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

Percentage Accurate: 96.9% → 97.5%

Time: 7.7s

Alternatives: 15

Speedup: 1.0×

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: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+202}:\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{\left(1 + t\right) - y}{z}, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 + \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+202)
   (- 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 <= -3.4e+202) {
		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 <= -3.4e+202)
		tmp = Float64(x - fma(a, Float64(Float64(Float64(1.0 + t) - y) / z), a));
	else
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / Float64(1.0 + Float64(t - z)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+202], N[(x - N[(a * N[(N[(N[(1.0 + t), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / N[(1.0 + N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e202

   1. Initial program 84.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 97.4%

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

   if -3.4e202 < z

   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. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 98.9

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 98.9

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

   4. Applied rewrites 98.9%

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

Alternative 2: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+182}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{-y}{z} \cdot a\\ \mathbf{elif}\;z \leq 10^{-274}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-177}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+63}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+182)
   (- x a)
   (if (<= z -1.16e-63)
     (- x (* (/ (- y) z) a))
     (if (<= z 1e-274)
       (- x (* y (/ a t)))
       (if (<= z 7.2e-177)
         (- x (* (fma (- y) t y) a))
         (if (<= z 6.6e+63) (- x (* (/ y t) a)) (- x a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+182) {
		tmp = x - a;
	} else if (z <= -1.16e-63) {
		tmp = x - ((-y / z) * a);
	} else if (z <= 1e-274) {
		tmp = x - (y * (a / t));
	} else if (z <= 7.2e-177) {
		tmp = x - (fma(-y, t, y) * a);
	} else if (z <= 6.6e+63) {
		tmp = x - ((y / t) * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+182)
		tmp = Float64(x - a);
	elseif (z <= -1.16e-63)
		tmp = Float64(x - Float64(Float64(Float64(-y) / z) * a));
	elseif (z <= 1e-274)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 7.2e-177)
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	elseif (z <= 6.6e+63)
		tmp = Float64(x - Float64(Float64(y / t) * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+182], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.16e-63], N[(x - N[(N[((-y) / z), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-274], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-177], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+63], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.90000000000000006e182 or 6.6000000000000003e63 < z

   1. Initial program 91.6%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if -1.90000000000000006e182 < z < -1.16e-63

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 89.3

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

   5. Applied rewrites 89.3%

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

   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 78.6%

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

   if -1.16e-63 < z < 9.99999999999999966e-275

   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 91.5

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 66.4%

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

   10. Applied rewrites 71.2%

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

   if 9.99999999999999966e-275 < z < 7.19999999999999965e-177

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   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 89.5%

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

   if 7.19999999999999965e-177 < z < 6.6000000000000003e63

   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 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.3%

      \[\leadsto x - \frac{y}{t} \cdot a \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.44 \cdot 10^{+172}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 10^{-274}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-177}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+63}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.44e+172)
   (- x a)
   (if (<= z 1e-274)
     (- x (* y (/ a t)))
     (if (<= z 7.2e-177)
       (- x (* (fma (- y) t y) a))
       (if (<= z 6.6e+63) (- x (* (/ y t) a)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.44e+172) {
		tmp = x - a;
	} else if (z <= 1e-274) {
		tmp = x - (y * (a / t));
	} else if (z <= 7.2e-177) {
		tmp = x - (fma(-y, t, y) * a);
	} else if (z <= 6.6e+63) {
		tmp = x - ((y / t) * a);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.44e+172)
		tmp = Float64(x - a);
	elseif (z <= 1e-274)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 7.2e-177)
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	elseif (z <= 6.6e+63)
		tmp = Float64(x - Float64(Float64(y / t) * a));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.44e+172], N[(x - a), $MachinePrecision], If[LessEqual[z, 1e-274], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-177], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+63], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.44000000000000007e172 or 6.6000000000000003e63 < 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 87.9

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

   5. Applied rewrites 87.9%

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

   if -1.44000000000000007e172 < z < 9.99999999999999966e-275

   1. Initial program 99.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.1

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

   5. Applied rewrites 90.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 63.8%

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

   10. Applied rewrites 66.6%

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

   if 9.99999999999999966e-275 < z < 7.19999999999999965e-177

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   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 89.5%

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

   if 7.19999999999999965e-177 < z < 6.6000000000000003e63

   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 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.3%

