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

Percentage Accurate: 96.8% → 99.6%

Time: 10.8s

Alternatives: 10

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: 96.8% 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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / (((t - z) + 1.0d0) / (z - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \color{blue}{a}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y - z}{\left(t - z\right) + 1}}\right)\right) \]

   3. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \frac{1}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

   4. un-div-inv N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{a}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{\left(t - z\right) + 1}{y - z}\right)}\right)\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\left(\left(t - z\right) + 1\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

   7. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(t - z\right), 1\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

   8. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \left(y - z\right)\right)\right)\right) \]

   9. --lowering--.f64 99.9%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

4. Applied egg-rr 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \frac{a}{t + \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.8e+17)
   (+ x (* z (/ a (+ t (- 1.0 z)))))
   (if (<= z 2.5e+42)
     (+ x (* y (/ a (- -1.0 t))))
     (+ x (/ a (/ (- 1.0 z) (- z y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+17) {
		tmp = x + (z * (a / (t + (1.0 - z))));
	} else if (z <= 2.5e+42) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x + (a / ((1.0 - z) / (z - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.8d+17)) then
        tmp = x + (z * (a / (t + (1.0d0 - z))))
    else if (z <= 2.5d+42) then
        tmp = x + (y * (a / ((-1.0d0) - t)))
    else
        tmp = x + (a / ((1.0d0 - z) / (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+17) {
		tmp = x + (z * (a / (t + (1.0 - z))));
	} else if (z <= 2.5e+42) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x + (a / ((1.0 - z) / (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+17:
		tmp = x + (z * (a / (t + (1.0 - z))))
	elif z <= 2.5e+42:
		tmp = x + (y * (a / (-1.0 - t)))
	else:
		tmp = x + (a / ((1.0 - z) / (z - y)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+17)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + Float64(1.0 - z)))));
	elseif (z <= 2.5e+42)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	else
		tmp = Float64(x + Float64(a / Float64(Float64(1.0 - z) / Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+17)
		tmp = x + (z * (a / (t + (1.0 - z))));
	elseif (z <= 2.5e+42)
		tmp = x + (y * (a / (-1.0 - t)));
	else
		tmp = x + (a / ((1.0 - z) / (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.8e+17], N[(x + N[(z * N[(a / N[(t + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+42], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(a / N[(N[(1.0 - z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e17

   1. Initial program 98.4%

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{a \cdot z}{\left(1 + t\right) - z}\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z \cdot a}{\color{blue}{\left(1 + t\right)} - z}\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\frac{a}{\left(1 + t\right) - z}}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{a}{\left(1 + t\right) - z}\right)}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \color{blue}{\left(\left(1 + t\right) - z\right)}\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \left(\left(t + 1\right) - z\right)\right)\right)\right) \]

      10. associate--l+ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \left(t + \color{blue}{\left(1 - z\right)}\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(1 - z\right)}\right)\right)\right)\right) \]

      12. --lowering--.f64 91.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right)\right) \]

   5. Simplified 91.5%

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

   if -4.8e17 < z < 2.50000000000000003e42

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 86.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 86.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot a}{\color{blue}{1} + t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{a}{1 + t}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{a}{1 + t}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{\left(1 + t\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \left(t + \color{blue}{1}\right)\right)\right)\right) \]

      6. +-lowering-+.f64 90.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{1}\right)\right)\right)\right) \]

   7. Applied egg-rr 90.6%

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

   if 2.50000000000000003e42 < z

   1. Initial program 92.1%

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

      1. associate-/r/ N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - z}{\left(t - z\right) + 1} \cdot \color{blue}{a}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \color{blue}{\frac{y - z}{\left(t - z\right) + 1}}\right)\right) \]

      3. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(a \cdot \frac{1}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

      4. un-div-inv N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{a}{\color{blue}{\frac{\left(t - z\right) + 1}{y - z}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{\left(t - z\right) + 1}{y - z}\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\left(\left(t - z\right) + 1\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\left(t - z\right), 1\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \left(y - z\right)\right)\right)\right) \]

      9. --lowering--.f64 99.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \color{blue}{\left(\frac{1 - z}{y - z}\right)}\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\left(1 - z\right), \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, z\right), \left(\color{blue}{y} - z\right)\right)\right)\right) \]

      3. --lowering--.f64 90.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(a, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, z\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right)\right) \]

