: 16

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

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 - z) + 1.0d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z) + 1.0d0) / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+30} \lor \neg \left(a \leq 5.2 \cdot 10^{+19}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{1 + \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.2e+30) (not (<= a 5.2e+19)))
   (- x (/ (- y z) (/ (+ (- t z) 1.0) a)))
   (- x (/ (* (- y z) a) (+ 1.0 (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.2e+30) || !(a <= 5.2e+19)) {
		tmp = x - ((y - z) / (((t - z) + 1.0) / a));
	} else {
		tmp = x - (((y - z) * a) / (1.0 + (t - 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) :: tmp
    if ((a <= (-4.2d+30)) .or. (.not. (a <= 5.2d+19))) then
        tmp = x - ((y - z) / (((t - z) + 1.0d0) / a))
    else
        tmp = x - (((y - z) * a) / (1.0d0 + (t - z)))
    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 <= -4.2e+30) || !(a <= 5.2e+19)) {
		tmp = x - ((y - z) / (((t - z) + 1.0) / a));
	} else {
		tmp = x - (((y - z) * a) / (1.0 + (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.2e+30) or not (a <= 5.2e+19):
		tmp = x - ((y - z) / (((t - z) + 1.0) / a))
	else:
		tmp = x - (((y - z) * a) / (1.0 + (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.2e+30) || !(a <= 5.2e+19))
		tmp = Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a)));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - z) * a) / Float64(1.0 + Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.2e+30) || ~((a <= 5.2e+19)))
		tmp = x - ((y - z) / (((t - z) + 1.0) / a));
	else
		tmp = x - (((y - z) * a) / (1.0 + (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.2e+30], N[Not[LessEqual[a, 5.2e+19]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(y - z), $MachinePrecision] * a), $MachinePrecision] / N[(1.0 + N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.2e30 or 5.2e19 < a

   1. Initial program 99.9%

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

   if -4.2e30 < a < 5.2e19

   1. Initial program 91.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 99.9

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 99.9

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

   4. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+30} \lor \neg \left(a \leq 5.2 \cdot 10^{+19}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{1 + \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{-y}{z} \cdot a\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+161}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- y) z) a))))
   (if (<= z -3.8e+161)
     (- x a)
     (if (<= z -6.2e+23)
       t_1
       (if (<= z 9.5e-9)
         (- x (* (- y z) (fma a z a)))
         (if (<= z 1.65e+89) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((-y / z) * a);
	double tmp;
	if (z <= -3.8e+161) {
		tmp = x - a;
	} else if (z <= -6.2e+23) {
		tmp = t_1;
	} else if (z <= 9.5e-9) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else if (z <= 1.65e+89) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(-y) / z) * a))
	tmp = 0.0
	if (z <= -3.8e+161)
		tmp = Float64(x - a);
	elseif (z <= -6.2e+23)
		tmp = t_1;
	elseif (z <= 9.5e-9)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	elseif (z <= 1.65e+89)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[((-y) / z), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+161], N[(x - a), $MachinePrecision], If[LessEqual[z, -6.2e+23], t$95$1, If[LessEqual[z, 9.5e-9], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+89], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e161 or 1.64999999999999987e89 < z

   1. Initial program 89.7%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 88.6

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

   5. Applied rewrites 88.6%

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

   if -3.8000000000000002e161 < z < -6.19999999999999941e23 or 9.5000000000000007e-9 < z < 1.64999999999999987e89