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

Alternative 4: 67.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.44 \cdot 10^{+172}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 10^{-274}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-177}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+63}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.44e+172)
   (- x a)
   (if (<= z 1e-274)
     (- x (* y (/ a t)))
     (if (<= z 7.2e-177)
       (- x (* (fma (- y) t y) a))
       (if (<= z 5.2e+63) (- x (/ (* a y) t)) (- x a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.44e+172) {
		tmp = x - a;
	} else if (z <= 1e-274) {
		tmp = x - (y * (a / t));
	} else if (z <= 7.2e-177) {
		tmp = x - (fma(-y, t, y) * a);
	} else if (z <= 5.2e+63) {
		tmp = x - ((a * y) / t);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.44e+172)
		tmp = Float64(x - a);
	elseif (z <= 1e-274)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 7.2e-177)
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	elseif (z <= 5.2e+63)
		tmp = Float64(x - Float64(Float64(a * y) / t));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.44e+172], N[(x - a), $MachinePrecision], If[LessEqual[z, 1e-274], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-177], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+63], N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.44000000000000007e172 or 5.2000000000000002e63 < 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 87.9

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

   5. Applied rewrites 87.9%

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

   if -1.44000000000000007e172 < z < 9.99999999999999966e-275

   1. Initial program 99.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.1

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

   5. Applied rewrites 90.1%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 63.8%

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

   10. Applied rewrites 66.6%

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

   if 9.99999999999999966e-275 < z < 7.19999999999999965e-177

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 99.9

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

   5. Applied rewrites 99.9%

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

   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 89.5%

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

   if 7.19999999999999965e-177 < z < 5.2000000000000002e63

   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 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 75.3%

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

Alternative 5: 87.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+182} \lor \neg \left(z \leq 6 \cdot 10^{+80}\right):\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{\left(1 + t\right) - y}{z}, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\left(1 + t\right) - z} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+182) (not (<= z 6e+80)))
   (- x (fma a (/ (- (+ 1.0 t) y) z) a))
   (- x (* (/ y (- (+ 1.0 t) z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+182) || !(z <= 6e+80)) {
		tmp = x - fma(a, (((1.0 + t) - y) / z), a);
	} else {
		tmp = x - ((y / ((1.0 + t) - z)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+182) || !(z <= 6e+80))
		tmp = Float64(x - fma(a, Float64(Float64(Float64(1.0 + t) - y) / z), a));
	else
		tmp = Float64(x - Float64(Float64(y / Float64(Float64(1.0 + t) - z)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+182], N[Not[LessEqual[z, 6e+80]], $MachinePrecision]], N[(x - N[(a * N[(N[(N[(1.0 + t), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.90000000000000006e182 or 5.99999999999999974e80 < z

   1. Initial program 91.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 96.2%

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

   if -1.90000000000000006e182 < z < 5.99999999999999974e80

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.6

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

   5. Applied rewrites 90.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+182} \lor \neg \left(z \leq 6 \cdot 10^{+80}\right):\\ \;\;\;\;x - \mathsf{fma}\left(a, \frac{\left(1 + t\right) - y}{z}, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\left(1 + t\right) - z} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+86} \lor \neg \left(t \leq 9.6 \cdot 10^{+42}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.08e+86) (not (<= t 9.6e+42)))
   (- x (* (- y z) (/ a t)))
   (- x (* (- y z) (/ a (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.08e+86) || !(t <= 9.6e+42)) {
		tmp = x - ((y - z) * (a / t));
	} else {
		tmp = x - ((y - z) * (a / (1.0 - 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 ((t <= (-1.08d+86)) .or. (.not. (t <= 9.6d+42))) then
        tmp = x - ((y - z) * (a / t))
    else
        tmp = x - ((y - z) * (a / (1.0d0 - 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 ((t <= -1.08e+86) || !(t <= 9.6e+42)) {
		tmp = x - ((y - z) * (a / t));
	} else {
		tmp = x - ((y - z) * (a / (1.0 - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.08e+86) or not (t <= 9.6e+42):
		tmp = x - ((y - z) * (a / t))
	else:
		tmp = x - ((y - z) * (a / (1.0 - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.08e+86) || !(t <= 9.6e+42))
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / t)));
	else
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / Float64(1.0 - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.08e+86) || ~((t <= 9.6e+42)))
		tmp = x - ((y - z) * (a / t));
	else
		tmp = x - ((y - z) * (a / (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.08e+86], N[Not[LessEqual[t, 9.6e+42]], $MachinePrecision]], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.07999999999999993e86 or 9.5999999999999994e42 < t

