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

Percentage Accurate: 97.0% → 99.5%

Time: 9.2s

Alternatives: 15

Speedup: 0.3×

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: 97.0% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+57} \lor \neg \left(t\_1 \leq 2.5 \cdot 10^{-71}\right):\\ \;\;\;\;x - t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{fma}\left(y, a, \left(-z\right) \cdot a\right)}{1 + \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (/ (+ (- t z) 1.0) a))))
   (if (or (<= t_1 -1e+57) (not (<= t_1 2.5e-71)))
     (- x t_1)
     (- x (/ (fma y a (* (- z) a)) (+ 1.0 (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (((t - z) + 1.0) / a);
	double tmp;
	if ((t_1 <= -1e+57) || !(t_1 <= 2.5e-71)) {
		tmp = x - t_1;
	} else {
		tmp = x - (fma(y, a, (-z * a)) / (1.0 + (t - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a))
	tmp = 0.0
	if ((t_1 <= -1e+57) || !(t_1 <= 2.5e-71))
		tmp = Float64(x - t_1);
	else
		tmp = Float64(x - Float64(fma(y, a, Float64(Float64(-z) * a)) / Float64(1.0 + Float64(t - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+57], N[Not[LessEqual[t$95$1, 2.5e-71]], $MachinePrecision]], N[(x - t$95$1), $MachinePrecision], N[(x - N[(N[(y * a + N[((-z) * a), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < -1.00000000000000005e57 or 2.49999999999999999e-71 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a))

   1. Initial program 99.8%

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

   if -1.00000000000000005e57 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < 2.49999999999999999e-71

   1. Initial program 92.5%

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

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. sub-neg N/A

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

      5. lift-neg.f64 N/A

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

      6. distribute-rgt-in N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-*.f64 99.9

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

   6. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq -1 \cdot 10^{+57} \lor \neg \left(\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq 2.5 \cdot 10^{-71}\right):\\ \;\;\;\;x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\mathsf{fma}\left(y, a, \left(-z\right) \cdot a\right)}{1 + \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 62.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+293}\right):\\ \;\;\;\;y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (/ (+ (- t z) 1.0) a))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+293)))
     (* y (/ a z))
     (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (((t - z) + 1.0) / a);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+293)) {
		tmp = y * (a / z);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (((t - z) + 1.0) / a);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+293)) {
		tmp = y * (a / z);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / (((t - z) + 1.0) / a)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+293):
		tmp = y * (a / z)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+293))
		tmp = Float64(y * Float64(a / z));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / (((t - z) + 1.0) / a);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+293)))
		tmp = y * (a / z);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+293]], $MachinePrecision]], N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < -inf.0 or 5.00000000000000033e293 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 60.2%

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

   10. Applied rewrites 68.2%

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

   if -inf.0 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < 5.00000000000000033e293

   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 61.8

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

   5. Applied rewrites 61.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq -\infty \lor \neg \left(\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq 5 \cdot 10^{+293}\right):\\ \;\;\;\;y \cdot \frac{a}{z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - z}{\frac{\left(t - z\right) + 1}{a}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \frac{a}{z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y z) (/ (+ (- t z) 1.0) a))))
   (if (<= t_1 (- INFINITY))
     (* y (/ a z))
     (if (<= t_1 5e+293) (- x a) (* (/ y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (((t - z) + 1.0) / a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (a / z);
	} else if (t_1 <= 5e+293) {
		tmp = x - a;
	} else {
		tmp = (y / z) * a;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - z) / (((t - z) + 1.0) / a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (a / z);
	} else if (t_1 <= 5e+293) {
		tmp = x - a;
	} else {
		tmp = (y / z) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - z) / (((t - z) + 1.0) / a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (a / z)
	elif t_1 <= 5e+293:
		tmp = x - a
	else:
		tmp = (y / z) * a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - z) / Float64(Float64(Float64(t - z) + 1.0) / a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(a / z));
	elseif (t_1 <= 5e+293)
		tmp = Float64(x - a);
	else
		tmp = Float64(Float64(y / z) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - z) / (((t - z) + 1.0) / a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (a / z);
	elseif (t_1 <= 5e+293)
		tmp = x - a;
	else
		tmp = (y / z) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] + 1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+293], N[(x - a), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < -inf.0

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 71.4%

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

   10. Applied rewrites 71.4%

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

   if -inf.0 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a)) < 5.00000000000000033e293

   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 61.8

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

   5. Applied rewrites 61.8%

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

   if 5.00000000000000033e293 < (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) #s(literal 1 binary64)) a))