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 83.9

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

   5. Applied rewrites 83.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 75.2%

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

   if -6.19999999999999941e23 < z < 9.5000000000000007e-9

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.2

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 79.2%

      \[\leadsto x - \left(y - z\right) \cdot \mathsf{fma}\left(a, \color{blue}{z}, a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+93}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-29}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+89}:\\ \;\;\;\;x - \frac{\left(-a\right) \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.95e+93)
   (- x a)
   (if (<= z -6.5e-29)
     (- x (* (/ y t) a))
     (if (<= z 9.5e-9)
       (- x (* (- y z) (fma a z a)))
       (if (<= z 1.65e+89) (- x (/ (* (- a) y) z)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.95e+93) {
		tmp = x - a;
	} else if (z <= -6.5e-29) {
		tmp = x - ((y / t) * a);
	} else if (z <= 9.5e-9) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else if (z <= 1.65e+89) {
		tmp = x - ((-a * y) / z);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.95e+93)
		tmp = Float64(x - a);
	elseif (z <= -6.5e-29)
		tmp = Float64(x - Float64(Float64(y / t) * a));
	elseif (z <= 9.5e-9)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	elseif (z <= 1.65e+89)
		tmp = Float64(x - Float64(Float64(Float64(-a) * y) / z));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.95e+93], N[(x - a), $MachinePrecision], If[LessEqual[z, -6.5e-29], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-9], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+89], N[(x - N[(N[((-a) * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.9500000000000001e93 or 1.64999999999999987e89 < z

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 81.9

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

   5. Applied rewrites 81.9%

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

   if -1.9500000000000001e93 < z < -6.5e-29

   1. Initial program 95.5%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 86.1

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

   5. Applied rewrites 86.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 73.1%

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

   if -6.5e-29 < z < 9.5000000000000007e-9

   1. Initial program 97.7%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.3%

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

   if 9.5000000000000007e-9 < z < 1.64999999999999987e89

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 86.8

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

   5. Applied rewrites 86.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 57.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 75.5%

       \[\leadsto x - \frac{\left(-a\right) \cdot y}{\color{blue}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{t} \cdot a\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+93}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-130}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{elif}\;z \leq 110000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y t) a))))
   (if (<= z -1.95e+93)
     (- x a)
     (if (<= z -6.5e-29)
       t_1
       (if (<= z 3.3e-130)
         (- x (* (- y z) (fma a z a)))
         (if (<= z 110000000000.0) t_1 (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / t) * a);
	double tmp;
	if (z <= -1.95e+93) {
		tmp = x - a;
	} else if (z <= -6.5e-29) {
		tmp = t_1;
	} else if (z <= 3.3e-130) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else if (z <= 110000000000.0) {
		tmp = t_1;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / t) * a))
	tmp = 0.0
	if (z <= -1.95e+93)
		tmp = Float64(x - a);
	elseif (z <= -6.5e-29)
		tmp = t_1;
	elseif (z <= 3.3e-130)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	elseif (z <= 110000000000.0)
		tmp = t_1;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+93], N[(x - a), $MachinePrecision], If[LessEqual[z, -6.5e-29], t$95$1, If[LessEqual[z, 3.3e-130], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 110000000000.0], t$95$1, N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9500000000000001e93 or 1.1e11 < z