   7. Simplified 90.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \frac{a}{t + \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{a}{\frac{1 - z}{z - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-154}:\\ \;\;\;\;x - \frac{y}{\frac{t}{a}}\\ \mathbf{elif}\;z \leq 2600000000:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+50)
   (- x a)
   (if (<= z -1.4e-154)
     (- x (/ y (/ t a)))
     (if (<= z 2600000000.0) (- x (* a y)) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+50) {
		tmp = x - a;
	} else if (z <= -1.4e-154) {
		tmp = x - (y / (t / a));
	} else if (z <= 2600000000.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+50)) then
        tmp = x - a
    else if (z <= (-1.4d-154)) then
        tmp = x - (y / (t / a))
    else if (z <= 2600000000.0d0) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+50) {
		tmp = x - a;
	} else if (z <= -1.4e-154) {
		tmp = x - (y / (t / a));
	} else if (z <= 2600000000.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+50:
		tmp = x - a
	elif z <= -1.4e-154:
		tmp = x - (y / (t / a))
	elif z <= 2600000000.0:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+50)
		tmp = Float64(x - a);
	elseif (z <= -1.4e-154)
		tmp = Float64(x - Float64(y / Float64(t / a)));
	elseif (z <= 2600000000.0)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+50)
		tmp = x - a;
	elseif (z <= -1.4e-154)
		tmp = x - (y / (t / a));
	elseif (z <= 2600000000.0)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+50], N[(x - a), $MachinePrecision], If[LessEqual[z, -1.4e-154], N[(x - N[(y / N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2600000000.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999997e50 or 2.6e9 < z

   1. Initial program 95.2%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 80.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 80.9%

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

   if -6.7999999999999997e50 < z < -1.40000000000000006e-154

   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

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 75.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 75.0%

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

   6. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{t}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{t}\right)\right) \]

      5. *-lowering-*.f64 57.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), t\right)\right) \]

   8. Simplified 57.9%

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{t}\right)}\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{t}{a \cdot y}}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{1}{\frac{\frac{t}{a}}{\color{blue}{y}}}\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{t}{a}}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{t}{a}\right)}\right)\right) \]

      6. /-lowering-/.f64 66.0%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{a}\right)\right)\right) \]

   10. Applied egg-rr 66.0%

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

   if -1.40000000000000006e-154 < z < 2.6e9

   1. Initial program 95.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 88.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 88.9%

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

   6. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

      2. *-lowering-*.f64 72.9%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   8. Simplified 72.9%

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

Alternative 4: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \frac{a}{t + \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+17)
   (+ x (* z (/ a (+ t (- 1.0 z)))))
   (if (<= z 1e+50) (+ x (* y (/ a (- -1.0 t)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+17) {
		tmp = x + (z * (a / (t + (1.0 - z))));
	} else if (z <= 1e+50) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d+17)) then
        tmp = x + (z * (a / (t + (1.0d0 - z))))
    else if (z <= 1d+50) then
        tmp = x + (y * (a / ((-1.0d0) - t)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+17) {
		tmp = x + (z * (a / (t + (1.0 - z))));
	} else if (z <= 1e+50) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+17:
		tmp = x + (z * (a / (t + (1.0 - z))))
	elif z <= 1e+50:
		tmp = x + (y * (a / (-1.0 - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+17)
		tmp = Float64(x + Float64(z * Float64(a / Float64(t + Float64(1.0 - z)))));
	elseif (z <= 1e+50)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+17)
		tmp = x + (z * (a / (t + (1.0 - z))));
	elseif (z <= 1e+50)
		tmp = x + (y * (a / (-1.0 - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+17], N[(x + N[(z * N[(a / N[(t + N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+50], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8e17

   1. Initial program 98.4%

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

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{a \cdot z}{\left(1 + t\right) - z}\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{z \cdot a}{\color{blue}{\left(1 + t\right)} - z}\right)\right) \]

      6. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(z \cdot \color{blue}{\frac{a}{\left(1 + t\right) - z}}\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{a}{\left(1 + t\right) - z}\right)}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \color{blue}{\left(\left(1 + t\right) - z\right)}\right)\right)\right) \]

      9. +-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \left(\left(t + 1\right) - z\right)\right)\right)\right) \]

      10. associate--l+ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \left(t + \color{blue}{\left(1 - z\right)}\right)\right)\right)\right) \]

      11. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{\left(1 - z\right)}\right)\right)\right)\right) \]