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-+.f64 93.4

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

   5. Applied rewrites 93.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 54.9%

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

   10. Applied rewrites 66.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq -\infty:\\ \;\;\;\;y \cdot \frac{a}{z}\\ \mathbf{elif}\;\frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \leq 5 \cdot 10^{+293}:\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+139} \lor \neg \left(z \leq 1.1 \cdot 10^{+177}\right):\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{\left(1 + t\right) - y}{z}, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{1 + \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+139) (not (<= z 1.1e+177)))
   (- x (fma a (/ (- (+ 1.0 t) y) z) 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 ((z <= -8.8e+139) || !(z <= 1.1e+177)) {
		tmp = x - fma(a, (((1.0 + t) - y) / z), 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 ((z <= -8.8e+139) || !(z <= 1.1e+177))
		tmp = Float64(x - fma(a, Float64(Float64(Float64(1.0 + t) - y) / z), a));
	else
		tmp = Float64(x - Float64(Float64(Float64(y - z) * a) / Float64(1.0 + Float64(t - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.8e+139], N[Not[LessEqual[z, 1.1e+177]], $MachinePrecision]], N[(x - N[(a * N[(N[(N[(1.0 + t), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] + a), $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 z < -8.7999999999999998e139 or 1.0999999999999999e177 < z

   1. Initial program 90.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 63.0

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

      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 63.0

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

   4. Applied rewrites 63.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto x - \color{blue}{\left(\left(a + -1 \cdot \frac{a \cdot y}{z}\right) - -1 \cdot \frac{a \cdot \left(1 + t\right)}{z}\right)} \]
   6. 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. associate-*r/ N/A

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

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

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. cancel-sign-sub N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

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

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

      14. associate-/l* N/A

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

   7. Applied rewrites 94.5%

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

   if -8.7999999999999998e139 < z < 1.0999999999999999e177

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 93.8

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

      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 93.8

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

   4. Applied rewrites 93.8%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+139} \lor \neg \left(z \leq 1.1 \cdot 10^{+177}\right):\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{\left(1 + t\right) - y}{z}, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(y - z\right) \cdot a}{1 + \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+177}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.00205:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \mathbf{elif}\;z \leq 4.65 \cdot 10^{+142}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+177)
   (- x a)
   (if (<= z 0.00205)
     (fma (- a) (/ y (+ 1.0 t)) x)
     (if (<= z 4.65e+142) (- x (* a (/ y (- 1.0 z)))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+177) {
		tmp = x - a;
	} else if (z <= 0.00205) {
		tmp = fma(-a, (y / (1.0 + t)), x);
	} else if (z <= 4.65e+142) {
		tmp = x - (a * (y / (1.0 - z)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+177)
		tmp = Float64(x - a);
	elseif (z <= 0.00205)
		tmp = fma(Float64(-a), Float64(y / Float64(1.0 + t)), x);
	elseif (z <= 4.65e+142)
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+177], N[(x - a), $MachinePrecision], If[LessEqual[z, 0.00205], N[((-a) * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 4.65e+142], N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999995e177 or 4.6499999999999999e142 < z

   1. Initial program 89.2%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 83.7

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

   5. Applied rewrites 83.7%

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

   if -1.34999999999999995e177 < z < 0.00205000000000000017

   1. Initial program 99.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 94.2

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

      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 94.2

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

   4. Applied rewrites 94.2%

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

   5. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 89.0

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

   7. Applied rewrites 89.0%

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

   if 0.00205000000000000017 < z < 4.6499999999999999e142

   1. Initial program 96.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 74.4

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 80.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+177}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 0.00205:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \mathbf{elif}\;z \leq 4.65 \cdot 10^{+142}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00052:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-42}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(z, a, a\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{1 + t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00052)
   (- x a)
   (if (<= z 3.7e-42)
     (- x (* (- y z) (fma z a a)))
     (if (<= z 2.1e+139) (fma (/ z (+ 1.0 t)) a x) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00052) {
		tmp = x - a;
	} else if (z <= 3.7e-42) {
		tmp = x - ((y - z) * fma(z, a, a));
	} else if (z <= 2.1e+139) {
		tmp = fma((z / (1.0 + t)), a, x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00052)
		tmp = Float64(x - a);
	elseif (z <= 3.7e-42)
		tmp = Float64(x - Float64(Float64(y - z) * fma(z, a, a)));
	elseif (z <= 2.1e+139)
		tmp = fma(Float64(z / Float64(1.0 + t)), a, x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00052], N[(x - a), $MachinePrecision], If[LessEqual[z, 3.7e-42], N[(x - N[(N[(y - z), $MachinePrecision] * N[(z * a + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+139], N[(N[(z / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999954e-4 or 2.0999999999999999e139 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 76.0

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

   5. Applied rewrites 76.0%

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

   if -5.19999999999999954e-4 < z < 3.7000000000000002e-42

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 81.4

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

   5. Applied rewrites 81.4%

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

   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 81.4%

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

   if 3.7000000000000002e-42 < z < 2.0999999999999999e139

   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 0

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

      1. cancel-sign-sub-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. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative 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 74.3