   1. Initial program 92.7%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 78.1

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

   5. Applied rewrites 78.1%

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

   if -1.9500000000000001e93 < z < -6.5e-29 or 3.2999999999999998e-130 < z < 1.1e11

   1. Initial program 97.6%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 88.8

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

   5. Applied rewrites 88.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.1%

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

   if -6.5e-29 < z < 3.2999999999999998e-130

   1. Initial program 97.4%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.2

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

   5. Applied rewrites 85.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 85.2%

      \[\leadsto x - \left(y - z\right) \cdot \mathsf{fma}\left(a, \color{blue}{z}, a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+161}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{-y}{z} \cdot a\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+67}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+161)
   (- x a)
   (if (<= z -7.4e+50)
     (- x (* (/ (- y) z) a))
     (if (<= z 3e+67) (- x (* (/ y (+ 1.0 t)) a)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+161) {
		tmp = x - a;
	} else if (z <= -7.4e+50) {
		tmp = x - ((-y / z) * a);
	} else if (z <= 3e+67) {
		tmp = x - ((y / (1.0 + t)) * a);
	} else {
		tmp = x - 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 (z <= (-3.8d+161)) then
        tmp = x - a
    else if (z <= (-7.4d+50)) then
        tmp = x - ((-y / z) * a)
    else if (z <= 3d+67) then
        tmp = x - ((y / (1.0d0 + t)) * a)
    else
        tmp = x - 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 (z <= -3.8e+161) {
		tmp = x - a;
	} else if (z <= -7.4e+50) {
		tmp = x - ((-y / z) * a);
	} else if (z <= 3e+67) {
		tmp = x - ((y / (1.0 + t)) * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+161:
		tmp = x - a
	elif z <= -7.4e+50:
		tmp = x - ((-y / z) * a)
	elif z <= 3e+67:
		tmp = x - ((y / (1.0 + t)) * a)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+161)
		tmp = Float64(x - a);
	elseif (z <= -7.4e+50)
		tmp = Float64(x - Float64(Float64(Float64(-y) / z) * a));
	elseif (z <= 3e+67)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+161)
		tmp = x - a;
	elseif (z <= -7.4e+50)
		tmp = x - ((-y / z) * a);
	elseif (z <= 3e+67)
		tmp = x - ((y / (1.0 + t)) * a);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+161], N[(x - a), $MachinePrecision], If[LessEqual[z, -7.4e+50], N[(x - N[(N[((-y) / z), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+67], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e161 or 3.0000000000000001e67 < z

   1. Initial program 90.1%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if -3.8000000000000002e161 < z < -7.4000000000000001e50

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 81.8

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.2%

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

   if -7.4000000000000001e50 < z < 3.0000000000000001e67

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 90.8

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

   5. Applied rewrites 90.8%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+161}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{+50}:\\ \;\;\;\;x - \frac{-y}{z} \cdot a\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+67}:\\ \;\;\;\;x - y \cdot \frac{a}{1 + t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+161)
   (- x a)
   (if (<= z -7.4e+50)
     (- x (* (/ (- y) z) a))
     (if (<= z 1.9e+67) (- x (* y (/ a (+ 1.0 t)))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+161) {
		tmp = x - a;
	} else if (z <= -7.4e+50) {
		tmp = x - ((-y / z) * a);
	} else if (z <= 1.9e+67) {
		tmp = x - (y * (a / (1.0 + t)));
	} else {
		tmp = x - 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 (z <= (-3.8d+161)) then
        tmp = x - a
    else if (z <= (-7.4d+50)) then
        tmp = x - ((-y / z) * a)
    else if (z <= 1.9d+67) then
        tmp = x - (y * (a / (1.0d0 + t)))
    else
        tmp = x - 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 (z <= -3.8e+161) {
		tmp = x - a;
	} else if (z <= -7.4e+50) {
		tmp = x - ((-y / z) * a);
	} else if (z <= 1.9e+67) {
		tmp = x - (y * (a / (1.0 + t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+161:
		tmp = x - a
	elif z <= -7.4e+50:
		tmp = x - ((-y / z) * a)
	elif z <= 1.9e+67:
		tmp = x - (y * (a / (1.0 + t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+161)
		tmp = Float64(x - a);
	elseif (z <= -7.4e+50)
		tmp = Float64(x - Float64(Float64(Float64(-y) / z) * a));
	elseif (z <= 1.9e+67)
		tmp = Float64(x - Float64(y * Float64(a / Float64(1.0 + t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+161)
		tmp = x - a;
	elseif (z <= -7.4e+50)
		tmp = x - ((-y / z) * a);
	elseif (z <= 1.9e+67)
		tmp = x - (y * (a / (1.0 + t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+161], N[(x - a), $MachinePrecision], If[LessEqual[z, -7.4e+50], N[(x - N[(N[((-y) / z), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+67], N[(x - N[(y * N[(a / N[(1.0 + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e161 or 1.9000000000000001e67 < z