      12. --lowering--.f64 91.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(a, \mathsf{+.f64}\left(t, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right)\right)\right)\right) \]

   5. Simplified 91.5%

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

   if -8e17 < z < 1.0000000000000001e50

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 86.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 86.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot a}{\color{blue}{1} + t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{a}{1 + t}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{a}{1 + t}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{\left(1 + t\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \left(t + \color{blue}{1}\right)\right)\right)\right) \]

      6. +-lowering-+.f64 90.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{1}\right)\right)\right)\right) \]

   7. Applied egg-rr 90.6%

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

   if 1.0000000000000001e50 < z

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 77.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 77.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+17}:\\ \;\;\;\;x + z \cdot \frac{a}{t + \left(1 - z\right)}\\ \mathbf{elif}\;z \leq 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e+53)
   (- x a)
   (if (<= z 1.3e+45) (+ x (* y (/ a (- -1.0 t)))) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+53) {
		tmp = x - a;
	} else if (z <= 1.3e+45) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.2d+53)) then
        tmp = x - a
    else if (z <= 1.3d+45) then
        tmp = x + (y * (a / ((-1.0d0) - t)))
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e+53) {
		tmp = x - a;
	} else if (z <= 1.3e+45) {
		tmp = x + (y * (a / (-1.0 - t)));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e+53:
		tmp = x - a
	elif z <= 1.3e+45:
		tmp = x + (y * (a / (-1.0 - t)))
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e+53)
		tmp = Float64(x - a);
	elseif (z <= 1.3e+45)
		tmp = Float64(x + Float64(y * Float64(a / Float64(-1.0 - t))));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.2e+53)
		tmp = x - a;
	elseif (z <= 1.3e+45)
		tmp = x + (y * (a / (-1.0 - t)));
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e+53], N[(x - a), $MachinePrecision], If[LessEqual[z, 1.3e+45], N[(x + N[(y * N[(a / N[(-1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999996e53 or 1.30000000000000004e45 < z

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 82.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 82.3%

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

   if -5.19999999999999996e53 < z < 1.30000000000000004e45

   1. Initial program 97.3%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 83.5%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 83.5%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y \cdot a}{\color{blue}{1} + t}\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(y \cdot \color{blue}{\frac{a}{1 + t}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{a}{1 + t}\right)}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \color{blue}{\left(1 + t\right)}\right)\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \left(t + \color{blue}{1}\right)\right)\right)\right) \]

      6. +-lowering-+.f64 88.6%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(a, \mathsf{+.f64}\left(t, \color{blue}{1}\right)\right)\right)\right) \]

   7. Applied egg-rr 88.6%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+53}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+45}:\\ \;\;\;\;x + y \cdot \frac{a}{-1 - t}\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-16}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 3200000000:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e-16) (- x a) (if (<= z 3200000000.0) (- x (* a y)) (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e-16) {
		tmp = x - a;
	} else if (z <= 3200000000.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d-16)) then
        tmp = x - a
    else if (z <= 3200000000.0d0) then
        tmp = x - (a * y)
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e-16) {
		tmp = x - a;
	} else if (z <= 3200000000.0) {
		tmp = x - (a * y);
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e-16:
		tmp = x - a
	elif z <= 3200000000.0:
		tmp = x - (a * y)
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e-16)
		tmp = Float64(x - a);
	elseif (z <= 3200000000.0)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e-16)
		tmp = x - a;
	elseif (z <= 3200000000.0)
		tmp = x - (a * y);
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e-16], N[(x - a), $MachinePrecision], If[LessEqual[z, 3200000000.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e-16 or 3.2e9 < z

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 78.1%

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

   if -7.5e-16 < z < 3.2e9

   1. Initial program 96.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{a \cdot y}{1 + t}\right)}\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(a \cdot y\right), \color{blue}{\left(1 + t\right)}\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \left(\color{blue}{1} + t\right)\right)\right) \]

      3. +-lowering-+.f64 86.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, y\right), \mathsf{+.f64}\left(1, \color{blue}{t}\right)\right)\right) \]

   5. Simplified 86.7%

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

   6. Taylor expanded in t around 0

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

      1. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(a \cdot y\right)}\right) \]

      2. *-lowering-*.f64 68.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(a, \color{blue}{y}\right)\right) \]