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 79.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00052:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-42}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(z, a, a\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{1 + t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4350000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+144}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4350000000000.0)
   (fma (/ z (- (+ 1.0 t) z)) a x)
   (if (<= t 1.1e+144)
     (- x (* (- y z) (/ a (- 1.0 z))))
     (fma (- a) (/ (- y z) t) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4350000000000.0) {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	} else if (t <= 1.1e+144) {
		tmp = x - ((y - z) * (a / (1.0 - z)));
	} else {
		tmp = fma(-a, ((y - z) / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4350000000000.0)
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	elseif (t <= 1.1e+144)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / Float64(1.0 - z))));
	else
		tmp = fma(Float64(-a), Float64(Float64(y - z) / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4350000000000.0], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], If[LessEqual[t, 1.1e+144], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-a) * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.35e12

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. cancel-sign-sub-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. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative 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 84.3

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

   5. Applied rewrites 84.3%

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

   if -4.35e12 < t < 1.09999999999999994e144

   1. Initial program 97.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 94.4

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

   5. Applied rewrites 94.4%

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

   if 1.09999999999999994e144 < t

   1. Initial program 92.5%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-lft-neg-in N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 94.8

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

   5. Applied rewrites 94.8%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4350000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+144}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y - z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+55} \lor \neg \left(z \leq 2.8 \cdot 10^{-34}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.7e+55) (not (<= z 2.8e-34)))
   (fma (/ z (- (+ 1.0 t) z)) a x)
   (fma (- a) (/ y (+ 1.0 t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.7e+55) || !(z <= 2.8e-34)) {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	} else {
		tmp = fma(-a, (y / (1.0 + t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.7e+55) || !(z <= 2.8e-34))
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	else
		tmp = fma(Float64(-a), Float64(y / Float64(1.0 + t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.7e+55], N[Not[LessEqual[z, 2.8e-34]], $MachinePrecision]], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], N[((-a) * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7000000000000001e55 or 2.79999999999999997e-34 < z

   1. Initial program 92.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. cancel-sign-sub-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. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative 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 84.2

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

   5. Applied rewrites 84.2%

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

   if -4.7000000000000001e55 < z < 2.79999999999999997e-34

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 97.1

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

      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 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 92.3

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

   7. Applied rewrites 92.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+55} \lor \neg \left(z \leq 2.8 \cdot 10^{-34}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+55} \lor \neg \left(z \leq 2.8 \cdot 10^{-34}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{\left(t + 1\right) - z}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.7e+55) (not (<= z 2.8e-34)))
   (fma (/ a (- (+ t 1.0) z)) z x)
   (fma (- a) (/ y (+ 1.0 t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.7e+55) || !(z <= 2.8e-34)) {
		tmp = fma((a / ((t + 1.0) - z)), z, x);
	} else {
		tmp = fma(-a, (y / (1.0 + t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.7e+55) || !(z <= 2.8e-34))
		tmp = fma(Float64(a / Float64(Float64(t + 1.0) - z)), z, x);
	else
		tmp = fma(Float64(-a), Float64(y / Float64(1.0 + t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.7e+55], N[Not[LessEqual[z, 2.8e-34]], $MachinePrecision]], N[(N[(a / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * z + x), $MachinePrecision], N[((-a) * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7000000000000001e55 or 2.79999999999999997e-34 < z

   1. Initial program 92.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. cancel-sign-sub-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. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative 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 84.2

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

   5. Applied rewrites 84.2%

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

   7. Applied rewrites 78.9%

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

   if -4.7000000000000001e55 < z < 2.79999999999999997e-34

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 97.1

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

      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 97.1

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

   4. Applied rewrites 97.1%

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

   5. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 92.3

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

   7. Applied rewrites 92.3%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+55} \lor \neg \left(z \leq 2.8 \cdot 10^{-34}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{\left(t + 1\right) - z}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00052:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-21}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(z, a, a\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.00052)
   (- x a)
   (if (<= z 7.2e-21)
     (- x (* (- y z) (fma z a a)))
     (if (<= z 2.1e+139) (fma (/ z t) a x) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.00052) {
		tmp = x - a;
	} else if (z <= 7.2e-21) {
		tmp = x - ((y - z) * fma(z, a, a));
	} else if (z <= 2.1e+139) {
		tmp = fma((z / t), a, x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.00052)
		tmp = Float64(x - a);
	elseif (z <= 7.2e-21)
		tmp = Float64(x - Float64(Float64(y - z) * fma(z, a, a)));
	elseif (z <= 2.1e+139)
		tmp = fma(Float64(z / t), a, x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.00052], N[(x - a), $MachinePrecision], If[LessEqual[z, 7.2e-21], N[(x - N[(N[(y - z), $MachinePrecision] * N[(z * a + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+139], N[(N[(z / t), $MachinePrecision] * a + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.19999999999999954e-4 or 2.0999999999999999e139 < z