   1. Initial program 90.1%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 87.8

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

   5. Applied rewrites 87.8%

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

   if -3.8000000000000002e161 < z < -7.4000000000000001e50

   1. Initial program 95.3%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 81.8

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

   5. Applied rewrites 81.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 77.2%

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

   if -7.4000000000000001e50 < z < 1.9000000000000001e67

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 90.8

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

   5. Applied rewrites 90.8%

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

   7. Applied rewrites 89.1%

      \[\leadsto x - y \cdot \color{blue}{\frac{a}{1 + t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 92.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+94}:\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{\left(1 + t\right) - y}{z}, a\right)\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+159}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{1 + \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{-y}{z}, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+94)
   (- x (fma a (/ (- (+ 1.0 t) y) z) a))
   (if (<= z 4.9e+159)
     (- x (/ (* (- y z) a) (+ 1.0 (- t z))))
     (- x (fma a (/ (- y) z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+94) {
		tmp = x - fma(a, (((1.0 + t) - y) / z), a);
	} else if (z <= 4.9e+159) {
		tmp = x - (((y - z) * a) / (1.0 + (t - z)));
	} else {
		tmp = x - fma(a, (-y / z), a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+94)
		tmp = Float64(x - fma(a, Float64(Float64(Float64(1.0 + t) - y) / z), a));
	elseif (z <= 4.9e+159)
		tmp = Float64(x - Float64(Float64(Float64(y - z) * a) / Float64(1.0 + Float64(t - z))));
	else
		tmp = Float64(x - fma(a, Float64(Float64(-y) / z), a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+94], N[(x - N[(a * N[(N[(N[(1.0 + t), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+159], N[(x - N[(N[(N[(y - z), $MachinePrecision] * a), $MachinePrecision] / N[(1.0 + N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(a * N[((-y) / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.10000000000000006e94

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

   5. Applied rewrites 92.5%

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

   if -1.10000000000000006e94 < z < 4.8999999999999996e159

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. associate-*l/ N/A

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

      5. lower-/.f64 N/A

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

      6. lower-*.f64 95.4

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

      7. lift-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 95.4

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

   4. Applied rewrites 95.4%

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

   if 4.8999999999999996e159 < z

   1. Initial program 81.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

   5. Applied rewrites 96.9%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 96.9%

      \[\leadsto x - \mathsf{fma}\left(a, \frac{-y}{\color{blue}{z}}, a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 + t\right) - z\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{\left(1 + t\right) - y}{z}, a\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+85}:\\ \;\;\;\;x - \frac{y}{t\_1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_1}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ 1.0 t) z)))
   (if (<= z -1.05e+94)
     (- x (fma a (/ (- (+ 1.0 t) y) z) a))
     (if (<= z 7.5e+85) (- x (* (/ y t_1) a)) (fma (/ z t_1) a x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 + t) - z;
	double tmp;
	if (z <= -1.05e+94) {
		tmp = x - fma(a, (((1.0 + t) - y) / z), a);
	} else if (z <= 7.5e+85) {
		tmp = x - ((y / t_1) * a);
	} else {
		tmp = fma((z / t_1), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(1.0 + t) - z)
	tmp = 0.0
	if (z <= -1.05e+94)
		tmp = Float64(x - fma(a, Float64(Float64(Float64(1.0 + t) - y) / z), a));
	elseif (z <= 7.5e+85)
		tmp = Float64(x - Float64(Float64(y / t_1) * a));
	else
		tmp = fma(Float64(z / t_1), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[z, -1.05e+94], N[(x - N[(a * N[(N[(N[(1.0 + t), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+85], N[(x - N[(N[(y / t$95$1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(z / t$95$1), $MachinePrecision] * a + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999995e94