   1. Initial program 97.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 97.6

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 97.6

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in t around inf

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

      1. lower-/.f64 88.2

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

   7. Applied rewrites 88.2%

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

   if -1.07999999999999993e86 < t < 9.5999999999999994e42

   1. Initial program 95.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 94.3

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

   5. Applied rewrites 94.3%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{+86} \lor \neg \left(t \leq 9.6 \cdot 10^{+42}\right):\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+149} \lor \neg \left(z \leq 1.15 \cdot 10^{-67}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.8e+149) (not (<= z 1.15e-67)))
   (fma (/ z (- (+ 1.0 t) z)) a x)
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.8e+149) || !(z <= 1.15e-67)) {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.8e+149) || !(z <= 1.15e-67))
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	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, -8.8e+149], N[Not[LessEqual[z, 1.15e-67]], $MachinePrecision]], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $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 < -8.8e149 or 1.15e-67 < z

   1. Initial program 93.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 88.9

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

   5. Applied rewrites 88.9%

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

   if -8.8e149 < z < 1.15e-67

   1. Initial program 99.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.9

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

   5. Applied rewrites 87.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+149} \lor \neg \left(z \leq 1.15 \cdot 10^{-67}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{-a}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.65e+31)
   (- x (* (- y z) (/ (- a) z)))
   (if (<= z 1.15e-67)
     (- 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 <= -1.65e+31) {
		tmp = x - ((y - z) * (-a / z));
	} else if (z <= 1.15e-67) {
		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 <= -1.65e+31)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(Float64(-a) / z)));
	elseif (z <= 1.15e-67)
		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, -1.65e+31], N[(x - N[(N[(y - z), $MachinePrecision] * N[((-a) / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-67], 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 < -1.64999999999999996e31

   1. Initial program 90.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 91.8

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

      8. lift-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 87.6

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

   7. Applied rewrites 87.6%

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

   if -1.64999999999999996e31 < z < 1.15e-67

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 91.1

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

   5. Applied rewrites 91.1%

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

   if 1.15e-67 < z

   1. Initial program 96.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 86.8

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

   5. Applied rewrites 86.8%

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

Alternative 9: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.44 \cdot 10^{+172}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-67}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{a}{\left(t + 1\right) - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.44e+172)
   (- x a)
   (if (<= z 1.15e-67)
     (- x (* (/ y (+ 1.0 t)) a))
     (fma z (/ a (- (+ t 1.0) z)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.44e+172) {
		tmp = x - a;
	} else if (z <= 1.15e-67) {
		tmp = x - ((y / (1.0 + t)) * a);
	} else {
		tmp = fma(z, (a / ((t + 1.0) - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.44e+172)
		tmp = Float64(x - a);
	elseif (z <= 1.15e-67)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	else
		tmp = fma(z, Float64(a / Float64(Float64(t + 1.0) - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.44e+172], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.15e-67], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(z * N[(a / N[(N[(t + 1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.44000000000000007e172

   1. Initial program 87.1%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 91.3

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

   5. Applied rewrites 91.3%

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

   if -1.44000000000000007e172 < z < 1.15e-67

   1. Initial program 99.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 87.7

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

   5. Applied rewrites 87.7%

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

   if 1.15e-67 < z

   1. Initial program 96.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 86.8

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

   5. Applied rewrites 86.8%

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

   7. Applied rewrites 85.1%

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

Alternative 10: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.44 \cdot 10^{+172} \lor \neg \left(z \leq 6.6 \cdot 10^{+63}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.44e+172) (not (<= z 6.6e+63)))
   (- x a)
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.44e+172) || !(z <= 6.6e+63)) {
		tmp = x - a;
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.44d+172)) .or. (.not. (z <= 6.6d+63))) then
        tmp = x - a
    else
        tmp = x - ((y / (1.0d0 + t)) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.44e+172) || !(z <= 6.6e+63)) {
		tmp = x - a;
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.44e+172) or not (z <= 6.6e+63):
		tmp = x - a
	else:
		tmp = x - ((y / (1.0 + t)) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.44e+172) || !(z <= 6.6e+63))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.44e+172) || ~((z <= 6.6e+63)))
		tmp = x - a;
	else
		tmp = x - ((y / (1.0 + t)) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.44e+172], N[Not[LessEqual[z, 6.6e+63]], $MachinePrecision]], N[(x - a), $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 < -1.44000000000000007e172 or 6.6000000000000003e63 < 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 87.9