   1. Initial program 92.2%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 76.0

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

   5. Applied rewrites 76.0%

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

   if -5.19999999999999954e-4 < z < 7.19999999999999979e-21

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 81.0

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

   5. Applied rewrites 81.0%

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

   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 81.0%

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

   if 7.19999999999999979e-21 < z < 2.0999999999999999e139

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. cancel-sign-sub-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. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative 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 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 78.0%

      \[\leadsto \mathsf{fma}\left(\frac{z}{t}, a, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00052:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-21}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(z, a, a\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -680000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-26}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -680000.0)
   (- x a)
   (if (<= z 8e-26)
     (- x (* (fma (- y) t y) a))
     (if (<= z 2.1e+139) (fma (/ z t) a x) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -680000.0) {
		tmp = x - a;
	} else if (z <= 8e-26) {
		tmp = x - (fma(-y, t, y) * a);
	} else if (z <= 2.1e+139) {
		tmp = fma((z / t), a, x);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -680000.0)
		tmp = Float64(x - a);
	elseif (z <= 8e-26)
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	elseif (z <= 2.1e+139)
		tmp = fma(Float64(z / t), a, x);
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -680000.0], N[(x - a), $MachinePrecision], If[LessEqual[z, 8e-26], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+139], N[(N[(z / t), $MachinePrecision] * a + x), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8e5 or 2.0999999999999999e139 < 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 77.4

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

   5. Applied rewrites 77.4%

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

   if -6.8e5 < z < 8.0000000000000003e-26

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto x - \left(y + -1 \cdot \left(t \cdot y\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 68.7%

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

   if 8.0000000000000003e-26 < z < 2.0999999999999999e139

   1. Initial program 97.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. cancel-sign-sub-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. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-commutative 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 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 78.0%

      \[\leadsto \mathsf{fma}\left(\frac{z}{t}, a, x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -680000:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-26}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+139}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+177} \lor \neg \left(z \leq 2.1 \cdot 10^{+139}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.35e+177) (not (<= z 2.1e+139)))
   (- x a)
   (fma (- a) (/ y (+ 1.0 t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.35e+177) || !(z <= 2.1e+139)) {
		tmp = x - a;
	} else {
		tmp = fma(-a, (y / (1.0 + t)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.35e+177) || !(z <= 2.1e+139))
		tmp = Float64(x - a);
	else
		tmp = fma(Float64(-a), Float64(y / Float64(1.0 + t)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.35e+177], N[Not[LessEqual[z, 2.1e+139]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[((-a) * N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.34999999999999995e177 or 2.0999999999999999e139 < z

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 82.8

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

   5. Applied rewrites 82.8%

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

   if -1.34999999999999995e177 < z < 2.0999999999999999e139

   1. Initial program 99.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 93.1

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

      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 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-/l* N/A

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

      4. distribute-lft-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. lower-fma.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-+.f64 86.0

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

   7. Applied rewrites 86.0%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+177} \lor \neg \left(z \leq 2.1 \cdot 10^{+139}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-a, \frac{y}{1 + t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -680000 \lor \neg \left(z \leq 1.5 \cdot 10^{-19}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -680000.0) (not (<= z 1.5e-19)))
   (- x a)
   (- x (* (fma (- y) t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -680000.0) || !(z <= 1.5e-19)) {
		tmp = x - a;
	} else {
		tmp = x - (fma(-y, t, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -680000.0) || !(z <= 1.5e-19))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -680000.0], N[Not[LessEqual[z, 1.5e-19]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8e5 or 1.49999999999999996e-19 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -6.8e5 < z < 1.49999999999999996e-19

   1. Initial program 99.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 94.2

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

   5. Applied rewrites 94.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto x - \left(y + -1 \cdot \left(t \cdot y\right)\right) \cdot a \]
   7. Step-by-step derivation

   8. Applied rewrites 68.7%

      \[\leadsto x - \mathsf{fma}\left(-y, t, y\right) \cdot a \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -680000 \lor \neg \left(z \leq 1.5 \cdot 10^{-19}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.9% 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 96.0%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 57.2

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

5. Applied rewrites 57.2%

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

6. Final simplification 57.2%

   \[\leadsto x - a \]
7. Add Preprocessing

Alternative 15: 16.8% 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 96.0%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 57.2

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

5. Applied rewrites 57.2%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 18.3%

   \[\leadsto -a \]

9. Final simplification 18.3%

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

Developer Target 1: 99.7% 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 2024318 
(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))))