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

   5. Applied rewrites 92.5%

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

   if -1.04999999999999995e94 < z < 7.49999999999999942e85

   1. Initial program 97.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 93.9

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

   5. Applied rewrites 93.9%

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

   if 7.49999999999999942e85 < z

   1. Initial program 86.2%

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

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 93.6

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

   5. Applied rewrites 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 + t\right) - z\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+94}:\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{-y}{z}, a\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+85}:\\ \;\;\;\;x - \frac{y}{t\_1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_1}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ 1.0 t) z)))
   (if (<= z -1.05e+94)
     (- x (fma a (/ (- y) z) a))
     (if (<= z 7.5e+85) (- x (* (/ y t_1) a)) (fma (/ z t_1) a x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 + t) - z;
	double tmp;
	if (z <= -1.05e+94) {
		tmp = x - fma(a, (-y / z), a);
	} else if (z <= 7.5e+85) {
		tmp = x - ((y / t_1) * a);
	} else {
		tmp = fma((z / t_1), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(1.0 + t) - z)
	tmp = 0.0
	if (z <= -1.05e+94)
		tmp = Float64(x - fma(a, Float64(Float64(-y) / z), a));
	elseif (z <= 7.5e+85)
		tmp = Float64(x - Float64(Float64(y / t_1) * a));
	else
		tmp = fma(Float64(z / t_1), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]}, If[LessEqual[z, -1.05e+94], N[(x - N[(a * N[((-y) / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+85], N[(x - N[(N[(y / t$95$1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(z / t$95$1), $MachinePrecision] * a + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999995e94

   1. Initial program 97.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

   5. Applied rewrites 92.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 92.5%

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

   if -1.04999999999999995e94 < z < 7.49999999999999942e85

   1. Initial program 97.7%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 93.9

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

   5. Applied rewrites 93.9%

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

   if 7.49999999999999942e85 < z

   1. Initial program 86.2%

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

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 93.6

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

   5. Applied rewrites 93.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{+93}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -2400000000:\\ \;\;\;\;x - \frac{y \cdot a}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.86e+93)
   (- x a)
   (if (<= z -2400000000.0)
     (- x (/ (* y a) t))
     (if (<= z 9.5e-9) (- x (* (- y z) (fma a z a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.86e+93) {
		tmp = x - a;
	} else if (z <= -2400000000.0) {
		tmp = x - ((y * a) / t);
	} else if (z <= 9.5e-9) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.86e+93)
		tmp = Float64(x - a);
	elseif (z <= -2400000000.0)
		tmp = Float64(x - Float64(Float64(y * a) / t));
	elseif (z <= 9.5e-9)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.86e+93], N[(x - a), $MachinePrecision], If[LessEqual[z, -2400000000.0], N[(x - N[(N[(y * a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-9], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8600000000000001e93 or 9.5000000000000007e-9 < z

   1. Initial program 93.0%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 76.2

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

   5. Applied rewrites 76.2%

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

   if -1.8600000000000001e93 < z < -2.4e9

   1. Initial program 94.2%

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

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 87.7

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

   5. Applied rewrites 87.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 71.1%

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

   if -2.4e9 < z < 9.5000000000000007e-9

   1. Initial program 97.8%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 81.5

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

   5. Applied rewrites 81.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.5%

      \[\leadsto x - \left(y - z\right) \cdot \mathsf{fma}\left(a, \color{blue}{z}, a\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+40}:\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{-y}{z}, a\right)\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-9}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+40)
   (- x (fma a (/ (- y) z) a))
   (if (<= z 7.6e-9)
     (- x (* (/ y (+ 1.0 t)) a))
     (fma (/ z (- (+ 1.0 t) z)) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+40) {
		tmp = x - fma(a, (-y / z), a);
	} else if (z <= 7.6e-9) {
		tmp = x - ((y / (1.0 + t)) * a);
	} else {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+40)
		tmp = Float64(x - fma(a, Float64(Float64(-y) / z), a));
	elseif (z <= 7.6e-9)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	else
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+40], N[(x - N[(a * N[((-y) / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e-9], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000005e40