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

   5. Applied rewrites 87.9%

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

   if -1.44000000000000007e172 < z < 6.6000000000000003e63

   1. Initial program 98.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 85.3

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

   5. Applied rewrites 85.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.44 \cdot 10^{+172} \lor \neg \left(z \leq 6.6 \cdot 10^{+63}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.44 \cdot 10^{+172} \lor \neg \left(z \leq 6.6 \cdot 10^{+63}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.44e+172) (not (<= z 6.6e+63))) (- x a) (- x (* y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.44e+172) || !(z <= 6.6e+63)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.44d+172)) .or. (.not. (z <= 6.6d+63))) then
        tmp = x - a
    else
        tmp = x - (y * (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.44e+172) || !(z <= 6.6e+63)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.44e+172) or not (z <= 6.6e+63):
		tmp = x - a
	else:
		tmp = x - (y * (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.44e+172) || !(z <= 6.6e+63))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.44e+172) || ~((z <= 6.6e+63)))
		tmp = x - a;
	else
		tmp = x - (y * (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.44e+172], N[Not[LessEqual[z, 6.6e+63]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.44000000000000007e172 or 6.6000000000000003e63 < 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 87.9

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

   5. Applied rewrites 87.9%

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

   if -1.44000000000000007e172 < z < 6.6000000000000003e63

   1. Initial program 98.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.2

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

   5. Applied rewrites 90.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 65.1%

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

   10. Applied rewrites 66.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.44 \cdot 10^{+172} \lor \neg \left(z \leq 6.6 \cdot 10^{+63}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+52} \lor \neg \left(z \leq 2.3 \cdot 10^{-29}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e+52) (not (<= z 2.3e-29)))
   (- 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 <= -3.3e+52) || !(z <= 2.3e-29)) {
		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 <= -3.3e+52) || !(z <= 2.3e-29))
		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, -3.3e+52], N[Not[LessEqual[z, 2.3e-29]], $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 < -3.3e52 or 2.29999999999999991e-29 < z

   1. Initial program 93.2%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 78.7

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

   5. Applied rewrites 78.7%

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

   if -3.3e52 < z < 2.29999999999999991e-29

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 90.9

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

   5. Applied rewrites 90.9%

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

   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 63.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+52} \lor \neg \left(z \leq 2.3 \cdot 10^{-29}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+175} \lor \neg \left(z \leq 4.8 \cdot 10^{+63}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+175) (not (<= z 4.8e+63))) (- x a) (* 1.0 x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+175) || !(z <= 4.8e+63)) {
		tmp = x - a;
	} else {
		tmp = 1.0 * x;
	}
	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 <= (-4.2d+175)) .or. (.not. (z <= 4.8d+63))) then
        tmp = x - a
    else
        tmp = 1.0d0 * x
    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 <= -4.2e+175) || !(z <= 4.8e+63)) {
		tmp = x - a;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+175) or not (z <= 4.8e+63):
		tmp = x - a
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+175) || !(z <= 4.8e+63))
		tmp = Float64(x - a);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+175) || ~((z <= 4.8e+63)))
		tmp = x - a;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+175], N[Not[LessEqual[z, 4.8e+63]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1999999999999998e175 or 4.8e63 < z

   1. Initial program 91.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 87.7

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

   5. Applied rewrites 87.7%

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

   if -4.1999999999999998e175 < z < 4.8e63

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 44.0

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

   5. Applied rewrites 44.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 45.1%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 57.5%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+175} \lor \neg \left(z \leq 4.8 \cdot 10^{+63}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
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 96.2%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 59.9

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

5. Applied rewrites 59.9%

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

Alternative 15: 17.1% 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 96.2%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 59.9

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

5. Applied rewrites 59.9%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 21.8%

   \[\leadsto -a \]
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 2024326 
(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))))