   8. Simplified 68.8%

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

Alternative 7: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq 114000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+19) (- x a) (if (<= z 114000000000.0) x (- x a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+19) {
		tmp = x - a;
	} else if (z <= 114000000000.0) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.1d+19)) then
        tmp = x - a
    else if (z <= 114000000000.0d0) then
        tmp = x
    else
        tmp = x - a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+19) {
		tmp = x - a;
	} else if (z <= 114000000000.0) {
		tmp = x;
	} else {
		tmp = x - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+19:
		tmp = x - a
	elif z <= 114000000000.0:
		tmp = x
	else:
		tmp = x - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+19)
		tmp = Float64(x - a);
	elseif (z <= 114000000000.0)
		tmp = x;
	else
		tmp = Float64(x - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+19)
		tmp = x - a;
	elseif (z <= 114000000000.0)
		tmp = x;
	else
		tmp = x - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+19], N[(x - a), $MachinePrecision], If[LessEqual[z, 114000000000.0], x, N[(x - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e19 or 1.14e11 < z

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 79.1%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 79.1%

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

   if -1.1e19 < z < 1.14e11

   1. Initial program 97.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 58.0%

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

Alternative 8: 55.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+231}:\\ \;\;\;\;0 - a\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.22e+231) (- 0.0 a) (if (<= a 5e+203) x (- 0.0 a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.22e+231) {
		tmp = 0.0 - a;
	} else if (a <= 5e+203) {
		tmp = x;
	} else {
		tmp = 0.0 - 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 (a <= (-1.22d+231)) then
        tmp = 0.0d0 - a
    else if (a <= 5d+203) then
        tmp = x
    else
        tmp = 0.0d0 - 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 (a <= -1.22e+231) {
		tmp = 0.0 - a;
	} else if (a <= 5e+203) {
		tmp = x;
	} else {
		tmp = 0.0 - a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.22e+231:
		tmp = 0.0 - a
	elif a <= 5e+203:
		tmp = x
	else:
		tmp = 0.0 - a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.22e+231)
		tmp = Float64(0.0 - a);
	elseif (a <= 5e+203)
		tmp = x;
	else
		tmp = Float64(0.0 - a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.22e+231)
		tmp = 0.0 - a;
	elseif (a <= 5e+203)
		tmp = x;
	else
		tmp = 0.0 - a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.22e+231], N[(0.0 - a), $MachinePrecision], If[LessEqual[a, 5e+203], x, N[(0.0 - a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.21999999999999998e231 or 4.99999999999999994e203 < a

   1. Initial program 99.7%

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

   3. Taylor expanded in z around inf

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

      1. --lowering--.f64 51.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{a}\right) \]

   5. Simplified 51.7%

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

   6. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(a\right) \]

      2. neg-sub0 N/A

         \[\leadsto 0 - \color{blue}{a} \]

      3. --lowering--.f64 49.2%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{a}\right) \]

   8. Simplified 49.2%

      \[\leadsto \color{blue}{0 - a} \]
   9. Step-by-step derivation

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(a\right) \]

      2. neg-lowering-neg.f64 49.2%

         \[\leadsto \mathsf{neg.f64}\left(a\right) \]

   10. Applied egg-rr 49.2%

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

   if -1.21999999999999998e231 < a < 4.99999999999999994e203

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 58.1%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{+231}:\\ \;\;\;\;0 - a\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0 - a\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{1}{\color{blue}{\frac{\frac{\left(t - z\right) + 1}{a}}{y - z}}}\right)\right) \]

   2. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{1}{\frac{\left(t - z\right) + 1}{a}} \cdot \color{blue}{\left(y - z\right)}\right)\right) \]

   3. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{a}{\left(t - z\right) + 1} \cdot \left(\color{blue}{y} - z\right)\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{a}{\left(t - z\right) + 1}\right), \color{blue}{\left(y - z\right)}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \left(\left(t - z\right) + 1\right)\right), \left(\color{blue}{y} - z\right)\right)\right) \]

   6. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \mathsf{+.f64}\left(\left(t - z\right), 1\right)\right), \left(y - z\right)\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right)\right), \left(y - z\right)\right)\right) \]

   8. --lowering--.f64 96.7%

      \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, \mathsf{+.f64}\left(\mathsf{\_.f64}\left(t, z\right), 1\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

4. Applied egg-rr 96.7%

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

5. Final simplification 96.7%

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

Alternative 10: 54.2% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in x around inf

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

5. Simplified 50.1%

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

Developer Target 1: 99.6% accurate, 1.0× 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 2024138 
(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))))