   1. Initial program 95.9%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

   5. Applied rewrites 89.8%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 89.9%

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

   if -1.05000000000000005e40 < z < 7.60000000000000023e-9

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 94.9

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

   5. Applied rewrites 94.9%

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

   if 7.60000000000000023e-9 < z

   1. Initial program 90.3%

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

   3. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. lower-+.f64 85.4

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

   5. Applied rewrites 85.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+40} \lor \neg \left(z \leq 160000000\right):\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{-y}{z}, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e+40) (not (<= z 160000000.0)))
   (- x (fma a (/ (- y) z) a))
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+40) || !(z <= 160000000.0)) {
		tmp = x - fma(a, (-y / z), a);
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e+40) || !(z <= 160000000.0))
		tmp = Float64(x - fma(a, Float64(Float64(-y) / z), a));
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e+40], N[Not[LessEqual[z, 160000000.0]], $MachinePrecision]], N[(x - N[(a * N[((-y) / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000005e40 or 1.6e8 < z

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. +-commutative N/A

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

   5. Applied rewrites 87.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 87.7%

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

   if -1.05000000000000005e40 < z < 1.6e8

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-+.f64 94.5

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

   5. Applied rewrites 94.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+40} \lor \neg \left(z \leq 160000000\right):\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{-y}{z}, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+161} \lor \neg \left(z \leq 1.65 \cdot 10^{+89}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{1 - z} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.8e+161) (not (<= z 1.65e+89)))
   (- x a)
   (- x (* (/ a (- 1.0 z)) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+161) || !(z <= 1.65e+89)) {
		tmp = x - a;
	} else {
		tmp = x - ((a / (1.0 - z)) * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.8d+161)) .or. (.not. (z <= 1.65d+89))) then
        tmp = x - a
    else
        tmp = x - ((a / (1.0d0 - z)) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.8e+161) || !(z <= 1.65e+89)) {
		tmp = x - a;
	} else {
		tmp = x - ((a / (1.0 - z)) * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.8e+161) or not (z <= 1.65e+89):
		tmp = x - a
	else:
		tmp = x - ((a / (1.0 - z)) * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.8e+161) || !(z <= 1.65e+89))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(a / Float64(1.0 - z)) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.8e+161) || ~((z <= 1.65e+89)))
		tmp = x - a;
	else
		tmp = x - ((a / (1.0 - z)) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.8e+161], N[Not[LessEqual[z, 1.65e+89]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8000000000000002e161 or 1.64999999999999987e89 < z

   1. Initial program 89.7%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 88.6

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

   5. Applied rewrites 88.6%

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

   if -3.8000000000000002e161 < z < 1.64999999999999987e89

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 79.8

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

   5. Applied rewrites 79.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.9%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 77.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+161} \lor \neg \left(z \leq 1.65 \cdot 10^{+89}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{a}{1 - z} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 73.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+88} \lor \neg \left(z \leq 150000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.55e+88) (not (<= z 150000000.0))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e+88) || !(z <= 150000000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.55d+88)) .or. (.not. (z <= 150000000.0d0))) then
        tmp = x - a
    else
        tmp = x - (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.55e+88) || !(z <= 150000000.0)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.55e+88) or not (z <= 150000000.0):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.55e+88) || !(z <= 150000000.0))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.55e+88) || ~((z <= 150000000.0)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.55e+88], N[Not[LessEqual[z, 150000000.0]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e88 or 1.5e8 < z

   1. Initial program 92.0%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -2.5499999999999999e88 < z < 1.5e8

   1. Initial program 98.1%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 78.4

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

   5. Applied rewrites 78.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 76.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+88} \lor \neg \left(z \leq 150000000\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.1% accurate, 8.8× speedup

Math

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

FPCore

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

C

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

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 - a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - a), $MachinePrecision]

Derivation

1. Initial program 95.6%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 58.2

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

5. Applied rewrites 58.2%

   \[\leadsto \color{blue}{x - a} \]
6. Add Preprocessing

Alternative 16: 16.4% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ -a \end{array} \]

FPCore

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

C

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

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 = -a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := (-a)

Derivation

1. Initial program 95.6%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 58.2

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

5. Applied rewrites 58.2%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 17.3%

   \[\leadsto -a \]
9. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 - z) + 1.0d0)) * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))